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.

Please help this one will give you extra points

Prime factorization of 60?

6, or 15,or 3,or 9



please help!!

Find the value of x.

-21x^2+35x=0
Solve for x

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?

PLEASE ANSWER I WILL MARK BRAINLEIST


The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units, of the other leg of the triangle?

Group of answer choices

3

Square root of 21

Square root of 29

7

A primatologist believes that rhesus monkeys possess curiosity. She reasons that, if this is true, then they should prefer novel stimulation to repetitive stimulation. An experiment is conducted in which 12 rhesus monkeys are randomly selected from the university colony and taught to press two bars. Pressing bar 1 always produces the same sound, whereas bar 2 produces a novel sound each time it is pressed. After learning to press the bars, the monkeys are tested for 15 minutes, during which they have free access to both bars. The number of presses on each bar during the 15 minutes is recorded. The resulting data are as follows:What is the alternative hypothesis? In this case, assume a nondirectional hypothesis is appropriate because there is insufficient empirical basis to warrant a directional hypothesis. What is the null hypothesis? Using ? = 0.052 tail, what is your conclusion? What error might you be making by your conclusion in part c?
Subject Bar 1 Bar 2
1 20 40
2 18 25
3 24 38
4 14 27
5 5 31
6 26 21
7 15 32
8 29 38
9 15 25
10 9 18

Find the product. Tell which strategy you used.
1. 5 X 7 X 20
2.

Camille has no more than $20.00 to spend each week for lunch and bus
fare. Lunch costs $3.00 each day, and bus fare is $0.75 each ride. Write an inequality for
this situation. Can Camille buy lunch 5 times and ride the bus 8 times in one week?

can some one help me please

an expression equivalent to –8(2s–5)–4

456x5 is what I can’t figure this out please help!!

What is the solution for this inequality?
8x<-32

Terry is an up and coming florist who specializes in weddings. He uses 5 roses, 3 daises, and 4 bundles of green filler to make one bouquet. If r is the cost of a rose and d is the cost of a daisy, and f is the cost of a bundle of green filler, which expression represents the cost for making 75 bouquets

Look at the incomplete multiplication problem below.

638 times 56 = 3828. 3828 + question mark = blank

What value is missing?
31,500
31,900
35,280
35,728

translation is the point (2, −6). At what coordinates is the image of point (−3, −2) located under the same translation?

it took jaivin 18 minutes to jog 4 laps . how many minutes did it to jog each lap at this rate?

I bought 5 1/2 yards of fabric. I used 2/3 of the fabric to make curtains. How much fabric did i use?

3 plus 2 =
wzsxdcfgvbhjnkrdfvgbh

Find the inverse of this function
g(x)=2(x-3)^5

GEOMETRY Write and solve an equation to find the value of x so that it figures have the same area.

A quality control manager is inspecting four digital scales to see if they accurately reflect a weight of 0 ounces. The table shows the weight displayed on four empty scales.

Empty Scale Weight Displays
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?

Tell whether -2 is a solution of the inequality n-5<8

what is the decimal value of 3/5​

In a lab a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio
of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?
1.3
1:4
1.5
1.6
Done
Intro

Si tienes 5 manzanas para comer durante la semana y te comes el 20% el primer día cuántas manzanas quedan para el resto de la seman?

At the produce store you can buy 4 bags of bananas for $29.88. How much would it cost if u were to buy 6 bags?

Jack has let out 40 m of kite string when he observes that his kite is directly above Jill. If Jack is 25 m from Jill, how high is the kite?​

HELP



The price of a necklace was increased by 10% to £121.
What was the price before the increase?

When she first purchased it, Soledad's computer had 500 GB of hard drive space. After six months, there
were only 407 GB available. Enter and solve an equation to find the amount of hard drive space that
Soledad used in the first six months. Uses as your variable.
- 500
The equation is
She has used
GB of memory