The signal has a fundamental period of 6 and contains exclusively odd harmonics (n = 1, 3, 5,...).
What is periodic signal?A periodic signal is one that repeats the same pattern or sequence of values over a set period of time, referred to as the period or duration of one cycle.
The given signal is:
f(t) = 3sin(t) + 2sin(3t)
To determine whether this signal is periodic or aperiodic, we need to check whether it repeats itself after a certain time interval.
For a signal to be periodic, there must be a value T such that:
f(t) = f(t+T) for all t
Let's first consider the first term of the signal: 3sin(t). This term is a sinusoidal function with a period of 2π. That is, it repeats itself every 2π units of t.
Now let's consider the second term of the signal: 2sin(3t). This term is also a sinusoidal function, but with a period of 2π/3. That is, it repeats itself every 2π/3 units of t.
To check whether the sum of these two terms is periodic, we need to find the smallest value of T for which the two terms will repeat themselves simultaneously. This is known as the fundamental period.
The fundamental period of a sum of two sinusoidal functions with different periods is given by the least common multiple (LCM) of the individual periods.
In this case, the individual periods are 2π and 2π/3. The LCM of these periods is:
LCM(2π, 2π/3) = 6π
Therefore, the fundamental period of the signal is 6π.
Since the signal is periodic, we can write it as a Fourier series:
f(t) = a0/2 + ∑(n=1 to infinity) [an*cos(nωt) + bn*sin(nωt)]
where:
ω = 2π/T = π/3 (fundamental angular frequency)
an = (2/T) ∫(0 to T) f(t)*cos(nωt) dt
bn = (2/T) ∫(0 to T) f(t)*sin(nωt) dt
Using the formulae for an and bn, we can calculate the coefficients of the Fourier series:
a0 = (1/T) ∫(0 to T) f(t) dt = 0 (since f(t) is odd)
an = (2/T) ∫(0 to T) f(t)*cos(nωt) dt = 0
bn = (2/T) ∫(0 to T) f(t)*sin(nωt) dt =
(2/6π) ∫(0 to 6π) [3sin(t) + 2sin(3t)]*sin(nωt) dt
Evaluating this integral, we get:
bn = [tex](2/π) [(-1)^{n-1} + (1/3)(-1)^{n-1}][/tex]
Therefore, the Fourier series of the signal is:
f(t) = ∑(n=1 to infinity) [(2/π) [(-1)^n-1 + (1/3)(-1)^n-1]]*sin(nπt/3)
So, the signal is periodic with a fundamental period of 6π, and it contains only odd harmonics (n = 1, 3, 5, ...).
Learn more about periodic signals on:
https://brainly.com/question/30426575
#SPJ11
suppose that β is an angle with cos β = − 5 6 and β is not in the third quadrant. compute the exact value of csc β . you do not have to rationalize the denominator.
β is an angle with cos(β) = -5/6 and β is not in the third quadrant, we need to compute the exact value of csc(β), without rationalizing the denominator.
Step 1: Determine the quadrant of angle β.
Since cos(β) = -5/6 and β is not in the third quadrant, then β must be in the second quadrant, as cosine values are negative in the second quadrant.
Step 2: Compute the sine of angle β.
We know that sin^{2}(β) + cos^{2}(β) = 1 (Pythagorean identity). So,
sin^{2}(β) + (-5/6)^{2} = 1
sin^{2}(β) + 25/36 = 1
sin^{2}(β) = 11/36
sin(β) = √(11/36) (since sin is positive in the second quadrant)
Step 3: Compute the exact value of csc(β).
Since csc(β) is the reciprocal of sin(β), then csc(β) = 1/sin(β).
csc(β) = 1/(√(11/36))
Therefore, the exact value of csc(β) is 1/(√(11/36)).
Learn more about quadrant at: https://brainly.com/question/863849
#SPJ11
β is an angle with cos(β) = -5/6 and β is not in the third quadrant, we need to compute the exact value of csc(β), without rationalizing the denominator.
Step 1: Determine the quadrant of angle β.
Since cos(β) = -5/6 and β is not in the third quadrant, then β must be in the second quadrant, as cosine values are negative in the second quadrant.
Step 2: Compute the sine of angle β.
We know that sin^{2}(β) + cos^{2}(β) = 1 (Pythagorean identity). So,
sin^{2}(β) + (-5/6)^{2} = 1
sin^{2}(β) + 25/36 = 1
sin^{2}(β) = 11/36
sin(β) = √(11/36) (since sin is positive in the second quadrant)
Step 3: Compute the exact value of csc(β).
