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2 years ago

In 3x + 2/3y - 15 < 0, the point (x,9) is a solution for the inequality shown. what is the possible value for x?

Mathematics

1 answer:

N76 [4]2 years ago

3 0

answer: 2

explanation:

if you plug in all of the numbers available for the equation and using 9 as a substitute for y, you'll see that it will either = 0 or be greater than 0

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Find the mass of the lamina that occupies the region D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye

Alona [7]

Answer:

The mass of the lamina is 1

Step-by-step explanation:

Let $\rho(x,y)$ be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

$m=\int\limits \int\limits_D \rho(x,y) \, dA$ .

From the question, the given density function is $\rho (x,y)=xye^{x+y}$ .

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

$I=\int\limits^1_0\int\limits^1_0xye^{x+y}dydx$ .

Since D is a rectangular region, we can apply Fubini's Theorem to get:

$I=\int\limits^1_0(\int\limits^1_0xye^{x+y}dy)dx$ .

Let the inner integral be: $I_0=\int\limits^1_0xye^{x+y}dy$ , then

$I=\int\limits^1_0(I_0)dx$ .

The inner integral is evaluated using integration by parts.

Let $u=xy$ , the partial derivative of u wrt y is

$\implies du=xdy$

and

$dv=\int\limits e^{x+y} dy$ , integrating wrt y, we obtain

$v=\int\limits e^{x+y}$

Recall the integration by parts formula: $\int\limits udv=uv- \int\limits vdu$

This implies that:

$\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy$

$\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}$

$I_0=\int\limits^1_0 xye^{x+y}dy$

We substitute the limits of integration and evaluate to get:

$I_0=xe^x$

This implies that:

$I=\int\limits^1_0(xe^x)dx$ .

$I=\int\limits^1_0xe^xdx$ .

We again apply integration by parts formula to get:

$\int\limits xe^xdx=e^x(x-1)$ .

$I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(-1)=1$ .

No unit is given, therefore the mass of the lamina is 1.

3 0

3 years ago

How much time is in between these two times?<br><br> Start: 11:34 A.M.<br><br> End: 10:23 P.M.

icang [17]

10 Hours and 49 Minutes.

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3 years ago

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Suppose you only have hundreds, ten's, and ones blocks. What are two different ways you could make the number 1,718

Viktor [21]

17 hundreds 1 ten 8 ones --- 17 hundreds 18 ones

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2 years ago

A Freight train is traveling 30 miles per hour. An automobile starts out from the same place 1 hour later and overtakes the trai

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40 I believe because the space of the auto mobile catching up to the train is 4 hours. 4 times 30 is 120 miles so u need to figure out a number that can reach 120 in three hours. 3 times 40 is 120

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2 years ago

A small square of side 2x is cut from the corner of a rectangle with a width of 10 centimeters and length of 20 centimeters. Wri

love history [14]

Find the area of the rectangle. You can find the area of a rectangle with the following formula:

$A = wl$

w = width, and l = length.

Plug in your width and length:

$20 * 10 = 200$

The area of the rectangle is 200 square centimeters.

The area of a square is also given by width * length. Multiply the sides together:

$2x * 2x = 4x^{2}$

The area of a square is 4x^2.

Because you're cutting away the square from the rectangle, you will subtract the area of the square from the area of the rectangle. The following equation will be your answer:

$200 - 4x^{2} cm^{2}$

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3 years ago