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I hope you and your family are doing well!
An angle is coterminal with another angle if it has the same terminal side as the other angle, but may have a different degree measure. In other words, coterminal angles are angles that are measured around the same point on the unit circle, but may start at different points.
To find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6, we can add or subtract multiples of 2π to -25π/6 until we get an angle between 0 and 2π.
For example, adding 2π to -25π/6 gives us:
-25π/6 + 2π = -π/6 + 2π = 7π/6
This angle is between 0 and 2π, so it is coterminal with -25π/6.
Alternatively, subtracting 4π from -25π/6 gives us:
-25π/6 - 4π = -29π/6 = -π/2
This angle is also between 0 and 2π, so it is coterminal with -25π/6.
Therefore, the angle between 0 and 2π in radians that is coterminal with -25π/6 is either 7π/6 or -π/2.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The statements true is :
The center of the circle lies on the x-axisThe radius of the circle is 3 units.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9How to calculate center of the circle ?The standard equation of a circle is expressed as:
x²+y²+2gx+2fy+C = 0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is x²+y² - 2x- 8 = 0
Get the center of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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Write an equation and solve.
The product of two consecutive integers is 29 more than their sum. Find the integers. Give your answers as comma-separated
numbers in ascending order.
The equation is n(n+1) = n + n+1 +29. The two consecutive integers are 6, 7 or -5, -4
How to write and solve an equation?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that: the product of two consecutive integers is 29 more than their sum.
Let the first integer and second integer be n and n+1 respectively
We can write the equation as:
n(n+1) = n + n+1 +29
n² + n = 2n + 30
n² + n - 2n - 30 = 0
n² + - n - 30 = 0
(n - 6) (n + 5) = 0
n - 6 = 0 or n + 5 = 0
n = 6 or n = -5
Thus, n+1 = 7 or n+1 = -4
Therefore, the two integers are 6, 7 or -5, -4
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What percentage of the area under the normal curve lies to the left of
Since the normal distribution is symmetric, the response is 50%.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.
As per the given information in the question,
According to the Empirical Rule, if a random variable is regularly distributed:
One standard deviation from the mean is found for 68% of the measurements.
The mean is within two standard deviations for 95% of the measurements.
99.7% of the measurements are found within three standard deviations of the mean.
Additionally, because of the symmetry of the normal distribution, 50% of the measurements fall below the mean, and 50% fall above.
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The top and bottom margins of a poster are 4 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.
The dimensions of the poster with the smallest area are; 27.75 cm x 27.75 cm
How to solve algebra word problems?Let "x" and "y" denote the length and the width of the poster.
We are told that the margin of a poster are 4 cm and the side margins are 4 cm.
The length of the print = x - 2(4) = x - 8
The width of the print = y - 2(4) = y - 8
The area of the print = length * width = (x - 8)(y - 8)
The area of the print is given as 390 square inches. Thus;
(x - 8)(y - 8) = 390
Making y the subject gives;
y = (390/(x - 8)) + 8
The area of the poster is; A = xy
Thus;
A = x[(390/(x - 8)) + 8]
A = (390x/(x - 8)) + 8x
Minimizing the area gives;
A' = 8 - (3120/(x - 8)²)
Equating to zero gives;
8 - (3120/(x - 8)²) = 0
8(x - 8)² = 3120
(x - 8)² = 3120/8
(x - 8)² = 390
x = 27.75 cm
y = (390/(27.75 - 8)) + 8
y = 27.75 cm
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Moira has 46 tickets left to sell for the show. Each ticket cost $34. How much will it cost to buy all of the remaining tickets
The total cost of all the remaining tickets for the show will be equal to $1564.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
Total tickets left = 46
Price of each ticket = $34
Then, the price of 46 tickets will be,
46 × 34
= $1564
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A company has 4,677 pounds of rock salt. A small town bought one-fifth of the rock salt. Then a landscaper bought 80 pounds of the rock salt that was left. How many pounds of rock salt, to the nearest hundredth, does the company have left?
As a result of it being so accessible, we became incredibly lax over the years.
How to buy and stock rock salt?Numerous snow removal companies had an excess of ice melt product due to the mild winter that just ended. Materials used to melt ice can be kept and used in the upcoming months with proper storage, according to experts. When it comes to applications for melting ice, rock salt rules in the Midwest.As a result of it being so accessible, we became incredibly lax over the years.Tom Barry, founder of Battle Creek Landscape Service, based in Battle Creek, Michigan, says that as this shortage developed, it has been his experience that you really want to plan ahead.The 2012–2013 season, according to Barry, saw reasonable prices. Salt prices have since increased as a result of a subsequent shortage.He claims, "I don't see them ever getting down that low."For 30 years, Battle Creek Landscape has been in operation and has provided snow removal services. It brings in roughly $1 million a year. Twenty people work during the busiest time of the year.The Complete Question.
