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Aleks04 [339]
2 years ago
15

Help Plz!!!!!!!!!!!!!!!!!!!

Mathematics
2 answers:
kari74 [83]2 years ago
7 0
-4 x -4 x -4= -64
Z = -4
solniwko [45]2 years ago
5 0
Just get the cube root and solve.

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Prove the following integration formula:
7nadin3 [17]

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
  • Integration Constant C
  • Integral 1:                      \int {e^x} \, dx = e^x + C
  • Integral 2:                     \int {sin(x)} \, dx = -cos(x) + C
  • Integral 3:                     \int {cos(x)} \, dx = sin(x) + C
  • Integral Rule 1:             \int {cf(x)} \, dx = c \int {f(x)} \, dx
  • Integration by Parts:    \int {u} \, dv = uv - \int {v} \, du
  • [IBP] LIPET: Logs, Inverses, Polynomials, Exponents, Trig

Step-by-step Explanation:

<u>Step 1: Define Integral</u>

\int {e^{au}sin(bu)} \, du

<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 = e^{au}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dv = sin(bu)du\\du = ae^{au}du \ \ \ \ \ \ \ \ \ v = \frac{-cos(bu)}{b}

<u>Step 3: Integrate Pt. 1</u>

  1. Integrate [IBP]:                                           \int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} - \int ({ae^{au} \cdot \frac{-cos(bu)}{b} }) \, du
  2. Integrate [Int Rule 1]:                                                \int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{a}{b} \int ({e^{au}cos(bu)}) \, du

<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 = e^{au}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dv = cos(bu)du\\du = ae^{au}du \ \ \ \ \ \ \ \ \ v = \frac{sin(bu)}{b}

<u>Step 5: Integrate Pt. 2</u>

  1. Integrate [IBP]:                                                  \int {e^{au}cos(bu)} \, du = \frac{e^{au}sin(bu)}{b} - \int ({ae^{au} \cdot \frac{sin(bu)}{b} }) \, du
  2. Integrate [Int Rule 1]:                                    \int {e^{au}cos(bu)} \, du = \frac{e^{au}sin(bu)}{b} - \frac{a}{b} \int ({e^{au} sin(bu)}) \, du

<u>Step 6: Integrate Pt. 3</u>

  1. 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]
  2. [Integral - Alg] Distribute Brackets:          \int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2} - \frac{a^2}{b^2} \int ({e^{au} sin(bu)}) \, du
  3. [Integral - Alg] Isolate Original Terms:     \int {e^{au}sin(bu)} \, du + \frac{a^2}{b^2} \int ({e^{au} sin(bu)}) \, du= \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}
  4. [Integral - Alg] Rewrite:                                (\frac{a^2}{b^2} +1)\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}
  5. [Integral - Alg] Isolate Original:                                    \int {e^{au}sin(bu)} \, du = \frac{\frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}}{\frac{a^2}{b^2} +1}
  6. [Integral - Alg] Rewrite Fraction:                          \int {e^{au}sin(bu)} \, du = \frac{\frac{-be^{au}cos(bu)}{b^2} + \frac{ae^{au}sin(bu)}{b^2}}{\frac{a^2}{b^2} +\frac{b^2}{b^2} }
  7. [Integral - Alg] Combine Like Terms:                          \int {e^{au}sin(bu)} \, du = \frac{\frac{ae^{au}sin(bu)-be^{au}cos(bu)}{b^2} }{\frac{a^2+b^2}{b^2} }
  8. [Integral - Alg] Divide:                                  \int {e^{au}sin(bu)} \, du = \frac{ae^{au}sin(bu) - be^{au}cos(bu)}{b^2} \cdot \frac{b^2}{a^2 + b^2}
  9. [Integral - Alg] Multiply:                               \int {e^{au}sin(bu)} \, du = \frac{1}{a^2+b^2} [ae^{au}sin(bu) - be^{au}cos(bu)]
  10. [Integral - Alg] Factor:                                 \int {e^{au}sin(bu)} \, du = \frac{e^{au}}{a^2+b^2} [asin(bu) - bcos(bu)]
  11. [Integral] Integration Constant:                     \int {e^{au}sin(bu)} \, du = \frac{e^{au}}{a^2+b^2} [asin(bu) - bcos(bu)] + C

And we have proved the integration formula!

6 0
2 years ago
Read 2 more answers
If the legs of the triangle are doubled in length what is the length of the hypotenuse
anygoal [31]
64+36=100 √100=10 (right ans=10)
3 0
3 years ago
1.)Find the height of a rectangular prism if the surface area is 148 cm2, the width is 4 cm and the length is 5 cm.
Contact [7]
1) surface of a rectangular prism=2(length x width)+2(length x height)+2(width x height)

Therefore:
148 cm²=2(5 cm x 4 cm)+2(5 cm x h)+2(4 cm x h)=
148 cm²=40 cm²+10 cm h+8 cm h
18 cm h=148 cm²-40 cm²
18 cm h=108 cm²
h=108 cm² / 18 cm=6 cm.

answer: height=6 cm 

2)
Volume of a rectangular prism= length x width x height 
therefore:
34 cm³=(1.7 cm)(0.5 cm) h
0.85 cm² h=34 cm³
h=34 cm³/0.85 cm²
h=40 cm.

answer: height=40 cm

3)
volume of a cylinder: πr²h
therefore.
118.79 ft³=πr²(5 ft)
r=√(118.79 ft³/5π ft)≈2.75 ft

answer: radius=2.75 ft

4)
 
Surface area of the pyramid with square base=4(A side)+A base
A side=(1/2)(8ft)(12 ft)=48 ft²
A base=(8 ft)(8 ft)=64 ft²

surface area=4(48 ft²)+64 ft²=256 ft²

Answer: the surface area of this pyramid would be 256 ft².

5)
surface of a cone=πrs+πr²
therefore:
radius=diameter/2=6.2 ft/2=3.1 ft
63.3 ft²=π(3.1 ft) s+π(3.1 ft)²
3.1π ft s=33.109 ft²
s=33.109 ft² /3.1π ft
s≈3.4 ft

Answer: the slant height would be 3.4 ft.

6)
volume of a square pyramid=(area of base x heigth)/3
therefore:
area of base=(6 ft)(6 ft)=36 ft²
126.97 ft³=36 ft² h /3
h=126.97 ft³/12 ft²=10.58 ft

answer: the height would be 10.58 ft.

7)
volume of a cone =(base x height)/3
base of a cone=πr²
therefore: 
199.23 cm³=πr²(9 cm)/3
r=√(199.23 cm³ / 3π cm)≈4.6 cm

answer: the radius would be 4.6 cm.

5 0
2 years ago
Please answer answer now fast
iren [92.7K]

Answer:

fge or fgc

I think that because its kinda like the same

5 0
2 years ago
Read 2 more answers
What is the speaker’s viewWhen I heard the learn'd astronomer;
Phantasy [73]
A. He feels tired and sick because the focus on the mechanical measurements of stars is not satisfying to him.<span>
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4 0
3 years ago
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