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trasher [3.6K]
3 years ago
9

One line passes through the points (-4, 2) and (0, 3); another line passes through the points

Mathematics
1 answer:
Luba_88 [7]3 years ago
5 0

Answer:

how are you working on a saturday night?

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
Evaluate 6(5-(6-5)-3​
IrinaK [193]

Answer:

Step-by-step explanation:

Evaluate 6(5-(6-5)-3​) =  6(5-1-3​)   {first solve innermost bracket}

                               = 6* (5-4) = 6*1 =6

4 0
3 years ago
Read 2 more answers
A=6e^2, which formula can be used to determine e, given A
padilas [110]

Answer:

A=6e2==6e2

e==6

e2A==6e2

Step-by-step explanation:

8 0
2 years ago
A given line has a slope of - ⅚.  (ie, m = -⅚)
Nastasia [14]

Answer:

Step-by-step explanation:

The slope of the line parallel to that line is -5/6 because parallel lines have the same slope.

8 0
3 years ago
A coupon subtracts $5.16 from the price (p) of a shirt. You pay $15.48 for the shirt after using the coupon. Write and solve an
lbvjy [14]

The equation would look like: p - 5.16 = 15.48

because the coupon subtracts 5.16 from p and the price you pay is 15.48

Solve the equation by adding 5.16 to both sides

p = 20.64

The original price of the shirt is $20.64

7 0
3 years ago
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