Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant

Answers

Answer 1

Answer:

[tex]\mathbf{ \dfrac{128}{3}}[/tex]

Step-by-step explanation:

Given that:

[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]

[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]

[tex]Then;[/tex]

[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]

[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]

[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]

[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]

[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]

[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]

[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]

[tex]\mathbf{V = \dfrac{128}{3}}[/tex]


Related Questions

how many roots does y= x^5- 4x^2+ 3x

A.3
B.4
C.5
D.6

(x^2 is the power to)

Answers

Answer: 4

Step-by-step explanation:

We can write the equation as

[tex]x(x-1)^{2}(x^{2}+2x+3)=0\\\\x=0, 1, -1 \pm i\sqrt{2}[/tex]

Therefore, there are 4 distinct roots.

Evaluate each function.
11) f(a) = 3a? + 3a; Find f(a – 2)

Answers

It is 5 hope dis helped

Thirty is what percent of 20?

Answers

Answer:

150 percent

Step-by-step explanation:

30/20. Multiply both sides by 5. 150/100. 30 is %150 of 20

Answer:

150

Step-by-step explanation: from goog  .le

Determine if each ordered pair is a part of the solution set of the linear inequality. Select Yes or No.
Ordered Pair
Yes
No
(0,-5)
O
(7, – 4)
O
(-6, -7)
o
(-4,1)
O
(4,8)
O

Answers

Answer:

yes

Step-by-step explanation:

ASAP HELP TYYY
A purse with a price of $58.45 has an 8% sales tax. What is the sales tax dollar amount?

Answers

It is $4.68. You do $58.45 times 0.08, which is $4.676, but you round that to $4.68.
58.45 x 0.08 = 4.676
4.67<6 round up above 5 round down below
4.68

PLEASE HELP D:

What is the area of a triangle that has a height of 10 feet and a base length of 8 feet?

A - 10 feet^2
B - 20 feet^2
C - 40 feet^2
D - 80 feet^2

Answers

Answer:

C. 40 ft²

Step-by-step explanation:

Triangle area formula:

A = bh/2, where b- base, h- height

We have:

b = 8 ft, h = 10 ft

The area is:

A = 8*10/2 = 40 ft²

Correct choice is C

A car dealer sets the sticker price of a car by taking 115% of the wholesale price. if a car sells wholesale at $17,000 what is the sticker price?​

Answers

Answer:

Step-by-step explanation:

sticker price = $17,000 × 1.15 = $19,550

at a farm the ratio of the number of hens to the number of ducks is 3:5 there are 125 ducks at the farm how many hens are there on the farm​

Answers

3 : 5

x : 125

125 ÷ 5 = 25

25 × 3 = 75

no. of hens = 75

It is 75 dude goodluck!!

The angles of a triangle are (x - 5), (x + 15)°
and (2x + 10). Given that the sum of the
angles of a triangle is 180°, calculate the size
of each angle.​

Answers

Answer:

35°, 55°, 90°

Step-by-step explanation:

Since all the angles of a triangle equal 180, add them all together and set them equal to 180.

(x-5)+(x+15)+(2x+10)=180

Now solve for each angle.

(40-5)

=35°

(40+15)

=55°

(2(40)+10)

=90°

Now check your work.

35°+55°+90°

=180°

In a triangle, its midsegment is (2x + 8) units long and its parallel side is (5x - 9) units long. How long is the midsegment?

Answers

Answer:

The midsegment is 58 units long.

Step-by-step explanation:

Midsegment Theorem:

It states that the length of the midsegment is half the length of the parallel side.

In this question:

Midsegment: 2x + 8

Parallel side: 5x - 9

Parallel side is double the midsegment. So, we use this to find x:

[tex]5x - 9 = 2(2x + 8)[/tex]

[tex]5x - 9 = 4x + 16[/tex]

[tex]x = 25[/tex]

Midsegment:

[tex]2x + 8 = 2(25) + 8 = 50 + 8 = 58[/tex]

The midsegment is 58 units long.

5th grade math. Correct answer will be marked brainliest.

Answers

The Answer is : 2,2

Answer:

(2,2)

Step-by-step explanation:

The horizontal line is always x, and the vertical line is always y. You can see that B is 2 to the right and 2 up, so the answer will be (2,2)

oscar earns extra money, m, working two weekends with his uncle. he is saving to buy a new scooter that costs $138. Fantasia says that Oscar needs to earn more than ​$7 each hour he works to have enough money to buy the scooter. Explain why she is incorrect.

Answers

Answer:

Step-by-step explanation:

30

The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?​

Answers

Answer:

No

Step-by-step explanation:

Because .5 = 7.2

So 1 = 14.4

A survey found that 68% of students do their homework before 10:00 P.M. Predict how many students out of 1,095 do their homework before 10:00 P.M.

