Forgot how to do it, help please.

A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol

k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

<u>Given the following data:</u>

Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

$W = 3 + L$ ......equation 1

$H = 4 + L$ ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

$Volume = length * width * height$ .....equation 3.

Substituting the values into equation, we have;

$224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}$

Rearranging the polynomial, we have;

$L^{3} + 7L^{2} + 12L - 224 = 0$

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

$(x - 3) = 0\\x = 3$

$P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0$

We would try with 4;

$P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0$

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

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3 years ago

Chuck runs laps around a track. The table shows how long it takes him to run different numbers of laps. How long would it take C

Vika [28.1K]

It would take him 25 minutes to run 5 laps

8 0

3 years ago

Read 2 more answers

2. Describe how to use the conjugate to divide 2 − i by 3 + 2i, and then find the quotient.

DaniilM [7]

Answer:

$\frac{4}{13}-\frac{7}{13}i$

Step-by-step explanation:

$\frac{2-i}{3+2i}$

Multiply and divide by the conjugate.

The conjugate is the denominator with the sign of the complex number the opposite of the denominator.

$\frac{2-i}{3+2i}\frac{3-2i}{3-2i}\\ =\frac{2\times (3-2i)-i\times (3-2i)}{3^2-(2i)^2}\\ =\frac{6-4i-3i+2i^2}{9+4}\\ =\frac{4-7i}{13}\\ =\frac{4}{13}-\frac{7}{13}i$

Quotient = $\frac{4}{13}-\frac{7}{13}i$

7 0

3 years ago

A researcher is interested in estimating the mean weight of a semi tracker truck to determine the potential load capacity. She t

uranmaximum [27]

Answer:

The degrees of freedom associated with this problem are 16.

Step-by-step explanation:

The degrees of freedom associated with a problem, independent of the confidence level, is the sample size subtracted by 1.

In this problem, we have that:

She takes a random sample of 17 trucks, so the sample size is 17.

This means that the degrees of freedom associated with this problem are 16.

4 0

3 years ago

What is the sum of n natural numbers: 1+2+...+n?

r-ruslan [8.4K]

If

$S=1+2+\cdots+(n-1)+n$

then we also have

$S=n+(n-1)+\cdots+2+1$

Pairing up the terms, we can find that

$2S=(1+n)+(2+n-1)+\cdots+(n-1+2)+(n+1)$

$2S=(n+1)+(n+1)+\cdots+(n+1)+(n+1)$

$S$ consists of $n$ terms, so there are $n$ copies of $n+1$ in the sum $2S$ . Then we find an immediate closed form for the sum:

$2S=n(n+1)\implies S=\dfrac{n(n+1)}2$

5 0

3 years ago