We have been given that the volume of cube is 64 cubic mm. We are asked to find the side length of the cube.
We will use volume of cube formula to solve our given problem.
, where
V = Volume of cube,
s = Side length of cube.
Upon substituting the given volume in above formula, we will get:

Now we will take cube-root on both sides of equation.
![\sqrt[3]{64}=\sqrt[3]{s^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B64%7D%3D%5Csqrt%5B3%5D%7Bs%5E3%7D)
![\sqrt[3]{4^3}=\sqrt[3]{s^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%5E3%7D%3D%5Csqrt%5B3%5D%7Bs%5E3%7D)
Using rule
, we will get:

Therefore, the side length of the cube is 4 mm.
The expression that represent the profit is given by P(r) = r⁴ - 3r³ - r² - 4
<h3>What is an
equation? </h3>
An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Profit is the difference between revenue and cost. Given that:
R(r) = 2r⁴ - 3r³ + 2r - 1 and C(r) = r⁴ - r² + 2r + 3
P(r) = R(r) - C(r)
P(r) = (2r⁴ - 3r³ + 2r - 1) - (r⁴ - r² + 2r + 3) = r⁴ - 3r³ - r² - 4
The expression that represent the profit is given by P(r) = r⁴ - 3r³ - r² - 4
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Answer:
42 inches
Step-by-step explanation:
Solving the inequality
we get 
Step-by-step explanation:
We need to solve the inequality 
Solving:

Multiplying 4 with terms inside the bracket.

Adding -36 on both sides:

Adding -6z on both sides


Divide both sides by 6

So, solving the inequality
we get 
Keywords: Solving inequalities
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The range of the function is {-34, -2, -20}
<h3>How to determine the range?</h3>
The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
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