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olya-2409 [2.1K]
3 years ago
9

Need Help with some Math

Mathematics
1 answer:
tatyana61 [14]3 years ago
4 0

Answer:

8

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial f(x) being divided by a factor in the form of (x-a), then the remainder of the polynomial is given by f(a).

We have the polynomial:

f(x)=3x^{15}-5x^{12}+7x^6-3x^2+12

And it is being divided by:

(x+1)

We can rewrite our factor as:

(x-(-1))

Therefore:

a=-1

Then our remainder will be:

f(-1)

Evaluate:

\begin{aligned} f(-1)&=3(-1)^{15}-5(-1)^{12}+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}

So, our remainder will be 8.  

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_____

If you feel the need to write an equation, you can let x represent the edge length of the base. Then the cost of the top and bottom will be ...

  top&bottom cost = 0.50·x²

The height of the box is 40/x², so the cost of the four sides will be ...

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  height = 40/x² = 40/4 = 10 . . . . . as above

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