Can someone please help me with this math problem I don’t understand it

Answer:

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Step-by-step explanation:

The equation of the line through the point [tex](x_o,y_o)[/tex] & [tex](x_1,y_1)[/tex] can be represented by:

[tex]y-y_o = m(x - x_o)[/tex]

Making m the subject;

[tex]m = \dfrac{y_1 - y_0}{x_1-x_0}[/tex]

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

[tex]m= \dfrac{2-1}{1-0}[/tex]

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

[tex]m = \dfrac{1-2}{4-1}[/tex]

[tex]m = \dfrac{-1}{3}[/tex]

∴

[tex]y-2 = -\dfrac{1}{3}(x-1)[/tex]

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

[tex]\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg][/tex]

[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]

Answer:

V≈1130.97cm³

Step-by-step explanation:

crown n add me plzz

Answer:

Oh, it's y=3x-4.

Because it's slope is 3 and it crosses through -4 on the y axis, we know that that would be the equation.

Good luck with the assignment man, let me know of anymore questions. :)

Answer:

Step-by-step explanation:

Math answers to fraction 1498 divided by 30 can be calculated as follows.

1498/30 math problems division = 49.9333333333. Therefore 49.9333333333 to 2 decimal places= 49.93

1498/30 divided by 2 » (1498/30) ÷ 2 » 49.9333333333 ÷ 2 = 24.9666666667

Answer:

The answer is nine :)

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

y=(2x)^(1/3)-7    wrong

y= -2(3x)^(1/6) wrong

y=-x^(1/2)+5 wrong

y=(x+2)^(1/4) wrong

Step-by-step explanation:

the correct answer is 6

Answer:

6

Step-by-step explanation:

Step 1:

2x + 9 = 21           Equation

Step 2:

2x = 12       Subtract 9 on both sides

Step 3:

x = 12 ÷ 2      Divide

Answer:

x = 6

Hope This Helps :)

Answer:

A: the 5.62 kilograms should be negative, since he is losing weight.

B: -5.62 + 1.4 is -4.22, which is how many kilograms Patrick lost in total.

Hope this helps :)

Answer:

1=50

2=90

3=60

4=60

5=60

6=60

7= 120

Step-by-step explanation:

Answer:

Wth.. Okay. The probablility is probably low, seeing as there is 25 questions. So I guess like .2? Not sure.

Answer: .12 grams of butter per cupcake

Step-by-step explanation:

1/12=x/100 this is what i found but this may or may not be the right answer but I am pretty sure that it is. Sorry if this doesn't help.

Answer:

21.5625

Step-by-step explanation:

So You would divide 258.75 / 12 = 26.5625

The radius of container is 2.6 inch.

The amount of space occupied by a three dimensional figure as measured in cubic units.

[tex]volume of cylinder= \pi r^{2} h[/tex]

where,

r is the radius

h is the height

According to the given question

shape of the container is cylindrical.

Height of the container, h = 12 inches

Volume of container = 258.75 cubic inches

for the radius of the container

volume of container = [tex]\pi r^{2}h[/tex]

258.75 = 3.14×[tex]r^{2}[/tex]×12

258.75 =37.68×[tex]r^{2}[/tex]

[tex]\frac{258.75}{37.68} =r^{2}[/tex]

[tex]6.9=r^{2}[/tex]

⇒ [tex]r = \sqrt{6.9} =2.62inch[/tex] = 2.6 inch

Hence, the radius of container is 2.6 inch.

Learn more about the volume of cylinder here:

https://brainly.com/question/16134180

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Answer:

I believe it is the first answer

Step-by-step explanation:

-50 because it is being translated down 50, and the sloped are equal

Answer:

nothing rn what do you need answered?

Step-by-step explanation:

Answer:

i have 0 questions to be answered anyway have a good day, week and happy new years and thanks for the points

Answer: gcf, hcf, gcd (42; 112) = 14 = 2 × 7: greatest (highest) common factor (divisor), calculated.

Step-by-step explanation:

Answer:14

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Function of the graph shown: y=3x+4

Answer:

slope is 1/6

Step-by-step explanation:

Answer:

This quadratic equation has 2 solutions.

Step-by-step explanation:

I assume the '?' in your question is meant to be power 2 (²), or else it would not be a quadratic equation. You could write it using the superscript version of 2.

We can solve this equation by expressing it in the form: ax² + bx + c

x² + 9x= -8

x² + 9x + 8 = 0

Now if you know the discriminant, you can simply plug in your values of a, b, and c to see how many solutions there are.

In this case, you would not need the discriminant as there are whole-number factors and hence this can simply be factorised.

x² + 9x + 8 = 0

(x + 8)(x + 1) = 0

For this equation to be true (= 0), x can equal -8 OR -1.

Hence, this quadratic equation has 2 solutions.

Answer:

D or A

Step-by-step explanation:

Answer:

960

Step-by-step explanation:

TRUST ME, mark me brainliest please

A.4

took the test

╰(*°▽°*)╯(☞ﾟヮﾟ)☞

Answer:

the answer is a i got a hundred on that tes a year ago

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

edge

[tex]Z_{1} +Z_{2}[/tex] represents Point A i.e., 3i.

Complex numbers are the numbers that are expressed in the form of

a + ib where, a, b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Given

The complex numbers z1 and z2 are graphed.

From the graph,

[tex]Z_{1} =3+i[/tex]

[tex]Z_{2} =-3+2i[/tex]

[tex]Z_{1} +Z_{2}= 3+i+(-3+2i)[/tex]

[tex]Z_{1} +Z_{2}= 3-3+i+2i[/tex]

[tex]Z_{1} +Z_{2}= 3i[/tex]

Option A is correct.

[tex]Z_{1} +Z_{2}[/tex] represent Point A i.e., 3i.

Find out more information about complex numbers here

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Answer:

1. -5a

Step-by-step explanation:

The definition of combining like terms is adding their coefficients, for example: 2x + 3x = (2+3)x = 5x.

So for this one, -21a+16a = (-21+16)a = -5a.

Answer: 59 1/2

Step-by-step explanation:

Answer:

The new elevation is -92 [tex]\frac{1}{8}[/tex] ft.

Step-by-step explanation:

-75 [tex]\frac{3}{4}[/tex] = -75[tex]\frac{6}{8}[/tex]

-75 [tex]\frac{6}{8}[/tex] + -16 [tex]\frac{3}{8}[/tex] = -91 [tex]\frac{9}{8}[/tex] = 92 [tex]\frac{1}{8}[/tex]

Answer:

with?

Step-by-step explanation:

Answer:

51:120

Step-by-step explanation:

since 120 is length in mm, it is the y value

since 50 is width in mm it is the x value

51mm:120mm

Answer:

8%

Step-by-step explanation:

Answer:

20 Mystery DVD’s

Step-by-step explanation:

32/8=4

4*5=20

Answer:

There are 20 Mystery DVD's.

Step-by-step explanation:

Since the ratio of Drama to Mystery is 8:5, then we can conclude that 32:x is another equivalent form of the ratio, given that 32 represents drama, and x represents the unknown number of mystery.  

Set up the ratios as 8/5 as one fraction, and 32/x as another, but make them equal each other.  Cross multiply the numerators and denominators, then you will get 8x=160

divide both sides to solve for x.

x=20