All categories

3 years ago

Find the value of x and y.

Mathematics

1 answer:

Cloud [144]3 years ago

7 0

Answer:

x=13

y=132

Step-by-step explanation:

............

You might be interested in

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs

JulsSmile [24]

Answer:

1) V = 12 π ㏑ 3

2) $\mathbf{V = \dfrac{328 \pi}{9}}$

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

$y = \dfrac{6}{x^2}, y =0 , x=1 , x=3$

Using Shell method to determine the required volume,

where;

shell radius = x; &

height of the shell = $\dfrac{6}{x^2}$

∴

Volume V = $\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx$

$V = 12 \pi ( In \ x ) ^3_{x-1}$

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius $r(x) = 6 - \dfrac{6}{x^2}$

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

$V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx$

$V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx$

Recall that:

$\int x^n dx = \dfrac{x^n +1}{n+1}$

Then:

$V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}$

$V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}$

$V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}$

$V = 36 \pi (\dfrac{82}{81})$

$\mathbf{V = \dfrac{328 \pi}{9}}$

The graph of equation for 1 and 2 is also attached in the file below.

5 0

4 years ago

Analyze the diagram below and complete the instructions that follow.<br><br> Find sin 60 degree

Effectus [21]

Given:

Right triangle

θ = 60°

To find:

sin 60°

Solution:

The reference image is attached below.

The given triangle is a right triangle.

θ = 60°

Using basic trigonometric ratio formula:

$$\sin \theta = \frac{\text{Opposite side to } \theta} {\text{Hypotenuse}}$

$$\sin 60^\circ = \frac{\text{Opposite side to } 60^\circ} {\text{Hypotenuse}}$

$$\sin 60^\circ = \frac{BC}{AC}$

The value of sin 60° = $\frac{\sqrt{3} }{2}$ .

$$\frac{\sqrt{3} }{2} = \frac{BC}{AC}$

In the given figure, the values of adjacent side, opposite side and hypotenuse are not given.

8 0

3 years ago

I need help with this this is hard

saveliy_v [14]

Answer:

n > -6 and n < 8! Heart it if it was helpful :D

Step-by-step explanation:

Okay! So n has to be bigger than -6, but smaller than 8. So the inequalities are n > -6 and n < 8!

8 0

3 years ago

Read 2 more answers

Es para estos momentos por fa

AlexFokin [52]

Answer:

Step-by-step explanation:

6 0

3 years ago

Sum of 1+3+5+7...+103

Levart [38]

1+3+5+7+103=119. I hope this is what you were asking for! :)

6 0

4 years ago