Find the volume of figure two using the volume formula make sure to identify length width height

Find The Volume Of Figure Two Using The Volume Formula Make Sure To Identify Length Width Height

Answers

Answer 1

Answer:

[tex]72\ units^3[/tex]

Step-by-step explanation:

Width = 3 units

Height = 4 units

Length = 6 units

Volume = Length * Width * Height

             =  6 * 3 * 4

             = 72 units cubed


Related Questions

Let h: all real numbers to all real number be defined by h(x)=|(x+2)(x-3)| determine the critical points of h

Answers

The critical points of h are -2 and 3

How to determine the critical points of a function?

Recall that  a critical point of a function y = f(x) is a point (c, f(c)) on the graph of f(x) at which either the derivative is 0 (or) the derivative is not defined.

The given function is h(x) = [(x+2)(x-3)]

Finding the product of the brackets

(x+2)(x-3) = x²-3x+2x-6

Collecting like terms to have

h(x) = x²-x -6

h(x) = [(x+2)(x-3)] =  x²-x -6

factorizing this to get

(x²-3x)+(2x-6) = 0

x(x-3) + 2(x-3) = 0

x+2 = 0 or x-3 = 0

x=-2 or x = 3

Therefore the critical points are -2 and 3

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What is the name of each labeled part?

Answers

A:dentrite

B: cell body

C:axon terminal

D:axon

E: nucleus

For questions 27, use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.


27. Every student brought a pencil or a pen. Marcie brought a pencil. Therefore, Marcie did not bring a pen.

Answers

In the Venn diagram , we can conclude that the statement is valid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here "Pen" and "Pencil". Since we know that every student brought a pen or a pencil, we know that there are no elements outside the 2 sets (these would be students who brought neither a pen or a pencil). Also, since every student brought a pencil or a pen, we also know that the overlap between the 2 sets is empty (this would be students who brought a pencil and a pen). So there are 2 areas remaining where students can be situated (1 and 2 in the picture).

We know that Marcie brought a pencil, so she is situated in area 2. This means she is outside the set "pen", and so she didn't bring a pen, and we can conclude that the statement is valid.

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You are going to deposit $23,500 today. You will earn an annual rate of 5.1 percent for 10 years, and then earn an annual rate of 4.5 percent for 13 years. How much will you have in your account in 23 years?

Answers

Answer:

$68,486.79

Step-by-step explanation:

the first 10 years:

23,500(1.051)^10=38,645.1522

the remaining 13 years:

38,645.1522(1.045)^13=68,486.78798

(round it)

SERIOUS AND CORRECT ANSWERS ONLY! What is the median for the following box plot?

Answers

Answer:

the median is 100

Step-by-step explanation:

the numbers are already in order so the number in the middle is 100.

What Is Equivalent To The Following Equation?
[tex]4.033865e + 17[/tex]

Answers

The answer would be 27.965181928

Find the exact value of the side lengths of a square root? Help!

Answers

Answer:

a) Area = 144, so Side length = √144 = 12

b) Area = 96, so Side length = √96 = 4√6

= sqrt96

c) Area = 36, so Side length = √36 = 6

d) Area = 35, so Side length = √35

= sqrt35

The desks in Joe's classroom are
arranged in 7 rows. Each row contains
5 desks. The equation that describes
the number of desks, d, in the
classroom is d÷ 7 = 5. How many
desks are in Joe's classroom?

Answers

35/7=5 so the answer is 35

Jen's patio has an area of
square feet. She is covering the area with 4200
small rocks.

What is the density of the rocks on the patio?

Answers

The density of the small rocks is 21 rocks per square feet.

How to find the density of rocks?

To find the density of rocks per square feet, we need to take the quotient between the total number of rocks and the area covered.

We know that the patio has an area of 200 square feet, and the total number of rocks is 4200, then here we only need to take the quotient between these two values.

Density = (4200 rocks)/(200 ft²) =  21 rocks per ft²

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Complete question:

"Jen's patio has an area of 200 square feet. She is covering the area with 4200 small rocks.

What is the density of the rocks on the patio?"

What is the result of multiplication of complex numbers
[tex] - \sqrt{3} + i \: and \: \frac{1}{8} (cos \: \frac{5\pi}{3} + i \: sin \: \frac{5\pi}{3} )[/tex]

Answers

The result of multiplication of complex numbers is ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3).

What is the result of multiplication of the complex number?

