21. find the volume of the solid of revolution formed if the area enclosed between the curves y=x² and y=(x-2)² is rotated about the x-axis using integration

Answers

Answer 1

Answer: What you need to do is get hold of the area underneath the curve y=x² from x=1 to x=0. You then spin this area 360 degrees about the x-axis and double the result as there is symmetry between y=x² and y=(x-2)².

Use the formula:

$Volume=\int _( a )^( b ){ \pi { y }^( 2 ) } dx$

Ok, so let's solve the problem...

$V=2\int _( 0 )^( 1 ){ \pi { x }^( 4 ) } dx\n \n =2{ \left[ \frac { \pi { x }^( 4+1 ) }{ 4+1 } \right] }_( 0 )^( 1 )$

$\n \n =2{ \left[ \frac { \pi { x }^( 5 ) }{ 5 } \right] }_( 0 )^( 1 )\n \n =2\left\{ \left( \frac { \pi }{ 5 } \right) -\left( 0 \right) \right\} \n \n =\frac { 2 }{ 5 } \pi$

Answer:

$\frac { 2 }{ 5 } \pi$ units cubed.

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Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.Given:
∠C, ∠F are rt. ∠'s; AC = DF; ∠B = ∠E

HL
LL
HA
LA

Answers

∠C and ∠F are right angles. So, the triangles are right triangles.

AC = DF are the short legs of both triangles.

∠B = ∠E.

In this scenario, the postulate is ASA (Angle-Side-Angle)

The remaining sides that must be noted to prove that the triangles are congruent are the long legs and hypotenuse.

CB = FE can be LL for congruence where tt states that if the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent.

Nameof postulate or theorem that supports the conclusion that the triangles are congruent is Angle-side-Angle (ASA).

Given information:

$\angle C,\; \angle F$ are right triangle, $AC=DF;\angle B=\angle E$

From the figure,

$\Delta ACB\;\&\;\Delta DFE$ are right angletriangle.

$AC=DF \;\;\;\;\{\rm{given}\} \n\angle B=\angle E \; \;\;\;\;\{\rm{given}\}$

And $\angle C=\angle F=90^\circ$

$\Delta ACB\;\cong\;\Delta DFE$ { $ASA$ congruence rule}

Hence, Nameof postulate ortheorem that supports the conclusion that the trianglesare congruent Angle-side-Angle.

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You have 160 boxes of cookies. In each case you can pack 8 boxes of cookies. How many cases would be filled from these boxes of cookies ?

Answers

160 boxes of cookies / 8 boxes per case = 20 cases that can be filled.

you divide 160 by 8 and you get 20. 20 cases will be filled

What is the equation of a line that is perpendicular to a line with a slope of 2 and passesthrough the point (-2, 0)?

Answers

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b So now we know the y-intercept and slope. We just put them together now

y=3x-7

Look at the broswer my friend you can do it

HELP ME OUT WITH THIS PLEASE

Answers

Equivalent rational numbers are generated by multiplying both the numerator and denominator by the same nonzero integer. These were calculated for -6/4, -4/12, and -12/10. The given numbers were then graphed on a number line and ordered from least to greatest.

For the first part of the question, equivalent rational numbers can be generated by multiplying both numerator and denominator by the same nonzero integer.

Therefore, equivalent rational numbers for -6/4 are: -12/8, -9/6, and -3/2. For -4/12, we have: -8/24, -2/6, and -1/3. For -12/10, we have: -24/20, -6/5, and -3/2.5.

The second part involves graphing the given numbers on a number line and then ordering them. The order from least to greatest would be: -9/5, -3.2, -3, 13/10, 2.5, and 4.

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The ratio of the muffins Baker A baked to the number of muffins Baker B baked was 8 : 5. The ratio of the number of muffins Baker B baked to the number of muffins BAker C baked was 4 : 3. If Baker C baked 150 muffins, how many more muffins did Baker A bake than Baker C?

Answers

Answer:

170 muffins

Step-by-step explanation:

We start from the ratio between baker B and C

The ratio of cakes baked by both is 4:3.

We know baker C baker 150 muffins:

This mathematically means:

B:C = 4:3 = B:150

This means 4/3 = B/150

B = (4 * 150)/3 = 200

Baker B baked 200 cakes

We now move back to the first statement

The ratio between baker A and B is 8:5

Mathematically, this means:

A:B = 8:5 = A:200

8/5 = A/200

A = (8 * 200)/5 = 320

The number of cakes baker A baker pass baker C would be 320 - 150 = 170 muffins

Final answer:

To solve the problem, use the given ratios to calculate the quantity of muffins each baker baked. Then compare the quantities to find the difference. The result is that Baker A baked 170 more muffins than Baker C.

Explanation:

In this question, you're given two ratios involving three bakers: A, B, and C. First, let's figure out how many muffins Baker B baked. We know that for every 4 muffins Baker B baked, Baker C baked 3 muffins. This gives us the ratio 4 : 3 for Baker B to Baker C. Since we know that Baker C baked 150 muffins, we can set up a simple proportion: 4/3 = B/150. Solving this proportion, we find that Baker B baked 200 muffins.

Now let's tackle the ratio of muffins baked by Baker A to Baker B, which is given as 8 : 5. Again, we can set up a proportion: 8/5 = A/200. Solving this, we find that Baker A baked 320 muffins.

The question asks how many more muffins Baker A baked than Baker C. Given that Baker A baked 320 muffins and Baker C baked 150 muffins, the difference is 320 - 150, which gives us 170. So, Baker A baked 170 more muffins than Baker C.

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The length of a football field is 120 yd. The width of the football field is 50 yd. Which is the correct unit of measurement to use when figuring out how much rope is needed to surround the field? A. yd B. yd2 C. yd3

Answers

a because u are trying to find the lengths and then just adding it to the widths. You don't need area so b is wrong, you are just simply adding so a is the right answer.

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