Answer:
No, those are not the correct measurements.
Step-by-step explanation:
Assuming that 9 will equal the hypotenuse we will use the Pythagorean theorem.
a = 5
b = 3
Well
So...that doesn't quite work out.
Let's change our equation to double check.
Once again, that doesn't work out.
So the final answer is, no. Those are not the correct measurements.
Problem 1
Answer: year 4
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The break-even point is when the profit is $0. You neither earn money nor lose it.
Plug in p(x) = 0 and solve for x
p(x) = x^3 - 4x^2 + 5x - 20
x^3 - 4x^2 + 5x - 20 = p(x)
x^3 - 4x^2 + 5x - 20 = 0 ... replace p(x) with 0
(x^3 - 4x^2) + (5x - 20) = 0
x^2(x - 4) + 5(x - 4) = 0
(x^2+5)(x - 4) = 0
x^2+5 = 0 or x-4 = 0
The equation x^2+5 = 0 has no real solutions; however x-4 = 0 solves to x = 4.
So plugging x = 4 into p(x) will lead to p(x) = 0. Meaning that the company breaks even at year 4.
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Problem 2
Answer: choice B) between 2.5 and 3.0; between 4.0 and 4.5
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Look at the f(x) column. Specifically we are looking for the times when the numbers change from positive to negative, or vice versa. Somewhere in between this change, y will have to equal 0 at some point (at least once). Note how in row 2 and row 3, we have f(x) = 1.1 change to f(x) = -0.8; so the change is from positive to negative.
This means f(x) = 0 for some x value between x = 2.5 and x = 3.5. Also, the same kind of logic applies for the last two rows of the table as well pointing to another root between x = 4.0 and x = 4.5 (check out the attached images)