The result of the multiplication of the complex number is determined as follows;

-√3 + i  x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply the bracket by grouping them as shown below;

= -√3 x ¹/₈ (cos 5π/3  + i sin 5π/3) + i x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply out the bracket;

= -√3/8 cos5π/3 -  i√3/8 sin5π/3 + i¹/₈cos5π/3 + ¹/₈sin5π/3

note: i x i = 1

Collect similar terms together and add them if any;

= ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3)

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The price of a gallon of unleaded gas has dropped to $2.78 today. Yesterday’s price was $2.85. Find the percentage decrease. Round your answer to the nearest tenth of a percent.

Answers

Percent decrease =

(difference in prices)/(original price) × 100

(2.85 - 2.78)/2.85 × 100

= (0.07)/2.85 ×100 ≈ 2.5%

WHICH DECIMAL IS EQUIVALIENT TO 13/20

Answers

Step-by-step explanation:

well, do the division. a fraction is nothing else.

13 divided by 20.

13/20 = 0.65

NO LINKS!! URGENT HELP PLEASE!!!

1.Change to exponential form

a. ln w = 7 + 6x


2. Solve for t using a logarithm with base a

a. 3a^(t/2) = 7

Answers

Answer:

1. w = [tex]\bold{e^{7+6x}}[/tex]

2. [tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Step-by-step explanation:

1.

a. The exponential form of a logarithmic equation is given by:

[tex]\bold{log_a(b) }[/tex]= c is equivalent to [tex]a^c = b[/tex]

Using this rule, we can rewrite the equation:

ln w = 7 + 6x as w = [tex]\bold{e^{7+6x}}[/tex]

Therefore, the exponential form of the given equation is w = [tex]\bold{e^{7+6x}}[/tex]

2.

a. To solve for t using a logarithm with base a, we can take the logarithm of both sides of the equation:

[tex]\bold{3a^\frac{t}{2} = 7 }\\\bold{log_a3a^\frac{t}{2}= log_a(7)}[/tex]

Using the rule of logarithms that log_a(b^n) = n*log_a(b), we can simplify the left side:

[tex]\bold{log_a(3) +\frac{t}{2} log_a(a) = log_a(7)}[/tex]

Since log_a(a) = 1 for any base a, we can simplify the expression further:

[tex]\bold{log_a(3) + \frac{t}{2}*1= log_a(7)}[/tex]

Now we can solve for t by isolating it on one side of the equation:

[tex]\bold{ \frac{t}{7} = (log_a(7) - log_a(3))} \\ \bold{t = 2(log_a(7) - log_a(3))}[/tex]

Therefore, the solution for t using a logarithm with base a is[tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Answer:

[tex]\textsf{1.} \quad w = e^{7 + 6x}[/tex]

[tex]\textsf{2.} \quad t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Step-by-step explanation:

Question 1

Exponential form is a way to represent a number using an exponent, where the base is raised to a power.

The natural logarithm function is the inverse of the exponential function:

[tex]\boxed{\ln x=y \iff x=e^y}[/tex]

Therefore we can use this definition to change the given equation to exponential form:

[tex]\begin{aligned}\ln w & = 7 + 6x\\\\e^{\ln w} & = e^{7+6x}\\\\w&=e^{7+6x}\end{aligned}[/tex]

Therefore, the exponential form of the equation is:

[tex]w = e^{7 + 6x}[/tex]

[tex]\hrulefill[/tex]

Question 2

To solve for t using a logarithm with base a, begin by taking the logarithm of both sides of the equation with base a:

[tex]\log_a (3a^{\frac{t}{2}})=\log_a(7)[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})=\log_a(7)[/tex]

Subtract logₐ(3) from both sides of the equation:

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})-\log_a (3)=\log_a(7)-\log_a (3)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a(7)-\log_a (3)[/tex]

[tex]\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\dfrac{t}{2}\log_a(a)=\log_a\left(\dfrac{7}{3}\right)[/tex]

Apply the log law:  logₐ(a) = 1

[tex]\dfrac{t}{2}(1)=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\dfrac{t}{2}=\log_a\left(\dfrac{7}{3}\right)[/tex]

Multiply both sides of the equation by 2:

[tex]2 \cdot \dfrac{t}{2}=2 \cdot \log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]t=2 \log_a\left(\dfrac{7}{3}\right)[/tex]

Finally, apply the log power law:

[tex]t= \log_a\left(\dfrac{7}{3}\right)^2[/tex]

[tex]t= \log_a\left(\dfrac{7^2}{3^2}\right)[/tex]

