The correct structure of the question is as follows:
The function f(x) = x^3 describes a cube's volume, f(x) in cubic inches, whose length, width, and height each measures x inches. If x is changing, find the (instantaneous) rate of change of the volume with respect to x at the moment when x = 3 inches.
Answer:
Step-by-step explanation:
Given that:
f(x) = x^3
Then;
V = x^3
The rate whereby V is changing with respect to time is can be determined by taking the differentiation of V
dV/dx = 3x^2
Now, at the moment when x = 3;
dV/dx = 3(3)^2
dV/dx = 3(9)
dV/dx = 27 cubic inch per inch
Suppose it is at the moment when x = 9
Then;
dV/dx = 3(9)^2
dV/dx = 3(81)
dV/dx = 243 cubic inch per inch
Answer:
10 times
Step-by-step explanation:
there are a total of 200 coins
each time he makes a selection the probability of selecting a dime is 40/200 or 1/5
if he makes 50 selections, the probability is 1/5(50) which is 10 times
Percent change is 100%
Step-by-step explanation:
- Step 1: Find the perimeter of the first garden when length = 6 ft and width = 4 ft
Perimeter = 2 (length + width)
= 2 (6 + 4) = 2 × 10 = 20 ft
- Step 2: Find the perimeter of the second garden when length = 12 ft and width = 8 ft (∵ dimensions are doubled)
Perimeter = 2 (12 + 8) = 2 × 20 = 40 ft
- Step 3: Find the percent change in perimeter
Percent Change = Final value - initial value/Initial Value × 100
= (40 - 20/20) × 100
= 1 × 100 = 100%
You are given
.. 11 dollars = 10 euros
Divide this equation by 11 to find the euro value of 1 dollar
.. 1 dollar = 10/11 euros
About 0.91 euros
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The decimal equivalent of 10/11 is the repeating decimal fraction 0.909090...
9514 1404 393
Answer:
c) 16,500 m³
d) 277,088 mm³
a) V = LWH
b) V = πr²h
Step-by-step explanation:
The relevant volume formulas are ...
- rectangular pyramid: V = 1/3LWH
- cylinder: V = πr²h
- rectangular prism: V = LWH
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13c. The pyramid formula above tells us the volume is ...
V = 1/3(60 m)(15 m)(55 m) = 16,500 m³
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13d. The cylinder formula above tells us the volume is ...
V = π(35 mm)²(72 mm) ≈ 277,088 mm³ ≈ 277 mL
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14a. The shape appears to be a rectangular prism, so its volume is given by the formula ...
V = LWH . . . . . where L, W, H represent the length, width, and height
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14b. The volume of a cylinder is given by the formula ...
V = πr²h . . . . . where r, h represent the radius and height (length)