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Write an equation perpendicular to y= 3/4x -1 that passes through the point (3,-3)
Answer:
y = -x or y= -2x+3 will work
A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.8 minutes and the standard deviation was 0.70 minutes.
a. What is the probability that calls last between 3.8 and 4.5 minutes?
b. What is the probability that calls last more than 4.5 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
c. What is the probability that calls last between 4.5 and 5.5 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
d. What is the probability that calls last between 3.5 and 5.5 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 6 percent of the calls. What is this time? (Round your z value to 2 decimal places and final answer to 2 decimal places.)
a) Probability that the calls last between 3.8 and 4.5 minutes is;
0.3413
b) The probability that calls last more than 4.5 minutes is;
0.1587
c) Probability that the calls last between 4.5 and 5.5 minutes is;
0.1511
d) Probability that the calls last between 4.5 and 5.5 minutes is; 0.6607
How to find the probability from z-scores?
The formula for z-score is;
z = (x' - μ)/σ
a) Probability that the calls last between 3.8 and 4.5 minutes is;
P(3.8 < x' < 4.5)
z1 = (3.8 - 3.8)/0.7
z1 = 0
z2 = (4.5 - 3.8)/0.7
z2 = 1
The p-value between the two z-scores is; p-value = 0.3413
b) The probability that calls last more than 4.5 minutes is;
P(x' > 4.5)
z = (4.5 - 3.8)/0.7
z = 1
P(x > Z) = 0.1587
c) Probability that the calls last between 4.5 and 5.5 minutes is;
P(4.5 < x' < 5.5)
z1 = (5.5 - 3.8)/0.7
z1 = 2.43
z2 = (4.5 - 3.8)/0.7
z2 = 1
The p-value between the two z-scores is; p-value = 0.1511
d) Probability that the calls last between 4.5 and 5.5 minutes is;
P(3.5 < x' < 5.5)
z1 = (3.5 - 3.8)/0.7
z1 = -0.43
z2 = (5.5 - 3.8)/0.7
z2 = 2.53
The p-value between the two z-scores is; p-value = 0.6607
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This is on pre-calculas please answer correctly.
For both cases time needs to double the invested money is 7.7016 years
What is continuous compounding?It is a mathematical expression define that interest can be compounded at any time even within any smallest period of time.
How do we calculate compounded continuously doubling money?When annual interest rate is given in a data along with invested money, we can calculate the years required to get doubled money by using the formula A= Pe∧(rt)
A is the double money of the investment
P is the investment
r is the annual interest rate
t time in years
as per question A=2P, r=0.09
2P =Pe∧(0.09t)
2= e∧(0.09t)
㏑2=0.09t
t= 7.7016 years
hence, it takes 7.7016 years to get double money
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Find 3A + 2B.
A =
95
- 3 7
[:] [4]
B =
16
3 - 1
the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]
What is matrix?
The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.
A = [tex]\left[\begin{array}{ccc}9&5\\1&6\\\end{array}\right][/tex], B =[tex]\left[\begin{array}{ccc}1&6\\3&-1\\\end{array}\right][/tex]
3A = [tex]\left[\begin{array}{ccc}27&15\\3&18\\\end{array}\right][/tex]
2B = [tex]\left[\begin{array}{ccc}2&12\\6&-2\\\end{array}\right][/tex]
3A + 2B = [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]
Hence, the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]
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Music Company A charges a $15 membership fee and $0.75 each to download a song. Music Company B charges $0.90 each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.
Linear Equation:The mathematical expressions that we used to find unknown numbers are called Linear Equations. These can be formed by variables and constant terms according to given conditions. Here we use variables like x, y, z, etc to represent unknown variables.
Here we have,
Music company A charges a $ 15 membership fee and a $ 0.75 for each downloaded song
Music company B charges $ 0.90 for each downloaded song without the membership fee
Given question
a. For what number of songs will both companies charge the same amount?
Let for x songs both companies will charge the same amount
Cost to download x songs from Company A
=> 15 + 0.75x
Cost to download x songs from Company B
=> 0.90x
As we assumed both costs are the same
=> 15 + 0.75x = 0.90x
=> 0.90x - 0.75 = 15
=> 0.15x = 15
-> x = 100
Therefore,
The number of songs that both companies will charge the same amount is 100.
b) You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money?
Cost of 150 that charges company A = 15 + 150(0.75)
= 15 + 150(0.75) = 15 + 112.5 = 127.5
Therefore,
Company A will charge $ 127.5 for 150 songs
Cost of 150 songs that charges company B = 150(0.90)
= $ 135
Company B will charge $ 135 for 150 songs
Therefore,
Company B will charge $ 135 for 150 songs
Thus,
To pay the least amount of money we need to choose Company B.
Therefore,
The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.
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I need help on this two column proof.
Answer:
Definition of an isosceles triangle
In triangle XYZ, m < Y= 38.25 and m < Z= 74.3. Determine the measure of the exterior angle to < X.
The measure for the exterior angle to the angle X of the triangle XYZ is 112.55°
How to find the exterior angle to angle XIn any triangle, an exterior angle is equal the sum of its two opposite interior angles is equals.
For the triangle XYZ, the exterior angle to the angle X is equal to the sum of the two opposite interior angles Y and Z
angle Y = 38.25° and angle Z = 74.3°
exterior angle to X = 38.25° + 74.3°
exterior angle to X = 112.55°
This implies that the angle X = 180° - 112.55° = 67.45°
and 67.45° + 38.25° + 74.3° = 180° which is true for the sum of interior angles of a triangle.
Thus, exterior angle to the angle X that is derived to be 112.55° is true for the triangle XYZ.
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Answer:
112.55
Step-by-step explanation:
i got it right
5/11 divided 4/11 =
29 divided by 6/7=
5/9 divided by 1 2/3=
5 3/5 divided by 3 1/2=
please help me!
Using division and multiplication, the values of the operation are 5/4, 203/6, 1/3 and 32/21 respectively
What are Division of NumbersDivision of numbers is the process of breaking down a number into definite proportions of value. In dividing a number, we are reducing it's size by a specific factor. The number to be divided is the dividend. The number by which we divide is the divisor.
In the question given, we have several division operations to carry out.
A) 5/11 ÷ 4/11
Since this are fractions, when we take the inverse of one of the values, we change the sign to multiplication.
5/11 * 11 / 4
This becomes 5/4
B) 29 ÷ 6 / 7
We can also do the same thing we did above by simply taking the inverse of the divisor and then change the sign to multiplication.
29 × 7 / 6 = 203/6
C) 5/9 ÷ 1 2/3
We have to first convert the mixed fraction into an improper fraction and the take the inverse of it and multiply.
5/9 ÷ 5/3
5/9 × 3/5 = 3/ 9 = 1/3
D) 5 3/5 ÷ 3 1/2
We also change the mixed fraction into improper fraction and then take inverse before multiplying.
16/3 ÷ 7/2
16/3 × 2/ 7 = 32/21
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What is the quotient of 3,487 divided by 44?
Answer:
79.25
Step-by-step explanation:
What is the quotient of 3,487 divided by 44?
3,487/44 = 79.25
Stephaine ran 3 miles in 30 minutes. At this rate, how long will it take for Stephaine to run 2 miles?\
Answer: It will take Stephanie 20 minutes to run 2 miles.
Step-by-step explanation:
Since 3 miles is equal to 30 minutes, let us find the number of minutes run per mile
divide 30 by 3
10-It takes 10 minutes to run 1 mile
multiply 10 by the number of miles, which is 2
2x10=20
20 minutes
Which equation best represents the graph of the polynomial function?
Responses
f(x)=x3−3x2−x+2
The equation of the polynomial on the given graph is: C. f(x) = x³ + 2x² - 5x - 6
Which equation represents the graphed polynomial?On the graph we can see a polynomial, let's analyze some key features so we can identify it. First, we can see that when x = 0 (at the y-axis) the graph intercepts the axis at y = -6. So the constant term is -6.
Then we can discard the first and fourth options. The remaining options are:f(x) = x³ - 2x² - 5x - 6f(x) = x³ + 2x² - 5x - 6
Also on the graph, you can notice that when x = -1 the function becomes zero, so let's evaluate these two options in x = -1
The first one gives:f(-1) = (-1)³ - 2*(-1)² - 5*-1 - 6f(-1) = -1 - 2 + 5 -6 = -4
So this option is not correct. The other function gives:f(x) = (-1)³ + 2*(-1)² - 5*(-1) - 6 = -1 + 2 + 5 -6 = 0
So we conclude that the correct option is the third one.f(x) = x³ + 2x² - 5x - 6
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What is a residual for a multiple regression model and the data that is used to create it? select one.