[tex]t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Therefore, the solution for t in terms of logarithm with base a is:

[tex]\boxed{t= \log_a\left(\dfrac{49}{9}\right)}[/tex]

Use the following table to help answer the question below.
State
Single-Earner
2-Person
3-Person
4-Person
Florida
$41,226
$52,259
$58,574
$69,009
Georgia
$40,691
$55,258
$61,104
$68,502
Missouri
$39,645
$51,568
$60,371
$71,059
Texas
$38,940
$55,859
$59,222
$66,381
Virginia
$48,362
$65,122
$74,151
$85,939

A family of three living in Georgia is thinking about filing bankruptcy. In order to file for Chapter 7 bankruptcy, what must be true about their monthly income?
a.
The family's monthly income must be less than $5,092.
b.
The family's monthly income must be more than $5,092.
c.
The family's monthly income must be less than $4,605.
d.
The family's monthly income must be more than $4,605.

Answers

The true statement about monthly income is "The family's monthly income must be less than $5,092." (option a).

The table provided shows the median income levels for different family sizes in various states, including Georgia. To determine whether the family of three is eligible for Chapter 7 bankruptcy, we need to compare their monthly income to the median income for a three-person family in Georgia, which is $61,104.

If the family's monthly income is less than the median income for their family size in their state, they are presumed to be eligible for Chapter 7 bankruptcy. In this case, the family's monthly income must be less than $61,104.

Looking at the table, we can see that the median income for a three-person family in Georgia is $61,104, which means that the family's monthly income must be less than $5,092 in order to be eligible for Chapter 7 bankruptcy.

Therefore, the correct answer is (a) - the family's monthly income must be less than $5,092 for them to be eligible to file for Chapter 7 bankruptcy.

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Question 2 (Essay Worth 10 points)
(01.03 MC)
Solve the equation √x+3+4=5 for the variable. Show each step of your solution process.

Answers

Solving the radical expression √(x + 3) + 4 = 5 for x gives x = -2

Solving the radical expression

From the question, we have the following parameters that can be used in our computation:

√(x + 3) + 4 = 5

Subtract 4 from both sides of the equation

So, we have

√(x + 3) = 1

Take the square of both sides

x + 3 = 1

So, we have

x = -2

Hence, the solution for x is -2

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What is the slope of the line below ?

Answers

Step-by-step explanation:

Slope  = rise / run

Using points ( -1/2  - 1/2 ) and (1/2, 0 )  

  rise = 1/2    run = 1

     rise / run = 1/2 /1 = 1/2 = slope

Let u = <-3, -1>. Find 7u.
a) <21, -7>
b) <21, 7>
c) <-21, 7>
d) <-21, -7>

Answers

Answer:

(d) <-21, -7>.

Step-by-step explanation:

To find 7u, we simply multiply each component of u by 7:

7u = 7<-3, -1> = <-37, -17> = <-21, -7>

A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if
there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The
results are given in the accompanying data table. Use a 0.01 significance level to test the claim that the sex of the
respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is
there a substantial difference?
Human activity Natural patterns Don't know
314
Male
Female
301
Click here to view the chi-square distribution table.
154
161
556
54

Answers

We fail to reject the null hypothesis, and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

How to solve

The problem boils down to the following hypotheses:

H0: The sex of the respondent is independent of the choice for the cause of global warming.

H1: The sex of the respondent is dependent on the choice for the cause of global warming.

Chosen level of significance: 0.01

Original Table ,also showing marginals and grand total

Human Activity Natural Patterns Don't Know Marginal Total

Male 323 158 39 520

Female 340 152 38 530

Marginal Total 663 310 77 1050(= Grand total)

Table of expected values :

Human Activity Natural Patterns Don't know

Male 328.343 153.524 38.133

Female 334.657 156.476 38.867

Test Statistic: X2 = (323-328.343)2 / 328.343 + (158-153.524)2 /153.524 + (39-38.133)2 / 38.133 + (340-334.657)2 /334.657 + (152-156.476)2 / 156.476 + ( 38-38.867)2 /38.867

= 0.46974 (approx) = (value of test statistic)

degree of freedom = (2-1)*(3-1)= 2

Therefore, X2 critical (critical value) = 9.210

So, we see that the value of the chi-square test statistic is less than the critical value for alpha=0.01

( 0.46974 < 9.210)

So, we fail to reject the null hypothesis,

and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

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Jeremiah has a mailing cylinder for posters that measures 12 inches long and 8 inches in diameter. What approximate volume can it hold? Use 3.14 for pi. Do not round. SHOW YOUR WORK.

