1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timurjin [86]
2 years ago
5

Find the particular solution of the differential equation? /=5^3+9^2, when =1, =8

Mathematics
1 answer:
kipiarov [429]2 years ago
3 0

Answer:

\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}

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>

  • Exponential Rule [Rewrite]:                                                                           \displaystyle b^{-m} = \frac{1}{b^m}

<u>Calculus</u>

Derivatives

Derivative Notation

Solving Differentials - Integrals

Integration Constant C

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

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

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

Step-by-step explanation:

*Note:

Ignore the Integration Constant C on the left hand side of the differential equation when integrating.

<u>Step 1: Define</u>

\displaystyle \frac{ds}{dt} = 5t^3 + \frac{9}{t^2}

t = 1

s = 8

<u>Step 2: Integrate</u>

  1. [Derivative] Rewrite [Leibniz's Notation]:                                                     \displaystyle ds = (5t^3 + \frac{9}{t^2})dt
  2. [Equality Property] Integrate both sides:                                                     \displaystyle \int {} \, ds = \int {(5t^3 + \frac{9}{t^2})} \, dt
  3. [Left Integral] Reverse Power Rule:                                                             \displaystyle s = \int {(5t^3 + \frac{9}{t^2})} \, dt
  4. [Right Integral] Rewrite [Integration Property - Addition]:                           \displaystyle s = \int {5t^3} \, dt + \int {\frac{9}{t^2}} \, dt
  5. [Right Integrals] Rewrite [Integration Property - Multiplied Constant]:     \displaystyle s = 5\int {t^3} \, dt + 9\int {\frac{1}{t^2}} \, dt
  6. [Right Integrals] Rewrite [Exponential Rule - Rewrite]:                               \displaystyle s = 5\int {t^3} \, dt + 9\int {t^{-2}} \, dt
  7. [Right Integrals] Reverse Power Rule:                                                         \displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{t^{-1}}{-1}) + C
  8. [Right Integrals] Rewrite [Exponential Rule - Rewrite]:                               \displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{1}{t}) + C
  9. Multiply:                                                                                                         \displaystyle s = \frac{5t^4}{4} + \frac{9}{t} + C

<u>Step 3: Solve</u>

  1. Substitute in variables:                                                                                 \displaystyle 8 = \frac{5(1)^4}{4} + \frac{9}{1} + C
  2. Evaluate exponents:                                                                                     \displaystyle 8 = \frac{5}{4} + \frac{9}{1} + C
  3. Divide:                                                                                                           \displaystyle 8 = \frac{5}{4} + 9 + C
  4. Add:                                                                                                               \displaystyle 8 = \frac{41}{4} + C
  5. [Subtraction Property of Equality] Isolate <em>C</em>:                                               \displaystyle \frac{-9}{4} = C
  6. Rewrite:                                                                                                          \displaystyle C = \frac{-9}{4}

Particular Solution: \displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}

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

Unit: Differentials Equations and Slope Fields

Book: College Calculus 10e

You might be interested in
Rocky lends $3000 to Ken at 10% per annum and the Ken lends the same sum to like at 12% per annum. Find kens gain over a period
zalisa [80]
Let t = time

Between Rocky and Ken:

3000 + 3000(.10)(t)

Between Ken and Mike:

3000 + 3000(.12)(t)

Kens gain = The difference

6 0
3 years ago
Carl works at a garment factory and sews buttons on shirts. For each shirt he completes that passes inspection, he earns $2. How
Ratling [72]

do 2*52 which gives you 104 so 104 dollars

6 0
3 years ago
Ariana plans to use $260 less than three-fourths of savings to buy a car. If the purchase price of the car is 9,340, how much do
tangare [24]

She has $12,488 in savings

Step-by-step explanation:

Ariana plans to use $260 less than three-fourths of savings to buy a car.

If the purchase price of the car is 9,340, we need to find how much

she has in savings

To find the savings

  • Assume that she has $x in savings
  • Write an equation of x
  • Solve the equation to find x

∵ She has $x in savings

∵ She plans to use $260 less than three-fourths of savings

- Three-fourths means \frac{3}{4} and less than means subtract

∴ She plans to use \frac{3}{4} x - 26

∵ The purchase price of the car is 9,340

- Equate the expression of x by 9,340

∴ \frac{3}{4} x - 26 = 9,340

Now let us solve the equation

∵ \frac{3}{4} x - 26 = 9,340

- Add 26 to both sides

∴ \frac{3}{4} x = 9,366

- Divide both sides by \frac{3}{4}

∴ x = $12,488

She has $12,488 in savings

Learn more:

You can learn more about word problems in brainly.com/question/3950386

#LearnwithBrainly

7 0
3 years ago
What is the percent of the figure is shaded?
Oxana [17]

Answer:

7/10 is shaded

so 7/10×100= 70%

7 0
2 years ago
Read 2 more answers
The difference of two numbers is 15. Five times the smaller is the same as 9 less than twice the larger. Find the numbers
Usimov [2.4K]

Answer:

x= -13

y= -28

Step-by-step explanation:

To find the two numbers, write a system of equations with x as one number and y as another:

x-y=15

5x=2y-9

Use substitution to substitute one equation into another. Then solve for the variable.

x=15+y into 5x=2y-9

becomes

5(15+y) = 2y-9

75+5y = 2y- 9

75+3y= -9

3y = -84

y= -28

To find x, substitute y= -28 into one equation.

x - (-28) = 15

x+28 =15

x = 15-28

x=-13




6 0
3 years ago
Other questions:
  • A jacket is on sale for 20% off the regular price. The sale price ism$50.00. What is the regular price of the jacket?
    15·2 answers
  • Find each product by distributing.<br> (2a - 5)(a? – 2a + 1)
    13·1 answer
  • It takes Lucas 3 hours to cycle from his home to his friends village but if travels 5 mph slower, it will take him 1.5 hours lon
    10·1 answer
  • What is the value of x
    15·1 answer
  • How can you express (15 + 30) as a multiple of a sum of whole numbers with no common factor?
    10·2 answers
  • Help me please trig hw
    7·1 answer
  • 5+5 also i like people
    15·2 answers
  • A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of t
    5·2 answers
  • Please help me solve this.<br> 15x+8=-2+14x
    9·1 answer
  • Translate this expression:<br> 8 less than y
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!