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3 years ago

Can I please get the congruence and the reason plz

Mathematics

1 answer:

lara31 [8.8K]3 years ago

8 0

can see the answer its blurry

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Evaluate the given integral by changing to polar coordinates.∫∫ x2y dA, where D is the top half of the disk with center the orig

amid [387]

Answer:

Required value is $\frac{1250}{3}$ .

Step-by-step explanation:

We have to find the value of,

$\int\int_{D} x^2y dA\hfill (1)$

where, $D=\{(5,\theta) : 0\leq r\leq 5, 0\leq \theta \leq \pi \}$

To convert it in polar form let $x=r\cos\theta, y=r\sin\theta$ and substitute in (1) we get,

$\int\int_{D} x^2y dA$

$=\int_{0}^{\pi}\int_{0}^{5}(r\cos\theta)^2(r\sin\theta)rdrd\theta$

Assuming,

$u=\cos \theta$ then,

$du=-\sin\theta d\theta\implies-du=\sin\thetad\theta[tex]For [tex]\theta=0, u=1$ and $\theta=\pi$ gives u=-1. Hence,

$\int\int_{D} x^2y dA$

$=\int_{0}^{\pi}\int_{0}^{5}(r\cos\theta)^2(r\sin\theta)rdrd\theta$

$=\int_{1}^{-1}u^2(-du)\int_{0}^{5}r^4dr$

$=\int_{-1}^{1}u^2du\int_{0}^{5}r^4dr$

$=\Big[\frac{u^3}{3}\Big]_{-1}^{1}\times\Big[\frac{r^5}{5}\Big]_{0}^{5}$

$=\frac{2\times 5^4}{3}=\frac{1250}{3}$

5 0

3 years ago

If a car travels at a speed of 25 mi/h for t hours, then travels 45 mi/h for m hours. What does the expression 25t + 45m represe

dlinn [17]

The expression of 25t +45m shows the total number of miles driven at both speeds. In order to solve this equation you would need to know the total number of hours driven in order to multiply that by the appropriate speed in terms of miles per hour.

6 0

4 years ago

PLEASE ANSWER I NEED TONIGHT TO FINISH:

Rom4ik [11]

Answer:

5/9 divided by 10

Step by step explanation:

The water is being divided evenly into the cups, so it's the amount of water divided by the amount of cups

7 0

2 years ago

The list below shows the number of books read by students in Abram’s class over the summer. What is the mode of the data3,6,12,4

Soloha48 [4]

We are given a set of data depicting the number of books read by students.

We are required to find the mode of the data.

In order to find the mode, we simply need to count each unique number and know how many times each number occurs.

The unique number with the largest frequency of occurence is the mode of the data.

The data given is:

$3,6,12,4,3,5,4,8,4,10,4,8,7,5,7$

We will represent each count for the unique numbers with a frequency table showing each unique number and the number of times it occurs.

This table is done below:

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2 years ago

salma is 1.45 meters tall. at 3p.m she measures the length of a tree's shadow to 29.35 meters. she stands 24.3 meters away from

Sophie [7]

Answer:

23.67

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers