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galina1969 [7]
3 years ago
10

What is the diameter of a sphere with a volume of

Mathematics
1 answer:
Rudiy273 years ago
8 0

Answer:

5.3 cm

Step-by-step explanation:

Given;

Volume of sphere V = 79cm^3

The volume of a sphere can be expressed as a function of its radius as;

V = (4/3)πr^3 .....1

Where r = radius

And we know that;

Radius = Diameter/2

r = d/2

Substituting into equation 1

V = (4/3)π(d/2)^3

V = (4/3)πd^3 × 1/8

V = (1/6)πd^3

Since the volume is given as 79 cm^3

79 = (1/6)πd^3

d^3 = 79×6/π

d = (79×6/π)^(1/3)

d = 5.323649930553 cm

Diameter d = 5.3 cm

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Kathy used 15 ounces of chocolate in her cookies. Cindy used 15% more chocolate in her cookies. How many ounces did Cindy use? (
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3 years ago
F(x)=<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2-4%7D" id="TexFormula1" title="\sqrt{x^2-4}" alt="\sqrt{x^2-4}" align="abs
hammer [34]

Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :

√(<em>x</em> ² - 4) = 1

<em>x</em> ² - 4 = 1

<em>x</em> ² = 5

<em>x</em> = ±√5

We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.

This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If <em>f(a)</em> = <em>b</em>, then  (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.

We have

<em>f(x)</em> = √(<em>x</em> ² - 4)   →   <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)

So if <em>a</em> = -√5 and <em>b</em> = 1, we get

(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)

(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.

3 0
3 years ago
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