Option d is correct
What is the "multiple regression" model:y=β0+β1x1+β2x2+β3x3+........+βkxk+ε
Where y is the "independent" variable and 0 to k are the "regression" coefficients. In a "multiple linear regression" model, the "independent" variables are x1, x2, x3,..., xk, and the "residual" or "error" term is.
The "residual" for the regression model is calculated using the following formula.
Residual=y-ŷ
Where y is the "independent variable's" "actual" value and is the "independent variable's" "predicted" value.
The "difference" between the "actual" value of the "dependent" variables and the corresponding "predicted" value when employing the "multiple regression" model is referred to as the "residual" in the "residual" formula.
A statistical technique for evaluating the relevance of a "multiple regression" model is the "F test." Linear models are A linear model is a statistic that explains the “relationship” between “response” and “predictor” variables. Using the “multiple regression” model, the “predicted” value of the “response” variable is denoted by ŷ.
hence option 4 is correct
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I understand you mean:
What is a residual for a multiple regression model and the data that is used to create it? Select one:
1.A statistic that is used to evaluate the significance of the multiple regression model
2.A statistic that explains the relationship between response and predictor variables
3.The predicted value of the response variable using the multiple regression model
4.The difference between the actual value of the response variable and the corresponding predicted value (regression error) using the multiple regression model
A sample of 200 g of an isotope decays to another isotope according to the function
How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
Dana Jones have amount after 7 years is $1560.97.
What is compounded continuously?
Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.
Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.
We have to find the amount after 7 years.
Consider, the formula
A = Pe^rt
where,
A is the amount after t years
P is the invested amount
r is the interest rate
t is the number of years
Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.
[tex]A = 1100e^0^.^0^5^(^7^)\\A= 1560.9743\\A = 1560.97[/tex]
Hence, Dana Jones have amount after 7 years is $1560.97.
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how do you do these. i don’t understand a single thing. can someone help.
For a parallelogram, g° = 36° and f° = 144°. and for pentagon, a° = 108° and h° = 36°.
What is a measurement of an angle?
Angles are measured in degrees (°) using a protractor. A protractor is a measuring device that is used to calculate or draw angles in terms of degrees.
In the first figure, adjacent angles of a parallelogram are supplementary.
so
f° + 36° = 180°
Solving this we get f° = 144°
Opposite angles of the parallelogram are equal
so g° = 36°
Now in figure 2,
A regular pentagon has all the interior angles of 108°.
a° = 105°
and exterior angles of 72°
So we can find h°
72° + 72° + h = 180°
h = 180° - 144°
h = 36°
Hence, for a parallelogram, g° = 36° and f° = 144°. and for pentagon, a° = 108° and h° = 36°.
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q
Put the following rational numbers in ascending order.
70%, 0.4, 14%
Answer:
0.4, 14%, 70%
Step-by-step explanation:
0.4= 0.4%
14= 14%
70= 70%
To produce the graph of y = ( x + 5 ) 2 − 2 from y = x 2 , you should
To produce the graph of y = (x+5)^2−2 from y=x , you should translate the graph left by 5 units, then downward by 2 units.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph. In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.
Here,
Translate the graph left by 5 units, then downward by 2 units, to create the graph of y = (x+5)^2-2 starting from y=x.
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for gas, and how
6. Andy's total bill for lunch is $20. The cost of the drink
is 15% of the total bill and the rest is the cost of the
food. What percent of the total bill did Andy's food
cost? What was the cost of his food?
Answer:
17 dollars
Step-by-step explanation:
100 - 15 = 85
85 percent of 20 = 17
Quick
Which statements about square roots are true? Check all that apply.
O The square root of a positive number cannot be negative.
O All positive numbers have two square roots.
O√189 because 9(2) = 18.
O √49 = 7 because 7(7) = 49.
O √25 = 5 because 5²= 25.
The true statements are:-
( 1 ) The square root of a positive number cannot be negative.
( 2 ) √49 = 7 because 7(7) = 49.
( 3 ) √25 = 5 because 5²= 25.
What is algebra?Algebra is one of the many branches of mathematics. Algebra, in broad terms, is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a thread that runs through almost all of mathematics.
The right statements are:-
( 1 )The square root of a positive number cannot be negative.
Example, √100 = 10
(2) √49 = √ ( 7 x 7 ) = 7
(3) √25 = √ ( 5 x 5 ) = 5
Hence, the correct statements are options A, D and E.
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Find the domain and solve.
