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3 years ago

The volume of a Rectangular Prism

Mathematics

1 answer:

seraphim [82]3 years ago

3 0

Answer:

C) 74 ft²

Step-by-step explanation:

3x3x4=36

1x1x2=2

36+36+2=74

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Find the following integral

ololo11 [35]

There's nothing preventing us from computing one integral at a time:

$\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2$

$\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2$

$\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx$

Expand the integrand completely:

$x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x$

Then

$\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}$

4 0

2 years ago

Ryan deposited $100 into his bank account. Later he withdrew $75 from the account. Write an expression that represents the chang

Novay_Z [31]

hello again!

so this is the answer!

100 - 75 = 25

So he starts off with 100 dollars and takes away 75, leaving him with 25

i hope this helped

6 0

3 years ago

Mike has a net spendable income of $1,400. He decides to set up a budget before looking for an apartment or a car. He sets up hi

Gala2k [10]

<span>B) Mike does not have enough money budgeted for food or medical expenses.</span>

5 0

3 years ago

4+48 divided by 4x3..................................

BartSMP [9]

Answer:

4.41666666667

Step-by-step explanation:

sorry if im wrong, have a nice day!

8 0

3 years ago

Read 2 more answers

Tyson wrote this expression to describe the total amount of points he won in both rounds of a game.

Rainbow [258]

We know that Tyson wrote this expression to describe the total amount of points he won in both rounds of a game.

The expression is f+15. Let variable f represent points.

The correct answer is B. Tyson doesn't know how many points he earned in the first round. He knows he earned a total of 15 points in the whole game.

7 0

3 years ago