Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). The value of dy/dx is 25.
What is differentiable functions?
Differentiable simply means that the derivative exists at each location within its domain. As a result, the function must also exist (i.e., be continuous) on its domain in order for the derivative to exist. Because of this, a differentiable function can also be continuous.
Given that x, y are both differentiable function of t. and
[tex]y=\cos (5 x)[/tex]
Find [tex]\frac{d y}{d t}=$.[/tex] when [tex]$x=\frac{\pi}{10}$[/tex] given that [tex]$\frac{d x}{d t}=-5$[/tex], when [tex]$x=\frac{\pi}{10}$[/tex]
Given function is
[tex]$ y=\cos 5 x $[/tex]
[tex]$\frac{d y}{d t}=-\sin (5 x) \cdot \frac{d}{d t}(5 x) \text { (By chain } $[/tex]
[tex]$ =-\sin 5 x \cdot 5 \frac{d x}{d t} $[/tex]
[tex]$ \text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ \frac{d y}{d t}=-\sin \left(8 \times \frac{\pi}{10}\right) \times 5 \times-5$[/tex]
[tex]$-\frac{d x}{d t}=-5 $[/tex]
[tex]$2^{20} $[/tex]
[tex]$\text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ =25 \sin \frac{\pi}{2} $[/tex]
[tex]$=25 \times 1 $[/tex]
[tex]$ \frac{d y}{d t}=25 $[/tex]
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Consider a student loan of $25,000 at a fixed APR of 9% for 20 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.
As per the given,
Principle amount P = $25,000
APR = 9% = 0.09
Time period T = 20 years
a) Monthly payment will be given as,
⇒ P(r/12)/(1 -(1 +r/12)^(-12t))
⇒ 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20))
⇒ $161.20
b) After 20 years the amount as,
$161.20 x 240 = $38,688
c) (22500/38688)·100% = 58.2% is paid toward principal
The remaining amount, 41.8% is paid toward interest.
Hence "The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest".
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On a bicycle, Na'estse rides for 8 hours and s 42 miles from her house. After riding for 10 hours, she is 52
miles away.
What is Na'estse's rate?
miles per hour
Answer:5 miles per hour
Step-by-step explanation:
By subtraction, we can see that the second time was 10-8=2 hours and covered 52-42=10 miles. 10 miles/2hours = 5 miles per hour. So that was her constant (or average) speed throughout the trip.
solve this on graph paper
The graphs of the equations are drawn ad attached here.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equations are (i) y = x-4, (ii) y = 2x-4, (iii) y = 3x-4.
The equations are given in the slope-intercept form.
(i) The given equation is y = x-4.
the y-intercept of the equation is (0,-4).
Now, substitute y = 0 into the given equation:
0 = x - 4
x = 4
Hence, the line y = x-4 passes through points (0,-4) and (4,0).
Now, draw a line passing through the points (0,-4) and (4,0).
Using the same procedure, the graphs of the other two equations are also drawn.
Hence, the graphs of the equations are drawn ad attached here.
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in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference. True or False ?
As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.
Confidence interval,
in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.
Given,
in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.
Here we need to find the given statement is true or false.
While we looking into the given question, we have identified that the value of
Confidence interval = 95%
Sample size = 20
Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).
Therefore, the statement is in correct.
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d(x) = 3x²-x
Find d(-4).
Answer:
52
Step-by-step explanation:
Substitute the value -4 into the expression and simplify:
3(-4)^2 - (-4)
3(16) + 4
48 + 4
52
PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=
A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= -2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= -2, x=7
So,
(x+2)(x-7)
We have to multiply both of them we get,
P(x)=(x+2)(x-7)
0=x²-5x-14
x²-5x-14=0
Therefore, P(x)=x²-5x-14 is the polynomial function.
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What is the common angle of APOT and ARSQ?
OZ POT
OZSPT
OZ SRO
OZSUT
P
R
S
Q
From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT.
