Hello from MrBillDoesMath!
Answer:
The first choice, y = x^3 + 5
Discussion:
Let
y = (x-5) ^ (1/3)
To find the inverse, sway x and y and then solve for y:
x = ( y - 5 )^(1/3) => cube both sides
x^3 = y - 5 => add 5 to both sides
x^3 + 5 = y
So the inverse is x^3 + 5, which is the first choice
Thank you,
MrB
Answer:
301.4
Step-by-step explanation:
Volume of a cylinder=pi*
*h. Assuming you want 3.14 for pi, we can substitue the 4m for r, 6 for h and 3.14 for pi.
V=3.14*
*6
V=301.44
Since you want to round to nearest tenths, the answer is 301.4
Answer:
43/12
Step-by-step explanation:
First we must find a common denominator for all 3 fractions, 1/2 cup, 2 1/3 cup, and 3/4 cup all share 12 as a common denominator.
However, let's convert 2 1/3 cup into an improper fraction: there are 2 (3/3 cups) here multiply (3/3) and (2/1) you get 6/3. Finally, add the remaining 1/3 to 6/3 and you get 7/3.
Now, to get all these fractions to have the same common denominator.
(1/2) ×(6/6)=(6/12)
(7/3)×(4/4)=(28/12)
(3/4)×(3/3)=(9/12)
Add them all together and your answer is: (43/12)
Multiplying both sides by
gives

so that substituting
and hence
gives the linear ODE,

Now multiply both sides by
to get

so that the left side condenses into the derivative of a product.
![\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E3v%5D%3D3x%5E2)
Integrate both sides, then solve for
, then for
:




![\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Csqrt%5B3%5D%7B1%2B%5Cdfrac%20C%7Bx%5E3%7D%7D%7D)