Since csc(β) is the reciprocal of sin(β), then csc(β) = 1/sin(β).
csc(β) = 1/(√(11/36))
Therefore, the exact value of csc(β) is 1/(√(11/36)).
Learn more about quadrant at: https://brainly.com/question/863849
#SPJ11
Complete the square to re-write the quadratic function in vertex form
Answer:
[tex]y= (x+\frac{1}{2})^2-8.25[/tex]
Step-by-step explanation:
First, we move the c in [tex]ax^2+bx+c[/tex] to the other side of the equation by adding 8 onto both sides:
[tex]x^2+x=8[/tex].
Then, since [tex]x^2\\[/tex] has no coefficient, we make the left side a perfect square trinomial by adding [tex](\frac{b}{2})^2[/tex] on both sides of the equation. We do this because adding this to the equation will make the left side equal to [tex](x\pm\frac{b}{2})^2[/tex] (plus-minus because the sign depends on if b is negative or positive):
[tex]x^2+x+\frac{1}{4}=8+\frac{1}{4}[/tex].
Then, simplify the left side:
[tex](x+\frac{1}{2})^2=8.25[/tex]
Finally, subtract 8.25 on both sides to make it vertex form:
[tex]y= (x+\frac{1}{2})^2-8.25[/tex]
Find the missing angles for angle 1 and angle 2 measurements round to the nearest 10th of a degree 
The missing angles in the right angle triangle are as follows:
∠1 = 53.1°
∠2 = 36.9°
How to find the angle of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The angles of the right angle triangle can be found using trigonometric ratios.
The sum of angles in a triangle is 180 degrees.
Therefore,
cos ∠1 = adjacent / hypotenuse
Hence,
cos ∠1 = 18 / 30
∠1 = cos⁻¹ 0.6
∠1 = 53.1301023542
∠1 = 53.1 degrees
Therefore,
∠2 = 180 - 90 - 53.1
∠2 = 36.9 degrees
learn more on right triangle here: https://brainly.com/question/29051936
#SPJ1
Write the sentence as an equation.
26 is 335 plus the product of 263 and p
Step-by-step explanation:
26 is 355 plus the product of 265 and p
26 = 355 + 265p
true or false. defects are additive in a multi-step manufacturing process.
The statement "defects are additive in a multi-step manufacturing process" is generally false.
It depends on the type of defects and the specific manufacturing process. In general, defects are not necessarily additive in a multi-step manufacturing process.
Some defects may be additive, meaning that they can accumulate or worsen as the manufacturing process progresses. For example, if a part is slightly out of tolerance in one step of the process, subsequent steps may exacerbate the deviation, leading to a larger defect in the final product.
On the other hand, some defects may be independent or even compensatory, meaning that they do not accumulate or cancel each other out as the process progresses. For example, if one step of the process introduces a defect in one dimension of a part, another step may correct the defect in another dimension, resulting in a final product that meets specifications.
Therefore, the statement "defects are additive in a multi-step manufacturing process" is generally false, as it depends on the specific types of defects and the manufacturing process being considered.
To learn more about manufacturing process visit: https://brainly.com/question/18851097
#SPJ11
The statement "defects are additive in a multi-step manufacturing process" is generally false.
It depends on the type of defects and the specific manufacturing process. In general, defects are not necessarily additive in a multi-step manufacturing process.
Some defects may be additive, meaning that they can accumulate or worsen as the manufacturing process progresses. For example, if a part is slightly out of tolerance in one step of the process, subsequent steps may exacerbate the deviation, leading to a larger defect in the final product.
On the other hand, some defects may be independent or even compensatory, meaning that they do not accumulate or cancel each other out as the process progresses. For example, if one step of the process introduces a defect in one dimension of a part, another step may correct the defect in another dimension, resulting in a final product that meets specifications.
Therefore, the statement "defects are additive in a multi-step manufacturing process" is generally false, as it depends on the specific types of defects and the manufacturing process being considered.
To learn more about manufacturing process visit: https://brainly.com/question/18851097
#SPJ11
Please provide Guidance ASAP on how to calculate the last question and answer this question.
How many years will it take to reach 50,000 pairs and what unrealistic assumptions were made in prediting the time it would take to reach 50,000 pairs?
