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2 years ago

7

7. Yin's cellphone plan costs $30 a month. She used 22.5 hours in May

1 answer:

aliya0001 [1]2 years ago

4 0

Answer:

CPM = ~$0.02

Step-by-step explanation:

$22.5 Hours = 1350Minuets\\\frac{30}{1350} = 0.0(2)\\$

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find the volume of the solid formed by revolving the region bounded by the graphs of y = 4x - x^2 and f(x) = x^2 from [0,2] abou

Neko [114]

Answer:

$v = \frac{32\pi}{3}$

or

$v=33.52$

Step-by-step explanation:

Given

$f(x) = 4x - x^2$

$g(x) = x^2$

$[a,b] = [0,2]$

Required

The volume of the solid formed

Rotating about the x-axis.

Using the washer method to calculate the volume, we have:

$\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx$

Integrate

$v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx$

$v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx$

Substitute values for a, b, f(x) and g(x)

$v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx$

Evaluate the exponents

$v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx$

Simplify like terms

$v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx$

Factor out 8

$v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx$

Integrate

$v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0$

$v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0$

Substitute 2 and 0 for x, respectively

$v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])$

$v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])$

$v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]$

$v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]$

Take LCM

$v = 8\pi [ \frac{16*4- 16 * 3}{12}]$

$v = 8\pi [ \frac{64- 48}{12}]$

$v = 8\pi * \frac{16}{12}$

Simplify

$v = 8\pi * \frac{4}{3}$

$v = \frac{32\pi}{3}$

or

$v=\frac{32}{3} * \frac{22}{7}$

$v=\frac{32*22}{3*7}$

$v=\frac{704}{21}$

$v=33.52$

8 0

2 years ago

Ben and Sam are driving in a lake.at 14 feet below the surface, ben spots sam 9 feet directly below him.find smash deprh

MAVERICK [17]

Sam's depth is 25 feet as 14 + 9 = 25

7 0

2 years ago

If the graph of a line goes from the upper left corner of the graph to the lower right corner, what can you say about its slope?

Viktor [21]

You can say that the slope is negative. A line on a graph that goes from the upper left corner to the bottom right is a negative slope.

4 0

2 years ago

-Question Worth 50Points!!-

iogann1982 [59]

Answer:

104.8 square feet

Step-by-step explanation:

To find the area of the figure, split it into two regular shapes: a rectangle and a semi-circle. Find the area of each and add it together.

Area of the rectangle is A = 8*10 = 80 square feet.

Are of semicircle is A = 1/2 πr² = 1/2 (3.1)(4²) = 1/2(3.1)(16) = 24.8 square feet.

Together the area is 80 + 24.8 = 104.8 square feet

5 0

2 years ago

Read 2 more answers

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

sergejj [24]

Answer

2

Step-by-step explanation:

(reorder terms)

<u>2x + 2x</u> = 8

collect like terms

<u>4x=8</u>

divide both sides of the equation

x = 2

3 0

2 years ago