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3 years ago

Find the radius and the center (x+3)2 + (y+8)2 = 81

Mathematics

1 answer:

wlad13 [49]3 years ago

4 0

Answer:

This means the center is (-3,-8) and the radius is 9

Step-by-step explanation:

(x+3)^2 + (y+8)^2 = 81

The equation of a circle can be written as

(x-h)^2 + (y-k)^2 = r^2 where the center is (h,k) and the radius is r

We can rewrite the above equation as

(x- -3)^2 + (y - -8)^2 = 9^2

This means the center is (-3,-8) and the radius is 9

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16/44 as its simplest form

lozanna [386]

If you mean by simplifing it then it must be 4/11

6 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

On a coordinate plane, an exponential function has a horizontal asymptote of y = 0. The function curves up into the first quadra

aleksandr82 [10.1K]

Answer:

The graph will show an initial value that is lower on the y-axis

Step-by-step explanation:

The exponential function has the next general form:

$y = ab^x$

where a is the initial amount and b is the base.

If the a value in the function is decreased, but remains greater than 0, the y-intercept of the curve decrease.

8 0

3 years ago

Read 2 more answers

How do you turn 9 and 3 5s as a decimal???

Zarrin [17]

Answer:

9.6

Step-by-step explanation:

As 9 and 3/5s, the 9 is whole so you do not change it. To make 3/5th into a decimal you increase the denominator into x/10. To make 5 into 10 you multiply 5x2=10. And since you changed the bottom you have to change the top and multiply it by 2. 3x2=6. So the 9 stays the same and since the first place beind the decimal is tenths, and youre fraction is now 6/10 you put it as 9.6.

Hope it helps!

8 0

3 years ago

What is an equation for the line that passes through the coordinates (2, 0) and (0, 3)?

alexdok [17]

Answer:
Not sure if this is correct but I hope this helps :)

8 0

3 years ago