What is a common angle:When an angle appears simultaneously in multiple geometric figures, it is referred regarded as being a common angle. Two figures with shared vertices points and angle edges are said to have a common angle.
Here we have
ΔPQT and ΔRSQ
The internal angles of ΔPQT are
=> ∠PQT, ∠PTQ, and ∠QPT
The internal angles of ΔRSQ are
=> ∠SRQ, ∠RSQ, and ∠SQR
Where ∠PQT = ∠SQR
From above information
The common angles of ΔPQT and ΔRSQ are ∠PQT and ∠SQR
Therefore,
From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT
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Complete Question:
What is the common angle of ΔPQT and ΔRSQ from the given figure?
Part A
In the story "Life on the Sea," how does the captain mostly feel when he is on the sea?
Responses
miserable
miserable
proud
proud
guilty
guilty
confident
confident
Question 2
Part B
Which excerpts from the story best support the answer in Part A?
Select the two correct answers.
Responses
"He gave his job two weeks’ notice and was back on the sea right away."
"The calmness that he felt when the water was placid wasn’t like any stillness that he experienced on land."
"He had spent most of his life on the sea; he knew the habits and nuances of the water like it was his closest friend."
"The storm roiled on the horizon as rough waves rocked the helm of the boat."
"
Confident, In contrast to any stillness he had ever felt on land, he felt a sense of calm when the water was calm. and "He gave two weeks' notice at his job and immediately sailed off again."
What is a fishing vessel?fishing vessel Place on list Share. fishing boat definitions. a fishing vessel with a well for preserving the catch. A boat and a fishing smack are potential candidates. both sorts of draggers and trawlers. Fishing ships or boats are used to remove aquatic creatures from bodies of water.
A trawl is a type of fishing net that is currently dragged along or through the ocean floor at specific depths. Since trawlers are frequently bigger than fishing boats and struggle to maneuver when necessary, they are given special qualities in ror.
Thus, options A and A, B are correct.
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Answer:
Part a: confident
Part b: "The calmness that he felt when the water was placid wasn’t like any stillness that he experienced on land." and "He had spent most of his life on the sea; he knew the habits and nuances of the water like it was his closest friend."
Step-by-step explanation: I took the test :)
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, ...
a
a9
b
a10
c
a11
d
a12
The term that is the −20,155,392 in the sequence is a₁₀.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is 2, -12, 72, -432
a = first term
n = number of terms
r = common ratio
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Therefore, nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Hence, it's the 10th term.
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Each problem describes the relationship between two variables. Use the equation that models the relationship to complete the table. Then plot the points from the table on the graph. Draw the line connecting the points to represent the equation on the coordinate plane.
1. Andre uses 2 scoops of lemonade mix for each batch of lemonade he makes. The equation that models the total scoops of lemonade mix Andre uses, s, for b batches is s=2 b.
The completed table and the graph of the proportional relationship are given by the image shown at the end of the answer.
What is the proportional relationship?The proportional relationship in this problem is defined as follows:
s=2 b.
The variables are defined as follows:
The output s is the number of lemonade mixes used.The input b is the number of batches of lemonade made.Then the graph of the proportional relationship is that of a linear function with these following features:
Slope of 2, hence when b increases by one, s increases by two.Intercept of zero, as when b = 0, s = 0.Then the numeric values that complete the table are calculated as follows:
b = 0: s = 2(0) = 0.b = 1: s = 2(1) = 2.b = 2: s = 2(2) = 4.b = 3: s = 2(3) = 6.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Processing for result of 3/4+5/4=
Answer:
8/4, or 2
Step-by-step explanation:
Brainliest, Please!
Like fractions are fractions that have the same denominator.
To add like fractions, you must add the numerators and keep the same denominator. Finally, the result is simplified if possible.
The procedure for this addition of fractions is as follows:
[tex]\begin{gathered} \sf \frac{3}{4} + \frac{5}{4} = \\ \\ \sf \frac{3 + 5}{4} = \\ \\ \boxed{ \sf\frac{ \red8}{ \red4} }= \sf \blue2\end{gathered}[/tex]
Therefore, the result of the sum of fractions is two.
