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3 years ago

Explain how to use a graph of the function f(x) to find f(3).

Mathematics

1 answer:

irga5000 [103]3 years ago

4 0

Answer:

In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0) . Then your line will cut the graph of f(x) at some point, that point's y-coordinate will be your value of f(3)

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Sabita made this table to relate two customary units of liquid volume

Pachacha [2.7K]

(1, 2)
(2, 4)
(3, 6)
(4, 8)
(5, 10)

2a = b is the relationship. Double a to get b.

Pints | Cups
1 2
2 4
3 6
4 8
5 10

There are 2 cups in each pint, so the table shows the relationship between 1-5 pints and cups.

5 0

3 years ago

Read 2 more answers

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified l

Sloan [31]

Answer:

The integral of the volume is:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

The result is: $V = 78.97731$

Step-by-step explanation:

Given

Curve: $x^2 + 4y^2 = 4$

About line $x = 2$ --- Missing information

Required

Set up an integral for the volume

$x^2 + 4y^2 = 4$

Make x^2 the subject

$x^2 = 4 - 4y^2$

Square both sides

$x = \sqrt{(4 - 4y^2)$

Factor out 4

$x = \sqrt{4(1 - y^2)$

Split

$x = \sqrt{4} * \sqrt{(1 - y^2)$

$x = \±2 * \sqrt{(1 - y^2)$

$x = \±2 \sqrt{(1 - y^2)$

Split

$x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}$

Rotate about x = 2 implies that:

$r = 2 - x$

So:

$r_1 = 2 - (-2 \sqrt{(1 - y^2)})$

$r_1 = 2 +2 \sqrt{(1 - y^2)}$

$r_2 = 2 - 2 \sqrt{(1 - y^2)}$

Using washer method along the y-axis i.e. integral from 0 to 1.

We have:

$V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy$

Substitute values for r1 and r2

$V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy$

Evaluate the squares

$V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy$

Remove brackets and collect like terms

$V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy$

$V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy$

Rewrite as:

$V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

Using the calculator:

$\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}$

So:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi * \frac{\pi}{4}$

$V =\frac{32\pi^2}{4}$

$V =8\pi^2$

Take:

$\pi = 3.142$

$V = 8* 3.142^2$

$V = 78.97731$ --- approximated

3 0

3 years ago

Oliver walks 5/8 of a mile in 1/6 of an hour. What is his unit rate in miles per hour?

stealth61 [152]

Answer:

3.75 miles per hour

Step-by-step explanation:

(5/8)/(1/6)=3.75 mph, or you could do 5/8 x 6, since 1/6 x 6 equals one hour

7 0

3 years ago

Read 2 more answers

7 x [{9+8)-(12-7)] answer

KatRina [158]

Answer:

Step-by-step explanation:

7×[17-5]

7×12

hope it will help

7 0

3 years ago

7/8 students own a bike . 72 is the difference between the ones that own a bike and ones that do not. how many were surveyed?

DerKrebs [107]

X + y is the number of students who were surveyed. x is the number who own a bike. y is the number who don't. the ratio of the ones who own a bike and the ones who were surveyed is x / (x + y) that ratio is 7/8. you get x / (x + y) = 7/8 multiply both sides of this equation by (x + y) to get x = (x + y) * 7/8 simplify to get x = 7/8 * x + 7/8 * y subtract 7/8 * x from both sides of this equation to get: 1/8 * x = 7/8 * y solve for x to get x = 7 * y this means that the number of students who own a bike is 7 times the number of students who don't. divide both sides of that equation by y to get x/y = 7/1. that means that the ratio of students who own a bike to the number of students who don't is equal to 7/1. the problem states that the difference between the number who own a bike and the number who don't is 72. this means that x - y = 72 from the equation of x = 7 * y, replace x with 7 * y in the equation of x - y = 72 to get: 7 * y - y = 72 simplify to get 6 * y = 72 divide both sides of that equation by 6 to get y = 72/6 = 12 this means that the number of students who do not own a bike is 12. since x = 7 * y, then x = 7 * 12 = 84. this means that the number of students who own a bike is 84. since the number of students is x + y, this means that the number of students who were surveyed is 84 + 12 = 96. let's see if this is right. 96 students were surveyed. 84 own a bike and 12 don't. the difference between the ones who own a bike and the ones who don't is 84 - 12 = 72. the ratio of the ones who own a bike and the number surveyed is 84/96 = 7/8. solution is 96 students were surveyed.

6 0

4 years ago

Read 2 more answers