Ask question

Ask question

All categories

4 years ago

14

Joshua Vernier received a raise after his first year on the job to $43,800 from his initial salary of $42,000 . What was his rai

se stated as a percentage ?

1 answer:

Vika [28.1K]4 years ago

8 0

The answer should be: 4.2857%
43,800-42000=1800.
1800 is 4.2857% of 42000

You might be interested in

Use natural logarithms to solve the equation. Round to the nearest thousandth. 6e4x - 2 = 3

frosja888 [35]

6 · e^(4x - 2) = 3
   e^(4x - 2) = .5
ln e^(4x - 2) = ln (.5)
4x - 2 = ln (.5)
   4x = ln (.5) + 2
   x = (ln (.5) + 2)/4
   x = 0.3267
   x ≈ 0.327

Answer: B

6 0

3 years ago

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>

Integrate [IBP]: $\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} - \int ({ae^{au} \cdot \frac{-cos(bu)}{b} }) \, du$
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>

Integrate [IBP]: $\int {e^{au}cos(bu)} \, du = \frac{e^{au}sin(bu)}{b} - \int ({ae^{au} \cdot \frac{sin(bu)}{b} }) \, du$
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>

Integrate [Alg - Back substitute]: $\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{a}{b} [\frac{e^{au}sin(bu)}{b} - \frac{a}{b} \int ({e^{au} sin(bu)}) \, du]$
[Integral - Alg] Distribute Brackets: $\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2} - \frac{a^2}{b^2} \int ({e^{au} sin(bu)}) \, du$
[Integral - Alg] Isolate Original Terms: $\int {e^{au}sin(bu)} \, du + \frac{a^2}{b^2} \int ({e^{au} sin(bu)}) \, du= \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}$
[Integral - Alg] Rewrite: $(\frac{a^2}{b^2} +1)\int {e^{au}sin(bu)} \, du = \frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}$
[Integral - Alg] Isolate Original: $\int {e^{au}sin(bu)} \, du = \frac{\frac{-e^{au}cos(bu)}{b} + \frac{ae^{au}sin(bu)}{b^2}}{\frac{a^2}{b^2} +1}$
[Integral - Alg] Rewrite Fraction: $\int {e^{au}sin(bu)} \, du = \frac{\frac{-be^{au}cos(bu)}{b^2} + \frac{ae^{au}sin(bu)}{b^2}}{\frac{a^2}{b^2} +\frac{b^2}{b^2} }$
[Integral - Alg] Combine Like Terms: $\int {e^{au}sin(bu)} \, du = \frac{\frac{ae^{au}sin(bu)-be^{au}cos(bu)}{b^2} }{\frac{a^2+b^2}{b^2} }$
[Integral - Alg] Divide: $\int {e^{au}sin(bu)} \, du = \frac{ae^{au}sin(bu) - be^{au}cos(bu)}{b^2} \cdot \frac{b^2}{a^2 + b^2}$
[Integral - Alg] Multiply: $\int {e^{au}sin(bu)} \, du = \frac{1}{a^2+b^2} [ae^{au}sin(bu) - be^{au}cos(bu)]$
[Integral - Alg] Factor: $\int {e^{au}sin(bu)} \, du = \frac{e^{au}}{a^2+b^2} [asin(bu) - bcos(bu)]$
[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

3 years ago

Read 2 more answers

What is a unit rate?

RideAnS [48]

Its a rate with 1as the second term

5 0

4 years ago

What is the value of (3/10)^3

Xelga [282]

Answer:

0.027

Step-by-step explanation:

8 0

3 years ago

Two angles are complementary. one angle measure 22 degrees. The other measure 2x degrees. solve for x.

snow_tiger [21]

Answer:

$x=34^\circ$

Step-by-step explanation:

Complementary angles sum up to $90^\circ$ .

$90-22=2x\\\\x=34^\circ$

Best Regards!

4 0

3 years ago

Read 2 more answers