Table 7. Analysis of Bald Eagle Recovery
What is the shape of the curve? J-shaped exponential curve
Doubling time from 1,000 to 2,000 4.73 years
Doubling time from 2,000 to 4,000 9.47 years
Doubling time from 4,000 to 8,000 18.94 years
Average doubling time 11.05 years
Doubling time increasing or decreasing? increasing
Starting number of breeding pairs 791 Year 1974
Theoretical prediction to reach 1,582 pairs Year 1979
Theoretical prediction to reach 3,164 pairs Year 1987
Theoretical prediction to reach 6,328 pairs Year 2002
Theoretical prediction to reach 12,636 pairs Year 2030
How many years to reach 50,000 pairs? 235 years
To calculate the time it would take to reach 50,000 pairs, we can use the average doubling time provided in the table. The shape of the curve is a J-shaped exponential curve.
which means that the number of pairs increases at an accelerating rate over time. Since the average doubling time is 11.05 years, we can determine the number of times we need to double the initial number of breeding pairs (791) to reach 50,000 pairs. By successively doubling the number of pairs and keeping track of the years passed, we reach 50,000 pairs in 235 years (as given in the table).
However, there are unrealistic assumptions made in predicting the time to reach 50,000 pairs. The main assumption is that the doubling time remains constant, while in reality, factors such as environmental limitations, availability of resources, and human intervention could cause the rate of growth to change over time.
Additionally, the model assumes that there are no significant negative events (such as disease outbreaks or natural disasters) that could negatively impact the bald eagle population during this period.
To know more factors click here
brainly.com/question/29128446
#SPJ11
1. Tom is gathering data on the music preferences of his classmates. He randomly surveyed
a sample of the total student population. There are 1,200 total students on campus.
Type
Pop
Rock
R&B
Rap
Country
Electronica
Other
Total
Proportion:
Number of
Students
30
28
22
24
17
11
18
150
a. Write and solve a proportion to find the approximate number of students on campus
who prefer R&B music.
Proportion:
Solution:
b. Write and solve a proportion to find the approximate number of students on campus
who prefer Pop or Rock music.
Solution:
Apr 22
dmentum Permission granted to copy for classroom use
3:10
Using the concept of proportion, we have that:
1) Approximate number of students who prefer R & B is: 176 students
2) Approximate number of students who prefer R & B is: 464 students
How to find the proportion from the table of values?Normally in table of values, we can easily tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.
We are told that there are a total of 1200 total students on the campus.
1) Total number of students = 1200
Total number surveyed = 150
Total who prefer R & B music = 22
Thus:
Approximate number of students who prefer R & B = (22/150) * 1200
= 176 students
2) Total number of students = 1200
Total number surveyed = 150
Total who prefer Pop or Rock music = 30 + 28 = 58
Thus:
Approximate number of students who prefer R & B = (58/150) * 1200
= 464 students
Read more about proportion at: https://brainly.com/question/1781657
#SPJ1
A researcher obtains a t =2.98 for a repeated-measures study using a sample of n = 8 participants. Based on this t value, what is the correct decision for a two-tailed test and an alpha of .05?
a. Return the null hypothesis.
b. Reject the null hypothesis.
c. Cannot answer the question with the information provided.
d. Fail to reject the null hypothesis.
Your answer: b. Reject the null hypothesis.
Explanation:
In a repeated-measures study using a sample of n = 8 participants, the researcher obtained a t-value of 2.98. For a two-tailed test with an alpha of .05.
To determine the correct decision for a two-tailed test with an alpha level of 0.05 based on a t-value of 2.98 for a repeated-measures study with a sample size of n = 8, we need to compare the t-value to the critical t-value for a two-tailed test at alpha level of 0.05 with 7 degrees of freedom, which is n - 1.
Using a t-table or a t-distribution calculator with 7 degrees of freedom and an alpha level of 0.05, we can find the critical t-value for this sample size is approximately 2.365(rounded to three decimal places).
Since the obtained t-value (2.98) is greater than the critical t-value (2.365), we would reject the null hypothesis.
Therefore, the correct decision for a two-tailed test with an alpha of 0.05 based on the given t-value of 2.98 is:
b. Reject the null hypothesis.
Know more about the alpha level click here:
https://brainly.com/question/13059612
#SPJ11
nollostidu2 bed enbelwand ris obsMA
7. A physician assistant applies gloves prior to examining each patient. She sees an
с и
3. smith
average of 37 patients each day. How many boxes of gloves will she need over the
span of 3 days if there are 100 gloves in each box?
sibain dossi
tawans
8. A medical sales rep had the goal of selling 500 devices in the month of November.
He sold 17 devices on average each day to various medical offices and clinics. By
how many devices did this medical sales rep exceed to fall short of his November
goal?
9. There are 56 phalange bones in the body. 14 phalange bones are in each hand. How
many phalange bones are in each foot?
10. Frank needs to consume no more than 56 grams of fat each day to maintain his
current weight. Frank consumed 1 KFC chicken pot pie for lunch that contained 41
grams of fat. How many fat grams are left to consume this day?
