Evaluate each expression: A.4(divided)1/3. B.3/8(divided)7/2 C. 3 1/2(divided)7/4

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 7x6, y

IgorC [24]

Answer:

The volume is $\frac{490\pi}{39}$ cubic units.

Step-by-step explanation:

The given curve is

$y=7x^6$

The given line is

$y=7x$

Equate both the functions to find the intersection point of both line and curve.

$7x^6=7x$

$7x^6-7x=0$

$7x(x^5-1)=0$

$7x=0\rightarrow x=0$

$x^5-1=0\rightarrow x=1$

According to washer method:

$V=\pi \int_{a}^{b}[f(x)^2-g(x)^2]dx$

Using washer method, where a=0 and b=1, we get

$V=\pi \int_{0}^{1}[(7x)^2-(7x^6)^2]dx$

$V=\pi \int_{0}^{1}[49x^2-49x^{12}]dx$

$V=49\pi \int_{0}^{1}[x^2-x^{12}]dx$

$V=49\pi [\frac{x^3}{3}-\frac{x^{13}}{13}]_0^1$

$V=49\pi [\frac{1^3}{3}-\frac{1^{13}}{13}-(0-0)]$

$V=49\pi [\frac{1}{3}-\frac{1}{13}]$

$V=49\pi (\frac{13-3}{39})$

$V=49\pi (\frac{10}{39})$

$V=\frac{490\pi}{39}$

Therefore the volume is $\frac{490\pi}{39}$ cubic units.

5 0

3 years ago

% ____of $10 = $1 Helppppppo

Len [333]

10% is equal to $10 = $1

7 0

3 years ago

Find the measure of the indicated angle to the nearest degree. 8 22 ?

Blizzard [7]

Answer:

21 degrees

Step-by-step explanation:

To find this, we are going to use the appropriate trigonometric ratio

The right angle faces the length 22 which is the hypotenuse

The marked angle faces the length 8 which makes it the opposite

The trigonometric ratio that links the two is the sine

The sine is the ratio of the opposite to the hypotenuse

So, we have it that;

sine ? = 8/22

? = arc sine 8/22

? = 21 degrees

4 0

3 years ago

Plz help me It's the same as the last question

AveGali [126]

Answer:

4x+4x+7x=180

15x=180

x=12

Step-by-step explanation:

8 0

3 years ago

Use the diagram shown. There are two lines which intersect each other and making angles 1 and 2. The opposite angles to 1 is 3,

Rufina [12.5K]

Answer:

I think that A, B, and C are correct.

Step-by-step explanation:

1. Since measures 2 and 3 are a linear pair, they equal 180 degrees. A is correct.

2. Since measures 3 and 4 are also a linear pair, they too equal 180 degrees. B is correct.

3. Measures 2 and 3 are already established to be 180 degrees (check answer 1) , and measures 3 and 4 are also 180 degrees (check answer 2). Since they are both 180 degrees, they are congruent (equal), so C is correct.

D is NOT correct. Measures 1 and 3 are equal because they are vertical angles. We also know that they are acute angles (less than 90) so adding them together will equal less than 180 degrees.

Measures 2 and 4 are equal because they are vertical angles, and they are obtuse (more than 90 degrees). Adding them together will equal more than 180 degrees.

Logic tells us that something less than 180 CANNOT be equal to something more than 180. This proves that 2 and 4 and 1 and 3 are not congruent.

D is WRONG

8 0

2 years ago