Answer: 343 in³
Explanation: In this problem, we're asked to find the volume of a cube.
It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.
<em>Volume = length × width × height</em>
In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.
So the formula for the volume of a cube is side × side × side or s³.
So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).
7 x 7 is 49 and 49 x 7 is 343.
So we have 343 in³.
So the volume of the given cube is 343 in³.
It's essential that you use " ^ " to indicate exponentiation if you want to communicate your ideas here accurately.
<span>x2e5x + 3xe5x − e5x = 0 should be written as
x^2e^(5x) + 3xe^(5x) - 1e^(5x) = 0.
e^(5x) can be factored out of all four terms, leaving us with
e^(5x) [x^2 + 3x - 1] = 0. e^(5x) is never zero, so no solution there.
However, we can set x^2 + 3x - 1 equal to zero and solve for x:
-3 plus or minus sqrt(3^2 - 4(1)(-1) )
x = ----------------------------------------------------
2
-3 plus or minus sqrt(13)
= ----------------------------------------
2
So the original equation has two roots.</span>
Answer:
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