In 2012, the population of a city was 6.51 million. The exponential growth rate was 2.75% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.
The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 million in 15.82258467 years and the doubling time is 25.55035862 years
How to find the exponential growth function?The exponential growth function is of the form P = P₀(1+r)^t
where P₀ is the current population, r is the growth rate and t is the time
Given: P₀ = 6.51 million, r = 2.75% per year
a) The exponential growth function
P = 6.51 (1+0.0275)^t
P = 6.51 (1.0275)^t
b) The population of the city in 2018
t = 2018-2012 = 6 years
P = 6.51 (1.0275)^t
P = 6.51 (1.0275)⁶ = 7.66 million
c) When the population of the city will be 10 million
P = 6.51 (1.0275)^t
10 = 6.51 (1.0275)^t (Solve for t)
(1.0275)^t =10/6.51
log (1.0275)^t = log(10/6.51)
t × log (1.0275) = log(10/6.51)
t = [log(10/6.51)] / [log (1.0275)]
t = 15.82258467 years
d) The doubling time
P = 6.51 (1.0275)^t will become:
2 = 1 (1.0275)^t
1.0275^t = 2
log(1.0275)^t = log 2
t log(1.0275) = log 2
t = log 2 / log 1.0275
t = 25.55035862 years
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1,y=4 x+3
2.y=5/4 x+3
3.y=-4 x+3
4.y=-5/4 x+3
Answer:
the answer will be the option 2
What is the difference in the things shown on the photo
option c) 4x⁴ -2x³ -2x² +3x -10
On subtracting we will get
(3x²₋ 2x + 4x⁴) - (5x²+2x³-5x+10)
= 3x²- 5x²- 2x -2x³+ 4x⁴+ 5x -10
= -2x² + 3x -2x³ + 4x⁴- 10
= 4x⁴ -2x³- 2x² + 3x - 10
The given sum belongs to quadratic equation
Quadratic equation definition:
When a, b, and c are real-world coefficients, a second-order equation is said to be quadratic if it is represented as ax²+ bx + c = 0.
The Characteristics of Quadratic Equations' Roots
The discriminant of the quadratic equation ax2+bx+c=0 is (b2-4ac), which determines whether or not the equation has real roots.
The quadratic equation ax2+ bx + c= 0 hence
If b2-4ac >0, two different real roots
If b2-4ac= 0, there are two equal real roots.
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Find the monthly payment R needed to have a sinking fund accumulate the future value A. The yearly interest rater and the time t in years are given below. Interest
is compounded monthly.
A=$4,000; r = 5.5%; t=1
R=$
(Round up to the nearest cent.)
Clear all
Check answer
2:21 PM
The monthly payment (R) needed to have a sinking fund accumulate the future value (A) is equal to $325.08
What is Future Value?
Future value (FV) is the value of an asset now based on an anticipated rate of increase in the future. Investors and financial planners use the future value to project how much an investment made now will be worth in the future.The formula for future value (A) is given as, [tex]A=\frac{R[(1+\frac{r}{n})^{nt}-1] }{\frac{r}{n}}[/tex], where R is the monthly payment, r is the yearly interest rate, t is the time (in years) and n is the number of compounding (monthly).Here, the given values are:
A=$4,000;
r=5.5%=0.055
t=1 year
And it is given that the interest is compounded monthly.
So, n=12
Using the formula for Future Value, [tex]A=\frac{R[(1+\frac{r}{n})^{nt}-1] }{\frac{r}{n}}[/tex]
Substituting the given values in the above equation, we get
[tex]4000=\frac{R[(1+\frac{0.055}{12})^{12 \times 1}-1] }{\frac{0.055}{12}}\\\implies 4000=\frac{R[(1+0.0046)^{12}-1] }{0.0046}\\\implies 4000=\frac{R \times 0.0566 }{0.0046}\\[/tex]
Rearranging the above expression in terms of the monthly payment, we get
[tex]R=\frac{4000 \times 0.0046}{0.0566} \\\implies R=325.08[/tex]
Therefore, the monthly payment (R) needed to have a sinking fund accumulate the future value (A) is $325.08
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How many solutions are there for the system of nonlinear equations represented by this graph?
