Answer:
...
Step-by-step explanation:
What is the degree of g(x) =5x +6x^7 - 8x^3
Answer:
7/9, 28/36
Step-by-step explanation:
14/18
Divide the numerator and denominator of 14/18 by 2: 7/9
Multiply the numerator and denominator of 14/18 by 2: 28/36
Explanation:
Let
and
. The differential volume dV of the cylindrical shells is given by
![dV = 2\pi x[f(x) - g(x)]dx](https://tex.z-dn.net/?f=dV%20%3D%202%5Cpi%20x%5Bf%28x%29%20-%20g%28x%29%5Ddx)
Integrating this expression, we get
![\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%20%3D%202%5Cpi%5Cint%7Bx%5Bf%28x%29%20-%20g%28x%29%5D%7Ddx)
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

or

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is




Answer:
He is 3 years old.
Step-by-step explanation:
3 times 9 is 27. She is 9 times older than her 3 year old son.
Next year he will be 4 and she will be 28. 4 times 7 is 28. She will be 7 times older than her son.
Answer:
$265.07
Step-by-step explanation:
The formula for the future value of an annuity is applicable.
A = P((1+r)^n-1)/r . . . . where r is the monthly interest rate and n is the number of months. P is the monthly payment, and A is the amount of the future value.
800 = P(1.006^3 -1)/(.006) = 3.018036P
P = 800/3.018036 ≈ 265.07
Sarafina's monthly payments need to be $265.07.
_____
This is about $1.60 less than the 266.67 she would deposit if she simply divided the desired balance by the number of months.
Because this number is rounded down, Sarafina will have a balance after 3 months of $799.99.