LAO
11. The rec center purchases premade smoothies in cases of 50. If the rec center sells
an average of 12 smoothies per day, how many smoothies will be left in stock after
4 days from one case?
12. Ashton drank a 24 oz bottle of water throughout the day at school. How many
ounces should he consume the rest of the day if the goal is to drink the
recommended 64 ounces of water per day?
13. Kathy set a goal to walk at least 10 miles per week. She walks with a friend 3
times each week and averages 2.5 miles per walk. How many more miles will she
need to walk to meet her goal for the week?
She will need to purchase 3 boxes of gloves.
He exceeded his goal by 10 devices.
There are 28 phalange bones in each foot.
There will be 2 smoothies left in stock after 4 days from one case.
Frank needs to consume no more than 15 grams of fat for the rest of the day.
How to calculate the word problemSince there are 100 gloves in each box, she will need 222/100 = 2.22 boxes of gloves. Since she cannot purchase a partial box, she will need to purchase 3 boxes of gloves.
The medical sales rep sold devices for a total of 17 x 30 = 510 devices in November. Since his goal was to sell 500 devices, he exceeded his goal by 510 - 500 = 10 devices.
Since there are 56 phalange bones in the body and 14 phalange bones in each hand, there are 56 - (14 x 2) = <<56-(14*2)= 28 phalange bones in each foot.
Frank needs to consume no more than 56 - 41 = 15 grams of fat for the rest of the day.
The rec center sells 12 smoothies per day for 4 days, for a total of 12 x 4 = 48 smoothies. Therefore, there will be 50 - 48 = 2 smoothies left in stock after 4 days from one case.
Since Ashton drank a 24 oz bottle of water, he still needs to drink 64 - 24 = 40 ounces of water for the rest of the day.
Kathy walks a total of 3 x 2.5 =7.5 miles with her friend each week. Therefore, she still needs to walk 10 - 7.5 = 2.5 more miles to meet her goal for the week.
Learn more about word problem on
https://brainly.com/question/21405634
#SPJ1
8.20. simplify (r∩s) ∩(s∩(r∩s)) as much as possible, using the set property theorems and exercise 8.16
The simplified expression is just the set s. First, we can use the associative property of intersection to rearrange the parentheses: (r∩s) ∩(s∩(r∩s)) = (r∩s) ∩((r∩s)∩s)
We can use the commutative property of intersection to switch the order of r and s in the first set:
(r∩s) ∩((r∩s)∩s) = (s∩r) ∩((r∩s)∩s)
Now, we can use the distributive property of intersection over intersection to expand (r∩s)∩s:
(s∩r) ∩((r∩s)∩s) = (s∩r) ∩r∩s
Finally, we can use the associative and commutative properties of intersection to rearrange the sets again and simplify:
(s∩r) ∩r∩s = s∩r∩r∩s = s∩(r∩r)∩s = s∩s = s
Therefore, the simplified expression is just the set s.
Learn more about parentheses here: brainly.com/question/28146414
#SPJ11
Write out the form of the partial fraction decomposition of the function appearing in the integral: 5 72 Determine the numerical values of the coefficients, A and B, where A B and -5x-72 2 5x - 66 denominator denominator B=
The numerical values of the coefficients A and B are:
A = -1/6
B = 1/6
To perform partial fraction decomposition, we need to break down the fraction into simpler terms.
The form of the partial fraction decomposition of the given function is:
5/(5x - 72) = A/(5x - 66) + B/(5x - 72)
Here, A and B are the coefficients we need to find. We can find them by cross-multiplying and equating the numerators of both sides of the equation:
5 = A(5x - 72) + B(5x - 66)
Now, we can substitute some values of x to get two equations in terms of A and B:
For x = 14:
5 = A(5(14) - 72) + B(5(14) - 66)
Simplifying and solving for A and B, we get:
A = 1/6
B = -1/6
For x = 12:
5 = A(5(12) - 72) + B(5(12) - 66)
Simplifying and solving for A and B again, we get:
A = -1/6
B = 1/6
Generally, for a function f(x) with a rational expression in the integral, we can use partial fraction decomposition to rewrite the expression as a sum of simpler fractions. This makes it easier to find the integral.
The coefficients A and B are constants in the simpler fractions, and their values can be determined by solving a system of linear equations.
Visit here to learn more about Coefficients:
brainly.com/question/27969435
#SPJ11
Carson has $50 in the bank to put towards a new e-bike. If every three
months afterwards he saves $20 additional dollars to put towards the
bike, how much will he have saved up for it after three years?
what do you call the factor or variable that is manipulated in an experiment? select one: a. a placebo b. the independent variable c. the control d. the dependent variable is. a correlated variable
The factor or variable that is manipulated in an experiment is called the independent variable. Therefore, the correct answer is b. the independent variable.
The independent variable is a factor or variable that is manipulated or changed by the researcher in an experiment to observe its effect on the dependent variable. It is also called the predictor variable because it is used to predict changes in the dependent variable. The researcher controls the independent variable and can vary it as needed to test different hypotheses. In contrast, the dependent variable is the factor or variable that is being measured or observed in response to the changes made in the independent variable.
For example, in an experiment to test the effect of different doses of medication on blood pressure, the independent variable is the medication dosage, while the dependent variable is the blood pressure readings. The researcher can manipulate the dosage of the medication and measure the effect on the blood pressure to determine the optimal dosage for treating high blood pressure.
It is important to carefully choose and control the independent variable in an experiment to ensure accurate and reliable results. Any extraneous or confounding variables that could affect the dependent variable must be controlled or eliminated to isolate the effect of the independent variable.
To learn more about independent variable, visit here
https://brainly.com/question/29430246
#SPJ4
let s=∑n=1[infinity]an be an infinite series such that sn=4−4n2. (a) what are the values of ∑n=110an and ∑n=416an? ∑n=110an=
The expression for the nth term an, for the infinite series s=∑n=1[infinity]an is ∑n=4¹⁶an = 468
We know that the sum of the first n terms of the series is given by sn. Therefore, we can find an expression for the nth term an by taking the difference between successive values of sn:
sn - sn-1 = an
(4-4n²) - (4-4(n-1)²) = an
Simplifying this expression, we get:
an = 8n - 4
Now we can use this expression to find the values of ∑n=1¹⁰an and ∑n=4¹⁶an:
∑n=1¹⁰an = a1 + a2 + ... + a10
= (81 - 4) + (82 - 4) + ... + (8*10 - 4)
= 76
Therefore, ∑n=1¹⁰an = 76.
Similarly,
∑n=4¹⁶an = a4 + a5 + ... + a16
= (84 - 4) + (85 - 4) + ... + (8*16 - 4)
= 468
Therefore, ∑n=4¹⁶an = 468.
Know more about expression here:
https://brainly.com/question/14083225
#SPJ11
consider the function f(x)=cot(x) 10 over the interval [−π,π3]. does the extreme value theorem guarantee the existence of an absolute maximum and minimum for f(x) on this interval?
The Extreme Value Theorem does not guarantee the existence of an absolute maximum and minimum for f(x) on this interval.
The extreme value theorem states that if a function is continuous over a closed interval, then it must have at least one absolute maximum and one absolute minimum on that interval. In the case of f(x) = cot(x) 10 over the interval [−π,π3], this function is continuous over the interval since it is the composition of two continuous functions (cot(x) and 10). Therefore, the extreme value theorem guarantees that there must be at least one absolute maximum and one absolute minimum for f(x) on this interval.
The Extreme Value Theorem states that if a function is continuous on a closed interval, then it has an absolute maximum and minimum on that interval. The function f(x) = cot(x) is not continuous over the interval [-π, π/3] due to the presence of vertical asymptotes, where the function is undefined. Therefore, the Extreme Value Theorem does not guarantee the existence of an absolute maximum and minimum for f(x) on this interval.
To learn more about Extreme Value Theorem, click here:
brainly.com/question/30760554
#SPJ11
for a nonsingular matrix a and nonzero scalar β, show that (βa)^(-1) = 1/β A^(-1)
To show that (βa)^(-1) = 1/β A^(-1), we can use the definition of the inverse of a matrix.
To show that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β, follow these steps:
1. Let's consider a nonsingular matrix A and a nonzero scalar β.
2. Multiply both sides of the equation by (βA).
On the left side, we have:
(βA)(βA)^(-1)
On the right side, we have:
(βA)(1/β A^(-1))
3. Apply the property of inverse matrices:
(βA)(βA)^(-1) = I, where I is the identity matrix.
4. On the right side, distribute the (βA) to both terms in the parentheses:
(βA)(1/β A^(-1)) = β(1/β) A(A^(-1))
5. β(1/β) simplifies to 1, and applying the property of inverse matrices again, A(A^(-1)) = I, so:
1 * I = I
Thus, we have shown that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β.
To learn more about inverse of a matrix visit : https://brainly.com/question/27924478
#SPJ11
find the requested higher-order derivative for the given function. d 2^y/dx^2 of y = 3 sin(x)+ x^2 cos(x)
The second derivative of y = 3sin(x) + [tex]x^{2 cosx}[/tex] is [tex]d^{2y}[/tex]/dx^2 = -3sin(x) - x²cos(x) + 2cos(x) - 2xsin(x).
