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GREYUIT [131]
3 years ago
8

Solve the equation for t A=s(t+r)x

Mathematics
1 answer:
tester [92]3 years ago
6 0

Answer:

t = (A/sx) - r

Step-by-step explanation:

Solve for t like this:

A = s(t+r)x\\A = sx(t+r)\\\\\frac{A}{sx} = t+r\\\frac{A}{sx} - r = t\\t= \frac{A}{sx} - r

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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
BRAINLIEST + POINTS
Amanda [17]

The company matches up to 8%.

Multiply her salary by 8%:

66410 x 0.08 = $5,312.80


Her company will match 50% ( which is half the amount)

Divide the 8% total by 2:

5312.80 / 2 = 2656.40


The answer is B.

5 0
3 years ago
At the end of school, Josh's teacher handed out 27 coupons for bowling during the summer to each student. The third week of
Zielflug [23.3K]

The answer would be 4 Coupons

5 0
3 years ago
Harry worked 7 hours last week. This is 1__3as many hours as Aidan worked. How many hours did Aidan work?
vitfil [10]

Answer:

21

Step-by-step explanation:

1/3= 0.33

7/0.33

7 0
2 years ago
Shane rode his bike for 2 hours and traveled 12 miles. At this rate how long would it take him to travel 22 miles?
ella [17]
It would take him about 3.67 hrs.
3 0
3 years ago
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