Answer:
Step-by-step explanation:
this is confusing b/c they are asking about two trains traveling at differnt speeds, but.. if you put the speeds together and make one train... imaginary.. ofc... traveling at the speed of both trains combined... when will it be 50 miles from the station?
maybe you can solve that? I'll solve it below.. but.. if you can.. try it now, on your own
below is my answer... don't look until you have solved yours :P
80+70= 150kph
when will this have traveled 50Km?
you may be able to see that it will take 1/3 of an hour to travel 50 km
so 60 minutes times 1/3 = 20 minutes :)
If we have a triangle with sides a,b,c then
b-a < c < b+a
describes the restriction of the length of side c, given sides a and b. This is due to the triangle inequality theorem.
a = 6
b = 9
b-a < c < b+a
9-6 < c < 9+6
3 < c < 15
<h3>Answer: The third side is between 3 cm and 15 cm. The third side cannot equal 3 cm, and it also cannot equal 15 cm. </h3>
i read in class 4 but I don't explain the answer
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!