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Otrada [13]
2 years ago
15

You buy a package of cheese for $2.50, a loaf of bread for $2.15, a cucumber for $.65, and some tomatoes for $3.50. Find the tot

al cost of the groceries
Mathematics
1 answer:
Savatey [412]2 years ago
4 0
Answer: $8.80
2.50+2.15+0.65+3.50= 8.80
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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
Help please!!!! it makes so sense
Tamiku [17]

Answer:

(- \frac{1}{5} , 0 )

Step-by-step explanation:

to find where the line crosses the x- axis, let y = 0 in the equation and solve for x

5x - 2(0) + 1 = 0

5x - 0 + 1 = 0

5x + 1 = 0 ( subtract 1 from both sides )

5x = - 1 ( divide both sides by 5 )

x = - \frac{1}{5}

the line crosses the x- axis at (- \frac{1}{5}, 0 ) or ( - 0.2, 0 )

4 0
1 year ago
Read 2 more answers
Im a 5th grader please help me. we a doing division 25÷3
lianna [129]

The answer is 8.333333 it goes on and 3 is repeating.


3 0
3 years ago
What’s the answer for the 1st problem
katrin [286]
The answer is x is less than 8
4 0
3 years ago
Read 2 more answers
25-3x-2-4x+5 has how many coefficients and how many expressions
adoni [48]

Answer:

This expression has 2 coefficients, (-3 and -4), because any number with a variable is a coefficient. That means 25, -2, and 5 are all constants, because they don't have variables.

Variables are the x's in this case.

I hope this answers your question :) Also if you like, can you mark me brainliest, please? It would really mean a lot to me :)

3 0
2 years ago
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