Expand 5⁴ WHAT IS THE ANSWER

Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

3 years ago

Solve the equation: -2(n+3)=13

Zolol [24]

Answer:

n is -9.5 ....hyuibgtyujhff

7 0

3 years ago

The minimum weekly commission earned to be a STAR sales person is $9000. If Sandra receives a 12% commission on the sale of all

katovenus [111]

Answer:

$numbers\ of\ cars \geq \frac{75000}{price\ of\ the\ car}$

Step-by-step explanation:

Hello, I can help you with this

Step 1

define

The minimum weekly commission earned to be a STAR sales person is $9000, let's name this value as M

if Sandra receives a 12% commisions of the sale of all cars, then that 12% must be equal or higher than 9000 in order to become a STAR sales person

Step 2

using a rule of three find the 100%

if

12% ⇔ $9000

then

100% ⇔x

the ratio is

$\frac{12}{9000}=\frac{100}{x}\\$

Now, solve for x

$\frac{12}{9000}=\frac{100}{x}\\\\\frac{12*x}{9000}=\frac{100}\\\\{12x}=9000*100\\\\12x=900000\\x=\frac{900000}{12}\\ x=75000\\$

so, Sandra must sell a minimun of $75000

Now, to give a response, we need to asume a only price for every car(p).

now, in matemathical terms.

the minimun number of cars she must to sell is

minum number of cars sandra has to sell to become a STAR sales person

is $\frac{75000}{price\ of\ the\ car} \\$

$\frac{75000}{price\ of\ the\ car} \\$

now, price of the car* number of the car = 75000

where

$numbers\ of\ cars \geq \frac{75000}{price\ of\ the\ car}$

Have a nice day

6 0

3 years ago

I don’t understand please help!

nikklg [1K]

Answer:

x > 10/3

x will always be greater that 10/3 never the same nor less.

Step-by-step explanation:

3/5x + 1/3 < 4/5x - 1/3

3/5x - 4/5x + 1/3 < -1/3

-1/5x + 1/3 < -1/3

-1/5x < -1/3 - 1/3

-1/5x < -2/3

-1/5x/-1 < -2/3/-1 (Since it is both divided by a negative the sign switches, the sign also switches with multiplication. *Note: it only switches if it is negative!*)

1/5x > 2/3

5 • 1/5x > 2/3 • 5

x > 2/3 • 5/1

x > 10/3

6 0

3 years ago

Find the inverse of the function. f(x) = -3x + 7

LUCKY_DIMON [66]

F(x) = -3x + 7
y = -3x + 7
x = -3y + 7
-3y + 7 = x
-3y = x - 7
y = -1/3x + 7/3
f^-1(x) = -1/3x + 7/3

8 0

2 years ago

Expand 5⁴ WHAT IS THE ANSWER​

Expand 5⁴ WHAT IS THE ANSWER