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3 years ago

5

Right triangle ABC is shown below. Write an equation that can be used to determine the angle measure, in degrees, of angle DBC.

Then determine the measure of n

1 answer:

Dmitry [639]3 years ago

5 0

Answer:

Step-by-step explanation:

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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

Which polynomial function of lowest degree with rational real coefficients

vfiekz [6]

Answer:

a polynomial with degree coefficient real number can be a negative number

i guessed i am not sure

7 0

2 years ago

Draw a line representing the "run" and a line representing the "rise" of the line. State the slope of the line in simplest form.

Igoryamba

Answer:

The answer is " $\bold{\frac{9}{13}}$ "

Step-by-step explanation:

In this question, the image file is missing, which is defined in the attached file. please find it.

$\to raise= y_2-y_1$

$=-1-(-10)\\\\=-1+10\\\\=9$

$\to run= x_2-x_1$

$=9-(-4)\\\\=9+4\\\\=13$

$\to \text{formula for slope} =\frac{rise}{run} =\frac{9}{13}$

7 0

3 years ago

Kareen ran 4.16 x 10^3 miles long

Savatey [412]

Which means she ran 4160 miles long
if this isn't the answer you wanted, please be more precise

6 0

3 years ago

Read 2 more answers

$32.00 for 10 cookies<br> Unit rate.

Nadya [2.5K]

Answer:

$32/10 = $3.2/cookie

Step-by-step explanation:

5 0

2 years ago