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F ind the volume under the paraboloid z=9(x2+y2) above the triangle on xy-plane enclosed by the lines x=0, y=2, y=x

olga nikolaevna [1]

Answer:

The answer is 48 units³

Step-by-step explanation:

If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

$V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {z} \, dx dy\\V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {9(x^{2}+y^{2})} \, dx dy$

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

$V=9\int\limits^2_0 {4y^{3}/3} \, dy$

After performing the elementary y integral we obtain the desired volume as below,

$V= 48 units^{3}$

4 0

3 years ago

Find the measure of the acute angles pls help

tangare [24]

Answer:

60 degrees

and

52 degrees

6 0

3 years ago

In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a sta

Rainbow [258]

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

4 0

2 years ago

Can someone help me please!!

ratelena [41]

The coordinates of E are (5.75, 0).

<h3>What is midpoint?</h3>

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

Given that, C is the midpoint of AB, D is the midpoint of CB and E is the midpoint of DB.

Formula for coordinates of midpoint,

(x, y) = [(x1+x2)/2, (y1+y2)/2]

Coordinates of C;

(x, y) = (-10+8)/2, (14-2)/2

(x, y) = (-1, 6)

Coordinates of D;

(x, y) = (-1+8)/2, (6-2)/2

(x, y) = (3.5, 2)

Coordinates of E;

(x, y) = (3.5+8)/2, (2-2)/2

(x, y) = (5.75, 0)

Hence, The coordinates of E are (5.75, 0).

For more references on midpoints, click;

brainly.com/question/28224145

#SPJ1

8 0

11 months ago

Find the sum of the first 5 terms of the infinite series: 8 + 18 + 28 +

Anna007 [38]

Answer:

8 + 18+ 28+ 38+ 48= 140

Step-by-step explanation:

3 0

3 years ago

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