Answers

Answer:

603.36 cubic inches.

Step-by-step explanation:

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

Volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

Answer:

6.8 with a sum of 09.28282

Step-by-step explanation:  

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

The volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

hope it helps!!!

I need help with this problem

Answers

The value of x when lines MN and PQ are equal is 7

How to determine the value of the variable

Let take note of the properties of a quadrilateral, they include;

A quadrilateral has four vertices.It has four sides.The sum of all interior angles of a quadrilateral shape is equal to 360° degrees.The shape could be a regular or an irregular shape.

From the information given in the diagram, we have that;

Line MN = Line PQ

Also, the expressions are;

MN = 7x + 13

PQ = 10x - 8

Now, equate the values, we get;

7x + 13 = 10x - 8

collect the like terms

7x - 10x = -8 - 13

subtract the like terms

-3x = -21

Divide both sides by the coefficient of x, we get

x = 7

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The radius of this ball is 9 millimeters. Which equation gives the ball's surface area, in square millimeters?

Answers

Step-by-step explanation:

the equality is: 4 × π × r × r

so the answer is

4 • π • 81

= 324π

Answer:

Step-by-step explanation:

SA= 4[tex]\pi[/tex]r²

    =4[tex]\pi[/tex]9²

    =324[tex]\pi[/tex] m² or 1017.88 m²

If a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 3 sixes?

Answers

The required probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

The probability of getting exactly k sixes in n rolls of a fair die is given by the binomial distribution formula:

[tex]P(k) = (n C k) * p^k * (1-p)^{(n-k)}[/tex]

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of getting exactly 3, 4, or 5 sixes in 5 rolls:

P(3) = (5 choose 3) * (1/6)³ * (5/6)² = 0.032

P(4) = (5 choose 4) * (1/6)⁴ * (5/6)¹ = 0.001

P(5) = (5 choose 5) * (1/6)⁵ * (5/6)⁰ = 0.00003

To get the probability of getting at least 3 sixes, we need to add up these probabilities:

P(at least 3 sixes) = P(3) + P(4) + P(5) = 0.032 + 0.001 + 0.00003 = 0.03303

Rounding to the nearest thousandth, the probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

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9. Based on the tire experiment, will it take more, fewer, or the same rotations for a monster truck with 6ft (72 inches) tires to travel one mile compared to the other 3 tires from before?
A. More
B.Fewer
C. The Same


10. What are the approximate amount of rotations it would take the monster truck to travel one mile?

120
280
560
631
880
1260

Answers

The approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

Now, Based on the tire experiment, it will take fewer rotations for a monster truck with 6ft (which is 72 inches) tires to travel one mile compared to the other 3 tires from before.

This is because larger tires have a greater circumference, which means they are able to cover more distance with each rotation.

Hence, For calculate the approximate amount of rotations it would take the monster truck to travel one mile, we need to use the formula:

Number of rotations = Distance traveled / Circumference of the tire

Since the distance traveled is one mile, which is equal to 5280 feet, we need to convert the tire diameter from feet to inches, and then calculate the circumference:

Hence, We get;

Circumference = π x Diameter Circumference

                        = 3.14 x 72 Circumference

                        = 226.08 inches

Now, we can calculate the number of rotations:

Number of rotations = 5280 feet / (12 inches/foot x 226.08 inches/rotation)

Number of rotations = 5280 / 2712.96

Number of rotations ≈ 1.947 rotations

or ≈ 1260 rotations per mile

Therefore, the approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

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find the inducated measure. circumference of a circle with a diameter of 5 inches​

Answers

The formula for the circumference of a circle is:

C = πd

where d is the diameter of the circle.

Substituting the given value of the diameter, we get:

C = π(5) = 5π

Therefore, the circumference of the circle is 5π inches.

Answer:

15.7 inches

Step-by-step explanation:

Circumference of circle = d x 3.14

d = 5 inches

Let's solve

5 x 3.14 = 15.7 inches

So, the circumference of the circle is 15.7 inches.

