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2 years ago

Which statement best describes f(6) = 12?

Mathematics

2 answers:

allsm [11]2 years ago

6 0

Answer:

When the input is 6, the output must be 12.

Step-by-step explanation:

Since you are "inputting" 6 the result or output must be 12

Hope this helps!

Sergio039 [100]2 years ago

5 0

Answer:

When the input is 6, the output must be 12.

Step-by-step explanation:

f(6) = 12

The input to the function is x which is 6 and the output is what f(6) equals which is 12

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Use the general slicing method to find the volume of the following solids. The solid whose base is the region bounded by the cur

Y_Kistochka [10]

Answer:

The volume is $V=\frac{64}{15}$

Step-by-step explanation:

The General Slicing Method is given by

Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is

$V=\int\limits^b_a {A(x)} \, dx$

Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is

The key observation is that the width is the distance between the upper bounding curve $y = 2 - x^2$ and the lower bounding curve $y = x^2$

The width of each square is given by

$w=(2-x^2)-x^2=2-2x^2$

This means that the area of the square cross section at the point x is

$A(x)=(2-2x^2)^2$

The intersection points of the two bounding curves satisfy $2 - x^2=x^2$ , which has solutions x = ±1.

$2-x^2=x^2\\-2x^2=-2\\\frac{-2x^2}{-2}=\frac{-2}{-2}\\x^2=1\\\\x=\sqrt{1},\:x=-\sqrt{1}$

Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is

$V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}$

5 0

2 years ago

Can u express 9 and 9 as a mixed number ? Why or why not ? 9and 9 means fraction

Lostsunrise [7]

Yes:

1 & 0/9
or
1 & 1/1

6 0

3 years ago

Help -x/3 > 5 A. X<15 B. X > -15 C. X < -15 D. X > 15

Genrish500 [490]

Answer:

Steps

-x/3 >5

Multiply both sides by 3

3(-x/3)>5.3

Simplify

-X> 15

Multiply both sides by - 1 (reverse the inequality)

(-x)(-1)<15(-1)

Simplify

X< -15

so C is the answer

8 0

1 year ago

PLEASE HELP DUE IN ! HOUR

alekssr [168]

Answer:

c. Mary charges $12.00 per hour for labor to paint houses. What is x, the number of hours Mary worked if she charged $240.00 for labor?

Step-by-step explanation:

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2 years ago

Read 2 more answers

How do I divide numbers by using long division.

Vsevolod [243]

The only rule to follow is

Divide dividend by divisor and the mention the quotient and things left after remains in place of remainder

Here is a sample

$\sf\Large\qquad\quad16\\ \begin{array}{cc} \cline{2 - 2}\sf 20 )&\sf \ 327\\&\sf - 20 \downarrow\\ \cline{2-2}& \sf \ \ \ \ 127\\ &\sf \ - 120 \\ \cline{2-2} & \sf \ \007 \\ \cline{2-2} \end{array}\\\\\\ \sf Divisor \rightarrow 20 \\ \\ \sf Quotient \rightarrow 16\\\\ \sf Remainder \rightarrow 7$

3 0

2 years ago