Answer:
x=3, multiplicity of 2
x=-5, multiplicity of 1
Step-by-step explanation:
f(x) = (x - 3)(x - 3)(x + 5)
Rewriting
f(x) = (x - 3)^2(x + 5)
Setting equal to zero
0 = (x - 3)^2(x + 5)
Using the zero product property
(x-3)^2 = 0 x+5 = 0
x-3 = 0 x= -5
x=3 x-5
Since x-3 was squared, the multiplicity is 2
X - the amount of ribbon she started with
![\frac{3}{8}x=6 \\ x=6 \times \frac{8}{3} \\ x=2 \times 8 \\ x=16](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7Dx%3D6%20%5C%5C%0Ax%3D6%20%5Ctimes%20%5Cfrac%7B8%7D%7B3%7D%20%5C%5C%0Ax%3D2%20%5Ctimes%208%20%5C%5C%0Ax%3D16)
She started with 16 feet of ribbon.
Answer:
1) Same side exterior angles
2) Corresponding Angles
3) Alternate Interior Angles
4) Same Side Interior Angles
5) Linear Pair
6) Vertical Angles
7) Alternate Exterior Angles
hope this helped! and thanks for uploading the image
Answer:
![\displaystyle \int {(x + 10)^2} \, dx = \frac{(x + 10)^3}{3} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%28x%20%2B%2010%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B%28x%20%2B%2010%29%5E3%7D%7B3%7D%20%2B%20C)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]: ![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
- Indefinite Integrals
- Integration Constant C
Integration Rule [Reverse Power Rule]: ![\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7Bx%5En%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E%7Bn%20%2B%201%7D%7D%7Bn%20%2B%201%7D%20%2B%20C)
U-Substitution
Step-by-step explanation:
*Note:
The answer below me is correct, but there is a simpler method to obtain the answer.
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle \int {(x + 10)^2} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%28x%20%2B%2010%29%5E2%7D%20%5C%2C%20dx)
<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:
![\displaystyle u = x + 10](https://tex.z-dn.net/?f=%5Cdisplaystyle%20u%20%3D%20x%20%2B%2010)
- [<em>u</em>] Differentiate [Basic Power Rule]:
![\displaystyle du = dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20du%20%3D%20dx)
<u>Step 3: Integrate Pt. 2</u>
- [Integral] U-Substitution:
![\displaystyle \int {(x + 10)^2} \, dx = \int {u^2} \, du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%28x%20%2B%2010%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bu%5E2%7D%20%5C%2C%20du)
- [Integral] Reverse Power Rule:
![\displaystyle \int {(x + 10)^2} \, dx = \frac{u^3}{3} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%28x%20%2B%2010%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bu%5E3%7D%7B3%7D%20%2B%20C)
- Back-Substitute:
![\displaystyle \int {(x + 10)^2} \, dx = \frac{(x + 10)^3}{3} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%28x%20%2B%2010%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B%28x%20%2B%2010%29%5E3%7D%7B3%7D%20%2B%20C)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Answer:
Thanks for the points broski. You shouldn't love a random stranger
Step-by-step explanation: