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2 years ago

What is three-fourths times a square of a number just write the equation

Mathematics

1 answer:

zavuch27 [327]2 years ago

5 0

Answer:

3/4(x^2)

Step-by-step explanation:

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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

2 years ago

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)?

Vilka [71]

Answer:(2,1) (8,3) (6,-3)

7 0

3 years ago

An employer with 500 employees gives out gives out 120 surveys but receives only 90 surveys completed by the employees. What are

leva [86]

Answer:

Population 120 given the survey, sample 90 who answered the survey.

Step-by-step explanation:

The entire amount of employees who even received the surveys at all was 120. Because the total number was 120, 120 is the population.

Only 90 out of 120 surveys were received, so 90 is the sample because it is part of 120.

Hope this helps :)

6 0

2 years ago

Which is the correct form of the quadratic formula?

d1i1m1o1n [39]

Answer:

The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it's vital that you be sure the equation is in this form.

Step-by-step explanation:

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3 years ago

Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°

lilavasa [31]

Answer:

2sinx.Cosx=cosx

2sin90°.cos90°=cos90°

2×1.0=0

0=0

4 0

2 years ago