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iogann1982 [59]
3 years ago
12

The base of a solid is a circle with radius 5. The cross sections of the solid perpendicular to a fixed diameter of the base are

squares. If the circle is centered at the origin and the cross sections are perpendicular to the x-axis, find the area A(x) of the cross section at x.

Mathematics
1 answer:
Aleks [24]3 years ago
3 0

Answer:

Step-by-step explanation:see attachment

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.
SashulF [63]

<u>ANSWER</u>

{r}^{2}  = 4  \cos2\theta

<u>EXPLANATION</u>

The Cartesian equation is

{( {x}^{2}  +  {y}^{2} )}^{2}  = 4( {x}^{2} -  {y}^{2}  )

We substitute

x = r \cos( \theta)

y = r \sin( \theta)

and

{x}^{2}  +  {y}^{2}  =  {r}^{2}

This implies that

{( {r}^{2} )}^{2}  = 4(( { r \cos\theta)  }^{2} -  {(r \sin\theta) }^{2}  )

Let us evaluate the exponents to get:

{r}^{4}  = 4({  {r}^{2} \cos^{2}\theta } -   {r}^{2}  \sin^{2}\theta)

Factor the RHS to get:

{r}^{4}  = 4{r}^{2} ({   \cos^{2}\theta } -   \sin^{2}\theta)

Divide through by r²

{r}^{2}  = 4 ({   \cos^{2}\theta } -   \sin^{2}\theta)

Apply the double angle identity

\cos^{2}\theta -\sin^{2}\theta=  \cos(2 \theta)

The polar equation then becomes:

{r}^{2}  = 4  \cos2\theta

7 0
3 years ago
Mathematical expression
Over [174]
Answer: has no equal sign
7 0
3 years ago
Read 2 more answers
2. Hasil dari<br>+<br>9,1-2<br>5<br>=<br>A. 6,5<br>B. 7,5<br>7<br>C. 6<br>30<br>D. 7<br>7<br>30​
sasho [114]

Answer:

Itu mudah 2.18

A.11

B.19

C.36

D.44

6 0
3 years ago
What is 5 divided by 5
Triss [41]

Answer:

1

Step-by-step explanation:

You have 5 jelly beans and 4 imaginary friends

You have to split the jellybeans between yourself and your pretend friends.

Each of you gets 1 jellybean

(Except you get all the jellybeans because your friends don't exist)

Hope this helps :)

6 0
3 years ago
HELP HELP HELP HELP<br> HELP HELP HELP HELP
Lelechka [254]

Answer:

Vertex - (2, -1)

Axis of Symmetry - x = 2

X intercept - (3,0) (1, 0)

Y intercept (0, 3)

Domain - (negative infinity, positive infinity)

Range - [-1, infinity)

Step-by-step explanation:

I graphed with desmos and found it.

5 0
2 years ago
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