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zmey [24]
2 years ago
13

1/3 of wall painted in 1/4 of an hour

Mathematics
1 answer:
Tatiana [17]2 years ago
4 0
Whats the question? or any specific information
You might be interested in
Find the solution of the differential equation f' (t) = t^4+91-3/t
Lynna [10]

Answer:

\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Algebra I</u>

  • Functions
  • Function Notation

<u>Calculus</u>

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]:                                                               \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Addition/Subtraction]:                                                       \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

Integration Property [Multiplied Constant]:                                                         \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}

\displaystyle f(1) = \frac{1}{4}

<u>Step 2: Integration</u>

<em>Integrate the derivative to find function.</em>

  1. [Derivative] Integrate:                                                                                   \displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt
  2. Simplify:                                                                                                         \displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt
  3. Rewrite [Integration Property - Addition/Subtraction]:                               \displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt
  4. [1st Integral] Integrate [Integral Rule - Reverse Power Rule]:                     \displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt
  5. [2nd Integral] Integrate [Integral Rule - Reverse Power Rule]:                   \displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt
  6. [3rd Integral] Rewrite [Integral Property - Multiplied Constant]:                 \displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt
  7. [3rd Integral] Integrate:                                                                                 \displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C

Our general solution is  \displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C.

<u>Step 3: Find Particular Solution</u>

<em>Find Integration Constant C for function using given condition.</em>

  1. Substitute in condition [Function]:                                                               \displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C
  2. Substitute in function value:                                                                         \displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C
  3. Evaluate exponents:                                                                                     \displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C
  4. Evaluate natural log:                                                                                     \displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C
  5. Multiply:                                                                                                         \displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C
  6. Add:                                                                                                               \displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C
  7. Simplify:                                                                                                         \displaystyle \frac{1}{4} = \frac{456}{5} + C
  8. [Subtraction Property of Equality] Isolate <em>C</em>:                                               \displaystyle -\frac{1819}{20} = C
  9. Rewrite:                                                                                                         \displaystyle C = -\frac{1819}{20}
  10. Substitute in <em>C</em> [Function]:                                                                             \displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}

∴ Our particular solution to the differential equation is  \displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}.

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

7 0
2 years ago
Complete the square to solve the equation below.
IceJOKER [234]
I believe it’s D. X=2
7 0
2 years ago
Given the equation, 3x + y = 2, solve for y
Vladimir79 [104]
Your answer will be y=-3x+2
3 0
1 year ago
Read 2 more answers
PART 1 40 points+brainless<br>i need help with these 5 questions
Paladinen [302]

1)   1/243 (Fraction)

2)   Equal to 1

3)   1/x^7 (1 over x, x to the power of 7)

4)   4

5)   Equal to 1

Hope I helped

7 0
2 years ago
A- 10<br> b- 70 <br> c- 110<br> d- 170
mylen [45]

Step-by-step explanation:

step 1. 2x + 50 and 7x are vertical angles

step 2. vertical angles are equal

step 3. 2x + 50 = 7x

step 4. 5x = 50, x= 10

step 5. <AEB = 2x + 50 = 2(10) + 50 = 70.

3 0
1 year ago
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