(d) log₄²(1+x²)=0.25
The domain and the solution of the equation log₄²(1+x²)=0.25 are x = ±1
How to determine the domain and the solution?From the question, we have the following parameters that can be used in our computation:
log₄²(1+x²)=0.25
In this case, the domain of the expression and the solution are the same
So, we start by taking the square root of both sides
log₄(1+x²) = 0.5
Next, we apply the change of base law of logarithm
So, we have
1 + x² = 4⁰°⁵
Evaluate the exponent
1 + x² = 2
Evaluate the like terms
x² = 1
Take the square root of both sides
x = ±1
Hence, the domain and the solution are x = ±1
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A 4-person grievance committee is to be selected out of 2 how many ways can the following committees be selected? Complete parts (A) through (E) below. (A) 3 from A and 1 from B A and B, with 11 and 30 people, respectively. in (B) 2 from A and 2 from B (C) All from A (D)4 people regardless of department (E) At least 3 from department A
According to the combination technique,
A) 3 from A and 1 from B = 16320
B) 2 from A and 2 from B = 29070
C) All from A = 3060
D) 4 people regardless of department = 73815
E) at least 3 from department A = 19380
In math combination technique is used to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Here we have given that 4-person grievance committee is to be selected out of 2 how many ways can the following committees be selected
And we need to find the following
Here we know that 4-person grievance committee is to be selected out of 2 departments, A and B, with 18 and 20 people.
In this one we have to find the number ways can the following committees be selected.
A) While the first condition is to 3 from A and 1 from B
Here the term "and" means to multiply
Then it can be written as
=> (18 people choose 3) x (20 people choose 1)
=> (18C3)(20C1) = (816)(20) = 16320
B) And then the next condition is 2 from A and 2 from B
In this one is written as,
=> (18 people choose 2) x (20 people choose 2)
=> (18C2)(20C2) = (153)(190) = 29070
C) All from A
which is equal to the following,
=> 18 people choose 4 = 18C4 = 3060
D) Next, we have to do the calculation for 4 people regardless of department
=> 18+20 or 38 people choose 4 = 38C4 = 73815
E) Finally, at least 3 from department A.
'In other words, it can be written as choose 3 from department A and choose 1 from department B or Choose 4 all from department A
Where "And" means to multiply and "or" means to add.
Therefore, the condition is written as,
=> [(18 people choose 3) times (20 people choose 1)] plus (18 people choose 4)
=> (18C3)(20C1) + (18C4) = (816)(20) + 3060 = 19380
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Pls help me it’s for my grade
Answer:
[tex]\frac{1}{4}s^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square and divide the result by 4.
help meeeeeeeeeee pleaseee
For an average intake of 2200 calories per day, the number of acres of land owned is 2.03
How to determine the number of acres?From the question, we have the following calories function that can be used in our computation:
C(x) = 270 ln(x + 1) + 1900
Also from the question, we have
Average intake of calories = 2200 inches
This means that
C(x) = 2200
So, we have the following equation
270 ln(x + 1) + 1900 = 2200
Subtract 1900 from both sides
270 ln(x + 1) = 300
Divide 270 from both sides
ln(x + 1) = 1.11
Take the exponent of both sides
x + 1 = 3.03
So, we have
x = 2.03
Hence, the number of acres is 2.03
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Solve, to two decimal places, the equation
The trigonometric equation is 5sin²x + 3sinx - 1 = 0.
What is a trigonometric equation?
A trigonometric equation is one that incorporates a variable-based trigonometric function. One illustration of a trigonometric equation is sin x + 2 = 1. This equation or one that is more complicated, such as sin2 x - 2 cos x - 2 = 0, can be used in the equations.
Here, we have
Given: (5/2)cos2x - 1/2 = 3sinx
We know that
cos2x = 1 - 2sin²x
Then our equation become
(5/2) (1 - 2sin²x) - 1/2 = 3sinx
5/2 - 5sin²x - 1/2 = 3sinx
2 - 5sin²x = 3sinx
-5sin²x + 2 - 3sinx = 0
5sin²x + 3sinx - 1 = 0
Hence, the trigonometric equation is 5sin²x + 3sinx - 1 = 0.
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Write an explicit formula for an, the nth term of the sequence 48, 12, 3, ....
The given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
What is the explicit formula?The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
An arithmetic sequence has the explicit formula aₙ = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms.
The nth term of arithmetic, geometric, or harmonic series is usually the explicit formula.
So, the sequence we have is as follows:
48, 12, 3, ....
The common ratio of the terms is 1/4, and the first term is 48.
The universal equation for a geometric sequence's n-th term is:
aₙ = a1·r^(n-1)
This is true when r = 1/4 and a1 = 48:
aₙ = 48·(1/4)^(n-1)
Therefore, the given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
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