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galben [10]
3 years ago
8

Samantha wants to find the height of a pine tree in her yard. She measures the height of the mailbox st 3ft and its shadow at 4.

8ft. Then she measures the shadow of the tree at 56ft. How tall is the tree?
Mathematics
1 answer:
Simora [160]3 years ago
7 0
The tree is about 35.01 feet tall.
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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.

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
Write 11.183 million in scientific notation.
babymother [125]
The answer is 1.1 x10^7
5 0
3 years ago
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Answer:

Thanks your amazing i hope you have a great day.

Step-by-step explanation:

3 0
3 years ago
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Find the area of the circle. Round to the nearest tenth. Use 3.14 or for . radius = 8 in.
Musya8 [376]

Answer:

201

Step-by-step explanation:

Pi x radius x Radius = area

3.14 x 8 x 8 = area

3.14 x 64 = 200.96

when you round 200.96 you get 201!  

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3 years ago
PLEASE ITS DUE TODAY. Which expression has a conffcient of 7?
gregori [183]

Answer:

the first one

Step-by-step explanation:

because x has an coefficient

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