How to find the second derivative of y = 3 sin(x) + x² cos(x)?To find the second derivative of y = 3 sin(x) + x² cos(x), we need to take the derivative of the first derivative of y with respect to x.
First, let's find the first derivative of y:
dy/dx = 3cos(x) - [tex]x^{2sin(x)}[/tex] + 2xcos(x)
Now, let's take the derivative of this expression with respect to x to find the second derivative:
[tex]d^{2y}[/tex]/dx² = -3sin(x) - x²cos(x) + 2cos(x) - 2xsin(x)
Therefore, the second derivative of y = 3sin(x) + [tex]x^{2 cosx}[/tex] is [tex]d^{2y}[/tex]/dx^2 = -3sin(x) - x²cos(x) + 2cos(x) - 2xsin(x).
Learn more about second derivative
brainly.com/question/29090070
#SPJ11
Consider the following. X = sin(t), y = csct), 0
Eliminate the parameter to find a Cartesian equation of the curve.
The Cartesian equation of the curve is Y = 1/X.
To the parameter and find a Cartesian equation of the curve using the given terms. Consider the following:
X = sin(t), Y = csc(t), and 0 ≤ t ≤ 2π
Step 1: Rewrite Y in terms of sin(t)
Since Y = csc(t), we know that csc(t) = 1/sin(t). Therefore, Y = 1/sin(t).
Step 2: Eliminate the parameter t
We already have X = sin(t), so we can substitute this into the equation for Y:
Y = 1/X
Step 3: Write the Cartesian equation of the curve
Now that we have eliminated the parameter t, the Cartesian equation of the curve is simply:
Y = 1/X
Therefore, the Cartesian equation of the curve is Y = 1/X.
Know more about Cartesian equation here:
https://brainly.com/question/14869452
#SPJ11
Can anyone Help with this?
The simplified form of the surd is 1 - 1/3√5
How do you rationalize a surd?Here are the general steps to follow when rationalizing a surd:
Identify the surd in the denominator of the fraction.
Multiply the numerator and denominator of the fraction by the conjugate of the denominator. The conjugate is obtained by changing the sign of the surd term in the denominator.
Simplify the resulting expression by expanding the brackets and collecting like terms.
If there is still a surd in the denominator, repeat the process until no surds remain in the denominator.
Given that;
√2 - √10/√2 + √10
Then;
√2 - √10/ √2 + √10 * √2 - √10/√2 - √10
2 -√20 - √20 + 10/2 -√20 + √20 + 10
2 - 2√20 + 10/2 + 10
12 - 2√20/12
1 - 1/3√5
Learn more about surd:https://brainly.com/question/30069850
#SPJ1
Below is the graph of equation y= |x−2|-1. Use this graph to find all values of x for the given values of y.
y>0
Step-by-step explanation:
if x=4. then it be |4-2|-1= 1
x=5 5-2-1 so 2
and so on
K is a field with 4 elements containing Z2 as subfield. Then in addition to 0, 1 from Z2, the field K has two extra elements; call these α and β.(a) Show that α + 1 = β.(b) Show that\small \alpha ^2= β
a. We have shown that α + 1 = β.
b. We have shown that α² = β.
What are elements?A substance that cannot be broken down into another substance is referred to as an element. Because each element is made up of its own type of atom, each element is distinct and distinct from the others.
Since K is a field with 4 elements, the nonzero elements of K form a cyclic group of order 3 under multiplication. Let us call this group G. Since G is cyclic, it has a unique generator, say g. Then we can write G = {1, g, g²}.
Now, since α and β are both in K but not in Z2, they must be elements of G. Moreover, since K contains Z2 as a sub-field, α and β must be roots of the polynomial x² + x + 1 over Z2. Therefore, we have the following possibilities for α and β:
α = g
β = g²
or
α = g²
β = g
a. Let us first consider the case where α = g and β = g². Then we have:
α + 1 = g + 1
= g² + g + 1 (since g³ = 1)
= β + α + 1 (since β = g² and α = g)
= β
Therefore, we have shown that α + 1 = β.
b. Next, we will show that α² = β. Using the same assumption that α = g and β = g², we have:
α² = g²
= β
Therefore, we have shown that α² = β.
Learn more about polynomials on:
https://brainly.com/question/4142886
#SPJ11
Need help with logic puzzle ASAP
The above is a logic puzzle. Logic puzzles challenge the mind and enhance critical thinking.
