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3 years ago

Simplify to create an equivalent expression 8(10-6q)+3(-7q-2)

Mathematics

1 answer:

Temka [501]3 years ago

4 0

Answer:

74-69q

Step-by-step explanation:

$8(10-6q)+3(-7q-2)\\\\80-48q-21q-6\\\\80-69q-6\\\\80-6-69q\\\\\boxed{74-69q}$

This can also be -69q + 74.

Hope this helps.

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rectangle A has a length of 24 meters and a width of 20 meters. rectangle B has the same area as rectangle A. the width of recta

blagie [28]

To solve this, first we'll find the area of the rectangle A,

Area=length × width
?=24m×20m
480m=24m×20m
480m squared=area of the rectangle A

now we'll find the width of rectangle B,
"the width of rectangle B is 12 meters less than the width of rectangle A",
20m-12m= 8m
8m=width of rectangle B

finally we'll find the length of rectangle B,
area of the rectangle B= 480msquared
width= 8m
length=? (to find this divide the area by the width)
480÷8=60m
length of the rectangle B=60m

7 0

3 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:

$I=\int\limits^1_0(xe^x)dx$ .

$I=\int\limits^1_0xe^xdx$ .

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

I WILL GIVE BRAINLIEST TO THE FIRST PERSON!A spinner has 8 equal-sized sections. The probability that the spinner will stop abov

FromTheMoon [43]

The chances of it spinning on blue is likely

3 0

3 years ago

Read 2 more answers

James had $15,345.21 withheld from his income one year. He

puteri [66]

Answer:

$2,373.23

Step-by-step explanation:

-Tax refund is determined by comparing your total income tax to the amount that was withheld for federal income tax.

-Assuming that the amount withheld for federal income tax was greater than your income tax for the year, you will receive a refund for the difference.

#Refund =Withheld -Actual Tax liability=$15345.21-$12971.98=$2,373.23

Hence James' tax refund will be $2,373.23

5 0

3 years ago

Marissa bought 2 and a half gallons of orange juice to make punch how many quarts of orange juice did. Marissa buy

Nookie1986 [14]

The answer is as follows:
There are 2 pints in a quart.
There are 2 quarts in a half gallon.
There are 2 half gallons in a gallon.
Therefore, we can conclude that there are 10 quarts of orange juice.

7 0

3 years ago