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3 years ago

24 and 1 fifth minus negative 14 and one third

Mathematics

2 answers:

Anastasy [175]3 years ago

8 0

the answer is 38.53 becauase it is...

Airida [17]3 years ago

5 0

Answer:

Exact Form:

4114/15

Decimal Form:

274.26(repeats)

Mixed Number Form:

274 4/15

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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:

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

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

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

It take 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same Pace, how many days will

ludmilkaskok [199]

Answer:

The workers will need 10 days to finish the job.

Step-by-step explanation:

To solve this question we can use a compound rule of three. We have:

10 road workers -> 5 days -> 2h/day

2 road workers -> x days -> 5h/days

The first thing we should do is analyze how the proportions between the variables work, if they're inversely or directly proportional. If we raise the number of workers we expect that the amount of days needed to finish the job lowers and if we raise the number of hours worked in a day we expect that the workers would need less days to finish the job. So we need to invert the fractions that are inversely proportional to the amount of days worked, then we have:

2 -> 5 -> 5

10-> x -> 2

x = (5*2*10)/(2*5) = 100/10 = 10 days

8 0

2 years ago

Which of the following is the least? A. 0.105 B. 0.501 C. 0.015 D. 0.15

Naddika [18.5K]

C is the least that is beause it is .015 which is smaller than 0.15

8 0

2 years ago

Can someone please explain to me how to solve this problem?

Svetradugi [14.3K]

Bro that is so easy!!

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3 years ago

Show the solution to each system of linear inequalities by graphing.

Lyrx [107]

142628281991919182726(35262627282

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2 years ago