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2 years ago

6

Find the area of the trapezoids

1 answer:

Vesna [10]2 years ago

3 0

1. Area=30
4.Area=3.68
2.Area=75

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Without overlapping, how many college basketball courts 94ft x 50ft would fit into a football field 360ft x 160ft?

Volgvan

Area of basketball court: 94 x 50 = 4700 square feet

area of football field: 360 x 160 = 57600 square feet

57600 / 4700 = 12.26

so 12 basketball courts

7 0

2 years ago

What is 1/10 of an income of $97.50?

Rashid [163]

1/10 of 97.50..." of " means multiply

1/10 * 97.50 = 97.50/10 = 9.75 <==

5 0

3 years ago

Read 2 more answers

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 function in vertex form is equivalent to f(x) = x2 + 8 – 16x?

irga5000 [103]

<span>The answer would be (f(x) = (x – 8)2 – 56)</span>

5 0

3 years ago

Read 2 more answers

The ratio of the rise to the run of the given triangle is __

Lemur [1.5K]

Answer:

1) 5/2 or 2.5

2) 5/2 or 2.5

Step-by-step explanation:

1) 5/2 = 2.5

2) 10/4 = 5/2 = 2.5

Because the hypotenuse of both are the segments of the same line and straight lines have the same gradient for all segments

4 0

2 years ago