Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. $$ R = \{(x,y) | 0\le x \le {\color{red}1}, -{\color{red}2} \le y \le {\color{red}4} \} $$

Answer:

51 cubic units

Step-by-step explanation:

[tex]3x+2y+z=12\\\Rightarrow z=12-3x-2y[/tex]

Now we integrate over volume integral over the range [tex]R = \{(x,y) | 0\le x \le {1}, -{2} \le y \le {4} \}[/tex]

[tex]V=\int_0^1\int_{-2}^4 12-3x-2y dydx\\ =\int_{-2}^4 12y-3yx-y^2|_4^{-2} dx\\ =\int_{0}^1 12\times4-3\times4x-16-[12\times-2-3\times-2x-4]dx\\ =\int_{0}^1 60-18xdx\\ =60x-9x^2|_{0}^1\\ =60-9\\ =51\ \text{cubic units}[/tex]

The volume of the solid is 51 cubic units.

Find the inverse of this function
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6, or 15,or 3,or 9



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PLEASE ANSWER I WILL MARK BRAINLEIST


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Group of answer choices

3

Square root of 21

Square root of 29

7

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Scale 1
–1 ounce
Scale 2
–2 ounces
Scale 3
0 ounces
Scale 4
–1 ounce

What is the average error in the scale displays?

Suppose Phil reads a book that contains 16 conspiracy theories. When he researches the theories, he finds that 75% of them are false. How many of the theories are true?

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31,900
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Subject Bar 1 Bar 2
1 20 40
2 18 25
3 24 38
4 14 27
5 5 31
6 26 21
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8 29 38
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1.3
1:4
1.5
1.6
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Intro

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