Answer:
Step-by-step explanation:
1) Change the fractions so that they all have common denominators (2/4 --> 20/40, 3/5 --> 24/40, 6/8 --> 30/40)
2) Add the numerators together (74/40)
3) Simplify as necessary
Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Distributive Property
- Equality Properties
<u>Algebra I</u>
- Combining Like Terms
- Factoring
<u>Calculus</u>
- Derivative 1:
![\frac{d}{dx} [e^u]=u'e^u](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Be%5Eu%5D%3Du%27e%5Eu)
- Integration Constant C
- Integral 1:

- Integral 2:

- Integral 3:

- Integral Rule 1:

- Integration by Parts:

- [IBP] LIPET: Logs, Inverses, Polynomials, Exponents, Trig
Step-by-step Explanation:
<u>Step 1: Define Integral</u>

<u>Step 2: Identify Variables Pt. 1</u>
<em>Using LIPET, we determine the variables for IBP.</em>
<em>Use Int Rules 2 + 3.</em>

<u>Step 3: Integrate Pt. 1</u>
- Integrate [IBP]:

- Integrate [Int Rule 1]:

<u>Step 4: Identify Variables Pt. 2</u>
<em>Using LIPET, we determine the variables for the 2nd IBP.</em>
<em>Use Int Rules 2 + 3.</em>

<u>Step 5: Integrate Pt. 2</u>
- Integrate [IBP]:

- Integrate [Int Rule 1]:

<u>Step 6: Integrate Pt. 3</u>
- Integrate [Alg - Back substitute]:
![\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{a}{b} [\frac{e^{au}sin(bu)}{b} - \frac{a}{b} \int ({e^{au} sin(bu)}) \, du]](https://tex.z-dn.net/?f=%5Cint%20%7Be%5E%7Bau%7Dsin%28bu%29%7D%20%5C%2C%20du%20%3D%20%5Cfrac%7B-e%5E%7Bau%7Dcos%28bu%29%7D%7Bb%7D%20%2B%20%5Cfrac%7Ba%7D%7Bb%7D%20%5B%5Cfrac%7Be%5E%7Bau%7Dsin%28bu%29%7D%7Bb%7D%20-%20%5Cfrac%7Ba%7D%7Bb%7D%20%5Cint%20%28%7Be%5E%7Bau%7D%20sin%28bu%29%7D%29%20%5C%2C%20du%5D)
- [Integral - Alg] Distribute Brackets:

- [Integral - Alg] Isolate Original Terms:

- [Integral - Alg] Rewrite:

- [Integral - Alg] Isolate Original:

- [Integral - Alg] Rewrite Fraction:

- [Integral - Alg] Combine Like Terms:

- [Integral - Alg] Divide:

- [Integral - Alg] Multiply:
![\int {e^{au}sin(bu)} \, du = \frac{1}{a^2+b^2} [ae^{au}sin(bu) - be^{au}cos(bu)]](https://tex.z-dn.net/?f=%5Cint%20%7Be%5E%7Bau%7Dsin%28bu%29%7D%20%5C%2C%20du%20%3D%20%5Cfrac%7B1%7D%7Ba%5E2%2Bb%5E2%7D%20%5Bae%5E%7Bau%7Dsin%28bu%29%20-%20be%5E%7Bau%7Dcos%28bu%29%5D)
- [Integral - Alg] Factor:
![\int {e^{au}sin(bu)} \, du = \frac{e^{au}}{a^2+b^2} [asin(bu) - bcos(bu)]](https://tex.z-dn.net/?f=%5Cint%20%7Be%5E%7Bau%7Dsin%28bu%29%7D%20%5C%2C%20du%20%3D%20%5Cfrac%7Be%5E%7Bau%7D%7D%7Ba%5E2%2Bb%5E2%7D%20%5Basin%28bu%29%20-%20bcos%28bu%29%5D)
- [Integral] Integration Constant:
![\int {e^{au}sin(bu)} \, du = \frac{e^{au}}{a^2+b^2} [asin(bu) - bcos(bu)] + C](https://tex.z-dn.net/?f=%5Cint%20%7Be%5E%7Bau%7Dsin%28bu%29%7D%20%5C%2C%20du%20%3D%20%5Cfrac%7Be%5E%7Bau%7D%7D%7Ba%5E2%2Bb%5E2%7D%20%5Basin%28bu%29%20-%20bcos%28bu%29%5D%20%2B%20C)
And we have proved the integration formula!
Answer:
It looks like the factored form of a polynomial
Step-by-step explanation:
In unfactored form, it would be this:
2r^2 + -2r + 1
Answer:
75 degrees
Step-by-step explanation:
30 + 75 = 105
180 - 105 = 75
Answer:
A
Step-by-step explanation:
y= x+1 at the same time y=4x+5
x+1= 4x+5, so answer is A