The findings based on the clues givenAccording to the clues given, Jane was seen checking out an action book after leaving either a Biology or History class. It was also determined that Jayson is enrolled in Biology and the student who checked out a fantasy book, Jose, has an English class immediately following Jenny's.
Furthermore, we were able to deduce that the individual who left a History class was the same person who checked out a mystery novel while the student studying French must have been present during 1st period.
Jaden, who is currently enrolled in Algebra class, is observed browsing through a Manga novel. It can be noted that while studying for academic subjects like Math, the temptation to deviate towards leisure reading material can often pose as a distraction.
Learn more Logic Puzzles:
https://brainly.com/question/31149956
#SPJ1
Find the linear approximation of a rational function and use it to estimate function values Question Find the linear approximation of f(x) = at x = 3 and use the approximation to estimate 29 Submit an exact answer in fractional form. Provide your answer below: L(2.9) = 1
To find the linear approximation of f(x) at x = 3, we need to calculate the derivative f'(x) and then use the formula for the linear approximation: L(x) = f(a) + f'(a)(x-a).
Step 1: Calculate the derivative f'(x) of the given function f(x).
As the function is not provided, I'll assume it's a general rational function, f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials. To find the derivative, use the quotient rule: f'(x) = (P'(x)Q(x) - P(x)Q'(x))/Q(x)^2.
Step 2: Evaluate f(3) and f'(3).
Once you find f'(x), plug in x=3 to get f(3) and f'(3).
Step 3: Use the linear approximation formula.
L(x) = f(3) + f'(3)(x-3).
Now, estimate L(2.9):
L(2.9) = f(3) + f'(3)(2.9-3) = f(3) - 0.1f'(3).
To provide an exact answer in fractional form, compute the numerical values of f(3) and f'(3) and substitute them in the equation above.
To know more about linear approximation click on below link:
https://brainly.com/question/1621850#
#SPJ11
Under what condition on bı, b2, b3 is this system solvable? Include b as a fourth column in elimination. Find all solutions when that condition holds: x + 2y – 2z = bi 2x + 5y - 4z = 62 4x + 9y - 8z = 63. 6 whnt on
The system is solvable only if [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex]. All solutions for the given condition are [tex]${(x, y, z) \mid x = \frac{1}{2}(2t - b_1 - b_2), y = \frac{1}{5}(4t + 2b_1 - 5b_2), z = t}$[/tex].
We can set up the augmented matrix as follows:
[tex]\begin{bmatrix}1 & 2 & -2 & b_1 \ 2 & 5 & -4 & b_2 \ 4 & 9 & -8 & b_3\end{bmatrix}[/tex]
We can row reduce this matrix to determine when the system is solvable and to find any solutions. Performing row operations, we get:
[tex]\begin{bmatrix}1 & 2 & -2 & b_1 \ 0 & 1 & 0 & 2b_1 - 5b_2 \ 0 & 0 & 0 & -b_1 + 2b_2 - b_3\end{bmatrix}[/tex]
So the system is solvable if and only if [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex]. In this case, we can solve for z in terms of y and x by expressing z as a free variable and solving for x and y in terms of z. We get:
[tex]\begin{align*}z &= t \y &= \frac{1}{5}(4t + 2b_1 - 5b_2) \x &= \frac{1}{2}(2t - b_1 - b_2) \\end{align*}[/tex]\begin{align*}
z &= t \
y &= \frac{1}{5}(4t + 2b_1 - 5b_2) \
x &= \frac{1}{2}(2t - b_1 - b_2) \
\end{align*}
where t is any real number. So the solutions are given by the set:
[tex]${(x, y, z) \mid x = \frac{1}{2}(2t - b_1 - b_2), y = \frac{1}{5}(4t + 2b_1 - 5b_2), z = t}$[/tex]
where t is any real number, and [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex].
Know more about system here:
https://brainly.com/question/30054947
#SPJ11
Find the area of the shape below.
Answer:
78.274 (Steps shown below)
Step-by-step explanation:
Rectangle Area
6 x 12 =50
Circle (put the 2 half circles together)
Circle area = π * r² = π * 9 [inch²] ≈ 28.274 [in²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 3 [inch] * 2 = 6 [inch]
Area of Circle= 28.274
20. In a school of 300 students, only 225 cleared an exam. If a sample of 10 of these students is taken, then the standard deviation of the sample proportion will be A) 0.03 B) 0.08 C) 0.24 D) 0.14 E) 0.02
The standard deviation of the sample proportion will be 0.14. So, the correct option is option D) 0.14.
The formula for the standard deviation of a sample proportion is given by:
standard deviation = √[p(1-p)/n]
where p is the proportion of successes in the population (i.e. the proportion of students who cleared the exam), and n is the sample size.