PLEASE I NEED HELP!! WILL MARK BRAINLIEST IF CORRECT!! TYY

Answers

Answer:

6.2

Step-by-step explanation:

For this we use a method called Pythagoras theorem.

to find '?' we will have to use this method

[tex]A^{2}[/tex] +[tex]B^{2}[/tex] =[tex]C^{2}[/tex]

since we don't know what A is we will name it x

[tex]x^{2}[/tex]+[tex]5^{2}[/tex]=[tex]8^{2}[/tex]

x+25=64

64-25=39

[tex]x^{2}[/tex]=39

x=[tex]\sqrt{39}[/tex]

x=6.2

For the following sequence: 6,15,24,33, ....
a) write an expression for the nth term:

Answers

The expression for the nth term of the sequence is 6 + 9(n - 1)

Writing an expression for the nth term:

From the question, we have the following parameters that can be used in our computation:

6,15,24,33,

In the above sequence, we can see that the current term is added to 9 to gett the next term

So, we have

First term, a = 6

Commin difference, d = 9

The nth term is

Tn = a + (n - 1)d

So, we have

Tn = 6 + 9(n - 1)

Hence, teh nth term is 6 + 9(n - 1)

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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 480 feet. Determine the​ flag's length and width if the length is 60 feet greater than the width. Use pencil and paper. Write three situations to which you could apply the resulting system of equations.

Answers

Answer:

Let x be the width of the flag in feet. Then the length of the flag is x + 60 feet. The perimeter of the flag is the sum of the lengths of its four sides, which is:

2(x + x + 60) = 4x + 120 feet

Setting this equal to 480 feet, we have:

4x + 120 = 480

Solving for x, we get:

4x = 360

x = 90

Therefore, the width of the flag is 90 feet and the length is 150 feet.

Three situations to which this system of equations could be applied are:

A farmer wants to plant a rectangular field of flowers. He knows the perimeter of the field but needs to determine the length and width in order to calculate the area and decide how many flowers to buy.

A carpenter wants to build a rectangular frame for a painting. She knows the perimeter of the frame but needs to determine the length and width in order to calculate the amount of wood needed and the cost.

A city planner wants to design a rectangular park. She knows the perimeter of the park but needs to determine the length and width in order to calculate the area and decide how many trees and benches to place in the park.

Solve for X and Y knowing it’s a kite

Answers

The matching lines mean they have the same length so 12=5x-y and 4=3x+y. From here you can set up a system of equations as follows:
5x-y=12
3x+y=4
If you were to combine these two equations (imagine smooshing them) the y values would cancel out and the following equation would be left.
8x=16
Divide both sides by 8 and you get x=2. Plug this x value in and solve for y in either of the original equations.
5(2)-y=12
10-y=12
-y=2
y=-2

The function f(x) = 7x + 3 is one-to-one.
a. Find an equation for f1, the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¹ (f(x)) = x.
a. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
OA. f'(x) =
for x #
OB. f¹(x) =
O c. f '(x) =
OD. f '(x)=
.
for all x
for x s
for x 2

Answers

An equation for f', the inverse function is: f¹(x) = (x - 3)/7, for x ≥ 4.

The equation is correct as it has been shown that f(f'(x)) = x and f'(f(x)) = x.

What is an inverse function?

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of function f. This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 7x + 3

x = 7y + 3

7y = x - 3

y' = f¹(x) = (x - 3)/7, for x ≥ 4.

Proof:

f(f'(x)) = f[(x - 3)/7] = 7[(x - 3)/7] + 3

f(f'(x)) = f[(x - 3)/7] = x - 3 + 3

f(f'(x)) = f[(x - 3)/7] = x.

f'(f(x)) = x

f'(f(x)) = f¹[(7x + 3)]

f'(f(x)) = (7x - 3 + 3)/7

f'(f(x)) = 7x/7

f'(f(x)) = x

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Answers

The value of h is 0.895, the arc cosine of h is 0.462 and it terminates in the correct quadrant

Lastly, the measure of angle θ is 1.46 π

Calculating the value of h

Given that

Terminal point = (-1.79, -0.89)

This means that

(x, y) = (-1.79, -0.89)

Also, we have

Radius, r = 2 units

So, the value of h is

h = |x|/r

This gives

h = |-1.79|/2

Evaluate

h = 0.895

Calculating the arc cosine of h

In part (a) of this solution, we have

h = 0.895

Take the arc cos of both sides

So, we have

cos⁻¹(h) = cos⁻¹(0.895)

Evaluate the arc cos using a calculator

So, we have the following representation

h = 0.462 rad

This angle is in the first quadrant

It means that the angle terminates in the correct quadrant

For the value of θ, we have the following

This is calculated as

θ = π + tan⁻¹(-0.89/-1.79)

Evaluate

θ = π + 0.46 π

Evaluate

θ = 1.46 π

Hence, the measure of angle θ is 1.46 π

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