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2 years ago

A sphere has a diameter of 14 ft. Which equation finds the volume of the sphere?

Mathematics

1 answer:

aev [14]2 years ago

6 0

Answer:

The volume of the sphere is 1436 in³

The equation is

V = ⁴⁄₃ * 3.14 * (7ft)³

Step-by-step explanation:

radius = half of diameter

d = 14ft

r = 14ft / 2 = 7ft

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius = 7ft

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (7ft)³

V = 4.187 * 343 in³

V = 1436 in³

The volume of the sphere is 1436 in³

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F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

f(x) and g(x) and not inverse functions

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

Hence, f(x) and g(x) and not inverse functions

4 0

2 years ago

What is the simplified form of the ninth root of x times the ninth root of x times the ninth root of x times the ninth root of x

Tomtit [17]

Let's convert the task into an example, simplifyng which will make us able to get the answer.
So, according to the task: $\sqrt[9]{x} * \sqrt[9]{x} * \sqrt[9]{x} * \sqrt[9]{x} 

= \sqrt[1/ 9 ]{x} * \sqrt[1/9]{x} * \sqrt[1/9]{x} * \sqrt[1/9]{x}$

Now we can simplify: $\sqrt[1/9]{x} + 1/9+1/9+1/9

= x^{4/9}$

So the answer is C:x to the four ninths power

6 0

2 years ago

Read 2 more answers

Make b the subject of this formula. a=9b

USPshnik [31]

Answer:

a = 9b

divide each side by 9

$\frac{a}{9}$ = b