In this case, p = 225/300 = 0.75, since in the school of 300 students 225 students cleared the exam. The sample size is n = 10, as sample of 10 of these students is taken.
Plugging these values into the formula, we get:
standard deviation = √[0.75(1-0.75)/10] = √[0.01875] = 0.1366
Rounding to two decimal places, the answer 0.14.
Know more about standard deviation here:
https://brainly.com/question/475676
#SPJ11
Find the exact length x of the diagonal of the rectangle.
x
8
4
The exact length x of the diagonal of the rectangle is the exact length of the diagonal is 4sqrt(5).
We can use the Pythagorean theorem to solve for the diagonal:
The Pythagorean Theorem is a fundamental principle in mathematics that describes the relationship between the sides of a right triangle.
It states that the sum of the squares of the two shorter sides (the legs) of a right triangle is equal to the square of the length of the longest side (the hypotenuse).
x^2 = 4^2 + 8^2
x^2 = 16 + 64
x^2 = 80
x = sqrt(80)
x = 4sqrt(5)
Thus, the exact length of the diagonal is 4sqrt(5).
For more details regarding Pythagorean theorem, visit:
https://brainly.com/question/14930619
#SPJ1
PLEASE HELP
Use technology or a z-distribution table to find the indicated area.
The weights of tomatoes in a bin are normally distributed with a mean of 95 grams
and a standard deviation of 3.6 grams.
Approximately
25% of the tomatoes weigh less than which amount?
93 g
96g
92g
90 g
Approximately 25% of the tomatoes weigh less than, given the standard deviation and mean, A. 93 g.
How to find the approximate amount ?25 % of tomatoes is the value that we are looking for. On the z - distribution table, the closest to this amount is 0.2486, and this has a z - score of - 0. 674.
With this z - score, we can use the z - score formula to find the amount that the 25 % of tomatoes weigh:
z = (x - μ) / σ
-0. 674 = (x - 95 ) / 3.6
x - 95 = -0. 674 x 3. 6
x = 95 - 2. 4264
x = 92. 5736
x = 93 grams
Find out more on the z - distribution table at https://brainly.com/question/24213960
#SPJ1
consider the set y1,y2,...,yk that are k linearly independant soluitions on (-[infinity],[infinity]) of a linear homogenous n^th order differential equation.The objective is to determine whether the set of solution is linearly dependent or not.
To determine whether the set of solutions y1, y2, ..., yk is linearly dependent or not, we need to calculate the Wronskian W(y1, y2, ..., yk) and check whether it is zero for some x in (-[infinity], [infinity]). If it is never zero, then the set of solutions is linearly independent. If it is zero for some x, then the set of solutions is linearly dependent.
To determine whether the set of solutions y1, y2, ..., yk is linearly dependent or not, we can use the Wronskian determinant. The Wronskian of a set of k functions is defined as:
W(y1, y2, ..., yk) = det [y1, y2, ..., yk; y1', y2', ..., yk'; ..., ..., ..., ...; y1^(k-1), y2^(k-1), ..., yk^(k-1)]
where y1', y2', ..., yk' are the first derivatives of y1, y2, ..., yk, respectively, and y1^(k-1), y2^(k-1), ..., yk^(k-1) are their (k-1)th derivatives.
If the Wronskian is nonzero for all x in (-[infinity], [infinity]), then the set of solutions is linearly independent. If the Wronskian is zero for some x in (-[infinity], [infinity]), then the set of solutions is linearly dependent.
Therefore, to determine whether the set of solutions y1, y2, ..., yk is linearly dependent or not, we need to calculate the Wronskian W(y1, y2, ..., yk) and check whether it is zero for some x in (-[infinity], [infinity]). If it is never zero, then the set of solutions is linearly independent. If it is zero for some x, then the set of solutions is linearly dependent.
to learn more about linearly dependent click here:
https://brainly.com/question/30556318
#SPJ11
If Bitcoin's share price crashed, from $60,000 to $19,500...what was the percent of decrease?
Answer:
67.5%
Step-by-step explanation:
To calculate the percentage decrease in the share price of Bitcoin, we can use the following formula:
Percentage decrease = ((original value - new value) / original value) x 100%
Here, the original value is the share price before the crash, which is $60,000, and the new value is the share price after the crash, which is $19,500.
Substituting these values into the formula, we get:
Percentage decrease = ((60,000 - 19,500) / 60,000) x 100%
= 40,500 / 60,000 x 100%
= 67.5%
Therefore, the percentage decrease in the share price of Bitcoin is 67.5%.