Answers

Answer:

744.6 or if you round it 745

Step-by-step explanation:

Step 1: Divide 1095 by 100

In this case, the number that we are "comparing" to 100 is 1095, so we must first normalize the number by dividing it by 100. The operation we have to solve is this:

1095/100= 1095÷100= 10.95

Step 2: Multiply 10.95 by 68 to get the solution

Now that we have our normalized number, 10.95, we just have to multiply it by 68 to get our final answer. The forumla for this is obviously quite simple:

10.95×68= 744.6

PLS SOLVE THIS I WILL GIVE BRAINLIEST BECAUSE THIS IS DUE IN THIRTY MINUTES. I WILL GIVE BRAINLIEST IF YOU ANSWER ALL OF THE PROBLEM.

Answers

So what u do is (29272829)+(-8382929)=(-7398)-n

Please help I don’t understand this

Answers

X=55 because if you follow the SOH,CAH,and TOA formula the angle is always the opposite of the degrees

5x-2y=44 and x=-4y solve for x

Answers

Answer:

I believe x is 8

Please I need help (dont answer if you don't know ill report you)

Answers

9514 1404 393

Answer:

  x = 25

Step-by-step explanation:

The marked angles are "vertical" angles, so are congruent.

  150° = (4x +50)°

  100 = 4x . . . . . . . . . . . divide by °, subtract 50

  25 = x . . . . . . . . . . divide by 4

hi please help......​

Answers

Answer:

9/20

Step-by-step explanation:

45%=45/100

hope this helps

what's nine times 4?​

Answers

Answer:

9 x 4 = 36

9 multiply by 4 is 36.

Answer:

36

Step-by-step explanation:

If you do 9 * 9 * 9 * 9 you would get 36.

Hence, study your nines. (lol)

Hope this helps! ;)

i will love you if u please answer this question PLSS

Answers

Answer:

On the dive boat deck

Step-by-step explanation:

This is above the water level and water level is considered to be 0

pls love me <3

Which statement is true?
A. (1,1) is the x- and y-intercept of the
function.
B. (0,1) is the x- and y-intercept of the function.
C. (0,0) is the x- and y-intercept of the function.
D. The function has no intercepts.

Answers

Answer:

C. (0,0) is the x- and y-intercept of the function.

Step-by-step explanation:

It is because the function is passing through the origin.

PLEASE HELP ITS URGENT DONT GUESS (also if you get it right ill mark you as brainliest)

Answers

Answer:

106.83ft

Step-by-step explanation:

29 + 29 + 19 = 77ft

Now we must calculate the semicircle, The diameter is 19ft

19ft x 3.14 = 59.66

since 59.66 would be a full circle, you divide it in half.

59.66/2=29.83

77+29.83=106.83ft

Find the surface area
Will give brainliest to first answer!!!!

Answers

120 I think I’m not sure

One angle of an isosceles triangle measures 70°. Which other angles could be in that isosceles triangle?

Answers

Answer:

Step-by-step explanation:

The total of all 3 angles in every triangle equals 180 degrees.  An isosceles triangle has two side lengths equal and two angle degrees equal.  

So you either have two angles with each having 70 degrees and the third angle is 40 degrees,  

70 + 70 + 40=180

OR

One angle of 70 degrees and two angles that are 55 degrees each.  

70 + 55 +55 =180

Answer:

Step-by-step explanation:The total of all 3 angles in every triangle equals 180 degrees.  An isosceles triangle has two side lengths equal and two angle degrees equal.  So you either have two angles with each having 70 degrees and the third angle is 40 degrees,   70 + 70 + 40=180OROne angle of 70 degrees and two angles that are 55 degrees each.   70 + 55 +55 =180

5y=585
what is y in da equation

Answers

Answer:

Step-by-step explanation:

5y = 585

Y = 585/5

Y = 117

Answer:

y = 117

Step-by-step explanation:

[tex]5y=585\\\\\frac{5y=585}{5}\\\\ \boxed{y=117}[/tex]

Hope this helps.

please help really need it will give thanx points

Answers

Answer:

62x49

Step-by-step explanation:

take away 16 from both sides

Mi-young is cooking kalguksu for a large family kalgusku is a korean soup with noodles. She makes two kinds of kalguksu,chicken and seafood.
Mi-young makes 24 cups of seafood kalguksu. This is 60% of the total kalguksu she makes

HELP I DONT PAY ATTENTION IN CLASS

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the ratio and percentages.

let's be the total kalguksu soup quantity be x

hence, 60% of x = 24 cups, so we get as

===> 60/100 * x = 24

=> 0.6*x = 24

hence, x ==> 24/0.6

=====> x = 40 cups

hence the answer is 40 cups are in total kalguksu soup.

Please help me please

Answers

Answer:

2

_

3

Step-by-step explanation:

i think at least hopefully

write the equation for the line that goes through point (12,5) with slope m= -2

Answers

Answer:

y=-2x+29

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-2(x-12)

y=-2x+24+5

y=-2x+29

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