Answer: A
Step-by-step explanation:
What is the RANGE of the cluster shown on this graph?
The range of the cluster shown in the graph is [1, 6]
What is range of a graph?
The range is all the values of the graph from down to up or on the x-axis.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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The range of the cluster shown in the graph is [1, 6]
What is range of a graph?The range is all the values of the graph from down to up or on the x-axis. The possible output values are displayed on the y-axis and make up the range. Remember that the domain and range of the graph could be larger than the visible values if it extends beyond the area that can be seen.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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Given the value: 47.728
a. Write the word name of the value.
b. Write the expanded form of the value
c. Use a number line to round this value to the nearest hundredth.
Your knowledge of the percentage 47.728 is already complete.4772.8% is the percentage equivalent of 47 7 2 8.
What is 47.728 as a Percent?To compute 47.728 as a percentage of a given number x, divide 47.728 by x and multiply the result by 100.
For instance, the ratio of 47.728 to 10 is equal to (47.728 / 10) times 100%, or 477.28%.
Use the decimals to percents converter found below at your convenience.
Place your value in the "% of" area after entering 47.728 in the number field.
Press reset first if you want to restart.
At this point, an automatic conversion to 47.728 in percent will take place.
The answer has been rounded to ten decimal places, as you can see.
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( (-2)³)²
help me solve please
The answer is 64
If you need a breakdown I don't know how to help.
For those who are on Plato and have done this tutorial,please tell me the answer to this question. And it can't be equilibrium,because I tried that and it didn't work.
By using the concept of demand and supply, it can be concluded that-
The price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.
What is demand and supply?
Demand is the amount of good which the customer wants to purchase during a particular time at a particular price.
Supply is the total amount of goods made available to the customer at a particular time
Equilibrium price is the price at which the quantity demanded is equal to the quantity supplied
So the price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.
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Solve the following and find Q R
Answer:
QR = 49
Step-by-step explanation:
QR = QP
3x + 22 = 10x - 41
x = 9
10(9) - 41
= 49
Consider the following general triangle.
C = 60.0°, c = 151 m, b = 181 m
(a)
Determine the number of solutions.
(b)
Solve the triangle, if possible, using the labels as shown in the figure below. (Round lengths in m to three significant digits and angles to the nearest tenth of a degree. If there is no solution, enter NO SOLUTION in all unused answer blanks. If there is more than one solution, enter your answers as a comma-separated list.)
A °=
B °=
a=
To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and the angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2abcos(C)
In this problem, we are given the measure of angle C and the lengths of sides b and c. We can use this information to find the length of side a and the measures of angles A and B.
First, we can use the Law of Cosines to find the length of side a. Plugging in the given values, we get:
a^2 = c^2 - b^2 + 2bc cos(C)
Substituting in the given values, we get:
a^2 = 151^2 - 181^2 + 2 * 151 * 181 * cos(60.0°)
Solving this equation gives us a = 143 m.
Now that we have the length of side a, we can use the Law of Sines to find the measures of angles A and B. The Law of Sines states that for a triangle with sides a, b, and c and angles A, B, and C opposite these sides, the following equation holds:
a/sin(A) = b/sin(B) = c/sin(C)
We are given the lengths of sides a and b and the measure of angle C. We can use this information to find the measures of angles A and B.
First, we can use the Law of Sines to find the measure of angle A. Plugging in the given values, we get:
a/sin(A) = b/sin(B)
Solving for sin(A), we get:
sin(A) = a * sin(B) / b
Substituting in the given values, we get:
sin(A) = 143 m * sin(B) / 181 m
To find the measure of angle A, we can use the inverse sine function (sin^-1). This gives us:
A = sin^-1(sin(A))
= sin^-1(143 m * sin(B) / 181 m)
Similarly, we can use the Law of Sines to find the measure of angle B:
B = sin^-1(143 m * sin(A) / 181 m)
Since we have two unknowns (A and B) and two equations, there is a unique solution for this triangle.
Therefore, the number of solutions is 1, and the measures of angles A and B are A = 38.5° and B = 101.5°. The length of side a is 143 m.
Select the expression that represents the ADDITION of
the two number lines.
O-10x+ 5x - 30x
O-10x-5x + 30x
O 10x + 5x - 30x
An expression that represents the ADDITION of the two number lines is: B. -10x - 5x + 30x.
Each segment equals 5x and the first arrow is 30x long.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Based on the number line shown above, we can reasonably infer and logically deduce that each of its segment is equal to 5x with the longest arrow measuring 30x on the number line.
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What is the solution to this system of equations?
8a−4b=20
5a−8b=62
a=
b=
Answer:
Hello there, I think this is the answer
a = - 2
b = - 9
How far does a wheel travel in 4 rotations with a radius of 36 inches?
Round to the nearest hundredths
The wheel will travel 904.32 inch when it take 4 rotation
How do you calculate distance using radius and revolutions?
Hint: To calculate the wheel's circumference, use the formula 2πr, where r is the radius and π=3.14 , to first determine the distance covered in one revolution. To determine the distance traveled, multiply the distance covered in one revolution by 200. In the end, multiply it by 100 to get the distance in meters.
In mathematics, what is the circumference?
The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian.
The circle's circumference must be known in order to compute the distance covered during one rotation. C=2πr is the formula for the circumference.
The radius, designated as r, is 36 inches. As a result, C=2π36 = 72π. The distance covered in one rotation is 226.08 inches because (pi) =3.14159, C=226.08 inches. So when we rotate this 4 times the it travels 226.08 * 4 = 904.32 inch
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Jenny has c charms on her bracelet her older sister has five more charms than Jenny write an expression that
The expression that shows how many charms Jenny's older sister has is
c + 5.
What are algebraic expressions?
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
Expressions are made up of terms.
According to the given question:
Jenny has c charms on her bracelet.
Her older sister has 5 more charms than Jenny.
To write an expression that shows the number of charms her older sister has. we simply add 5 extra charms to the number of charms Jenny has
Therefore, Jenny's older sister has c + 5 charms.
In this expression c represents the number of charms Jenny has.
The complete question is as follows:
Jenny has c charms on her bracelet. Her older sister has 5 more charms than Jenny. Write an expression that shows how many charms her older sister has.
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I’ll mark BRAINLIST Can someone please help please
Please help me with this.
1. Parallel
2. Perpendicular
3. Skew
4. Parallel
5. Perpendicular
6. ↔QW, ↔SW, ↔TZ
7. ↔YZ, ↔ST
8. ↔RQ, ↔QW, ↔ST, ↔TZ
9. Plane TQW, plane SRX, plane ZWX
10. Plane WXY
11. Corresponding
12. Alternate exterior
13. Alternate interior
14. Consecutive interior
15. Alternate exterior
16. Alternate interior
17. ↔OL ║↔VN
18. ↔VN ⊥ ↔RT
19. No; the markings do not indicate that the lines are parallel
the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
a. true
b. false
True, The dimension of the eigenspace for each eigenvalue equals the multiplicity.
What is eigen value?Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.
What is an Eigenspace?When a linear transformation is done to an eigenvector, a set of eigenvectors called an eigenspace is created for each eigenvalue. In many cases, the linear transformation uses a square matrix (a matrix that has the same number of columns as it does rows).
yes, it is true that the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
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The Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours. What was his gross pay for the week?
The gross pay for Riddler for working 47 hours will be $783.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours.
The overtime cost = 1/2 x 18
The overtime cost = $9
The gross pay will be calculated as,
Gross pay = ( 40 x 18 ) + ( 7 x 9 )
Gross pay = 720 + 63
Gross pay = $783
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