For the exterior angles(s) given, name the remote interior angles

The ratio of students packing lunch to those buying lunch is 2 : 9. The number of students buying lunch is how many times the nu

DedPeter [7]

Answer:

4.5 times

Step-by-step explanation:

Packing to Buying is 2:9

Therefore, Buying to Packing will be 9:2.

9/2 = 4.5

4 0

2 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

13. A bakery is having a buy 4, get 1 free sale on cakes. This sale is eguivalent to what percentage off the regular price of al

exis [7]

Answer: 20

Step-by-step explanation:

3 0

2 years ago

Plzzzzzzzzzzzzz help ;-;

Goshia [24]

Answer:

option A

associative property of addition

5 0

3 years ago

Read 2 more answers

8. Misty created the number pattern below. 32, 28, 24, 20, ... If n represents a number in this pattern, which rule could be use

geniusboy [140]

Answer:

An = 32 - (4*(n-1))

Step-by-step explanation:

the starting term for this pattern is 32 (which you will need to include in the "rule")

you also know that the next term is the previous term - 4

so!

we can write this pattern as

An = 32 - (4*(n-1))

An = any number of term in the pattern

- ex). A2 = 28, A3 = 24, etc

n = the nth term

- the 3rd term = 24, the fourth term = 20, etc

4 0

2 years ago

For the exterior angles(s) given, name the remote interior angles​

For the exterior angles(s) given, name the remote interior angles