Question

Add: x-2/x-6 -4+ 4/x^2

a. -24+4x+22x^2-3x^3/x^2(x-6)
b. 1/3+3
c. -4(x-2)
d. -4(x-2)+4/(x-6)
e. none of the above

Answer 1

) Use disks: each disk has radius R = y = 1/x³, so
V = ∫[a,b] πR² dx = π∫[1,3] dx/x^6 = (-π/5)x^-5 |[1,3] = (-π/5)(0.0041 - 1) ≈ 0.63

b) k affects the limits; you're asked to find where
(-π/5)x^-5 |[1,k] = (-π/5)x^-5 |[k,3]
-π/5 cancels;
k^-5 - 1 = 3^-5 - k^-5
2k^-5 = 1 + 3^-5 = 1.0041
k ≈ 1.148 ←
Check:
1.148^-5 - 1 = -0.498
3^-5 - 1.148^5 = -0.498 √

-0.498 * (-π/5) = 0.313 ≈ half the volume found in (a)

Answer 2

Oh okay, hang on, I'll show you step by step.

Answer 3

thank you @Aimee98 :)

Answer 4

Write out the equation:
\[x - \frac{ 2 }{ x } - 6 - 4 + \frac{ 4 }{ x^2 }\]

Answer 5

alright.

Answer 6

Then, simplify:
\[x - \frac{ 2 }{ x } + \frac{ 4 }{ x^2 } - 10\]

Answer 7

okay

Answer 8

Then lastly, cross multiply:
\[x - \frac{ 2 (x - 2 + 5 x^2 }{ x^2 }\]

Answer 9

So you answer?

Answer 10

your*

Answer 11

one second finishing the math now.

Answer 12

this is the same answer i got when i did the math. x^3-10x^2-2x+4/x^2

Answer 13

is that correct?

Answer 14

It looks excellent to me! When you got this last time was it wrong?