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Zina [86]
3 years ago
12

The table shows the outputs, y, for different inputs, x:

Mathematics
1 answer:
Colt1911 [192]3 years ago
5 0
The table is about geomaetry???
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ANOTHER ONE, The graph of a linear function is shown.Which word descibes the slope?
Trava [24]

This is a negative graph because the graph go to the left with a negative slope. Y=-1/2x
5 0
3 years ago
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.

Or

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
Which one is it I need to know quick and I’ll mark you Brainly
QveST [7]

Answer: i think

the corrcect answer is 0.5*10^-1

Step-by-step explanation:

hope this helps

5 0
3 years ago
Write and simplify an algebraic expression to represent the area of the shaded region. The image is below.
Lena [83]

(x+2)^2 - 1\cdot(x-5) = x^2 + 2\cdot2x + 2^2 - (x - 5) = x^2 + 4x + 4 - x + 5 = x^2 + 3x + 9

4 0
3 years ago
What is the solution to –2(8x – 4) < 2x + 5?
Contact [7]

The solution to –2(8x – 4) < 2x + 5 is x > 1/6

<h3>How to solve the inequality?</h3>

The expression is given as:

–2(8x – 4) < 2x + 5

Expand

-16x + 8 < 2x + 5

Evaluate the like terms

-18x < -3

Divide both sides by -18

x > 1/6

Hence, the solution to –2(8x – 4) < 2x + 5 is x > 1/6

Read more about inequalities at:

brainly.com/question/11613554

#SPJ1

4 0
2 years ago
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