The formula for the volume of a quarter-sphere is simply one-fourth of the volume of the sphere. So the volume of a quarter-sphere:
V = (1/4) (4/3) (π r³)
or
V = (1/3) (π r³)
Since we are given with the radius of 70 feet, the volume is
V = (1/3) (π) (70³)
V = 359,189 cubic feet
<u><em>Answer:</em></u>
Part a .............> x = 11
Part b .............> k = 57.2
Part c .............> y = 9.2
<u><em>Explanation:</em></u>
The three problems deal with inverse variation between two variables
An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)
<u>Mathematically, an inverse variation relation is represented as follows:</u>

where x and y are the two variables and k is the constant of variation
<u><em>Now, let's check the givens:</em></u>
<u>Part a:</u>
We are given that y = 3 and k = 33
<u>Substitute in the original relation and solve for x as follows:</u>

<u>Part b:</u>
We are given that y = 11 and x = 5.2
<u>Substitute in the original relation and solve for k as follows:</u>

<u>Part c:</u>
We are given that x=7.8 and k=72
<u>Substitute in the original relation and solve for y as follows:</u>
to the nearest tenth
Hope this helps :)
Answer:
(f · g)(x) = 4x³ + x² - 20x - 5
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
- Combining Like Terms
- Expand by FOIL (First Outside Inside Last)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 4x + 1
g(x) = x² - 5
(f · g)(x) is f(x)g(x)
<u>Step 2: Find (f · g)(x)</u>
- Substitute: (f · g)(x) = (4x + 1)(x² - 5)
- Expand [FOIL]: (f · g)(x) = 4x³ - 20x + x² - 5
- Combine like terms: (f · g)(x) = 4x³ + x² - 20x - 5
Answer:
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Step-by-step explanation: