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zlopas [31]
2 years ago
6

Find the area of the trapezoids

Mathematics
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
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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
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