Consider this scatter plot.<br><br><br> A. Line A<br> B. Line B<br> C. Line C<br> D. None

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

4 years ago

PLSS HELP geometry it's about relations within triangles. need help solving for variables

ValentinkaMS [17]

Using the definition of congruent triangles, the missing measurements are:

23. m = 7; LO = 14; NO = 14

24. x = 15; m∠QTS = 90°

25. p = 3; IJ = 15; KJ = 15

26. r = 3; UW = 48

27. y = 7; m∠DEF = 50°

28. m = 5; p = 10

<h3>What are Congruent Triangles?</h3>

If two triangles are congruent, then all its corresponding sides and angles are equal.

23. The two triangles are congruent by SAS, therefore:

LO = NO

m + 7 = 2m

7 = 2m - m

7 = m

m = 7

LO = NO = m + 7 = 7 + 7 = 14

LO = 14

NO = 14

24. But triangles are congruent by SSS, therefore:

3x = 5x - 30

3x - 5x = -30

-2x = -30

x = 15

m∠QTS = 2(3x) = 6x = 6(15)

m∠QTS = 90°

25. Both triangles are congruent by ASA, therefore:

4p + 3 = 3p + 6

4p - 3p = -3 + 6

p = 3

IJ = KJ = 4p + 3 = 4(3) + 3 = 15

IJ = 15

KJ = 15

26. The two triangles are congruent by SAS, therefore:

5r + 9 = 8r

9 = 8r - 5r

9 = 3r

9/3 = r

r = 3

UW = 2(8r) = 16r = 16(3)

UW = 48

27. Both triangles are congruent by SSS, therefore:

3y + 4 = 5y - 10

3y - 5y = -4 - 10

-2y = -14

y = 7

m∠DEF = 2(3y + 4) = 6y + 8 = 6(7) + 8

m∠DEF = 50°

28. Both triangles are congruent by SSS, therefore:

2m = 10

m = 10/2

m = 5

2p - 5 = p + 5

2p - p = 5 + 5

p = 10

Learn more about congruent triangles on:

brainly.com/question/1675117

#SPJ1

3 0

2 years ago

The population of a town with a 20162016 population of 87 comma 00087,000 grows at a rate of 1.91.9% per year. a. Find the rate

SCORPION-xisa [38]

Answer:

Given,

The initial population, P = 87,000,

Annual rate of increasing, r = 1.9 %,

a) Thus, the population after t years,

$A=P(1+\frac{r}{100})^t$

$A=87000(1+\frac{1.9}{100})^{t}$

$=87000(1+0.019)^t$

$=87000(1.019)^t$

$87000(1.019)^t=87000e^{kt}$

Where, k is the rate constant,

By comparing,

$\implies k=log(1.019)=0.00817418400643\approx 0.00817$

Hence, the approximate value of k is 0.00817.

And, the exponential growth function would be,

$A=87000e^{0.00817t}$

b) If A = 145,000,

$145000=87000(1.019)^t$

By using graphing calculator,

We get,

$t=27.14\approx 27$

The year after 27 years from 2016 is 2043.

Hence, in 2043 the population reach 145,000.

6 0

4 years ago

Can i get help with 4,6, and 8 PLEASE HELP!!!!!!!!!! IM GONNA RUN OUTTA TIME!!!!

gogolik [260]

They are all even numbers

8 0

3 years ago

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.

irakobra [83]

The given polynomial is f(x) = x² - 2x - 6

Rewrite the function by completing the square.
f(x) = [x² - 2x] - 6
= [(x-1)² - 1] - 6
= (x-1)² - 7

In vertex form,
f(x) = (x-1)² - 7

The vertex is located at (1, -7).
Because the leading coefficient is +1, the curve opens upward.

Answer: f(x) = (x - 1)² - 7

8 0

4 years ago

Consider this scatter plot. A. Line A B. Line B C. Line C D. None