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
ra1l [238]
2 years ago
5

Find the function y = f(t) passing through the point (0, 18) with the given first derivative.

Mathematics
1 answer:
monitta2 years ago
4 0

Answer:

\displaystyle y = \frac{t^2}{16} + 18

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
  • Coordinates (x, y)

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (0, 18)

\displaystyle \frac{dy}{dt} = \frac{1}{8} t

<u>Step 2: Find General Solution</u>

<em>Use integration</em>

  1. [Derivative] Rewrite:                                                                                         \displaystyle dy = \frac{1}{8} t\ dt
  2. [Equality Property] Integrate both sides:                                                        \displaystyle \int dy = \int {\frac{1}{8} t} \, dt
  3. [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:                 \displaystyle y = \int {\frac{1}{8} t} \, dt
  4. [Right Integral] Rewrite [Integration Property - Multiplied Constant]:           \displaystyle y = \frac{1}{8}\int {t} \, dt
  5. [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:              \displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C
  6. Multiply:                                                                                                             \displaystyle y = \frac{t^2}{16} + C

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

  1. Substitute in point [Function]:                                                                         \displaystyle 18 = \frac{0^2}{16} + C
  2. Simplify:                                                                                                             \displaystyle 18 = 0 + C
  3. Add:                                                                                                                   \displaystyle 18 = C
  4. Rewrite:                                                                                                             \displaystyle C = 18
  5. Substitute in <em>C</em> [Function]:                                                                                \displaystyle y = \frac{t^2}{16} + 18

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

Unit: Integration

Book: College Calculus 10e

You might be interested in
Company A: A 2-column table with 5 rows. The first column is labeled hours with entries 5, 12, 20, 29, 42. The second column is
ryzh [129]

Answer:

The correct answer is C.

Step-by-step explanation:

I took the test

8 0
3 years ago
Read 2 more answers
Para armar un prisma cuadrangular, Edgar trazó la plantilla y lo dividió en seis secciones, como se muestra en la imagen
Llana [10]

Answer:

1. x^{2} + x^{2} + (10\cdot x) \cdot (4)

Step-by-step explanation:

(This exercise is written in Spanish and therefore explanation will be held in such language)

El área de este polígono regular es la suma de las áreas de los 4 rectángulos y 2 cuadrados, es decir:

A_{tot} = 4\cdot A_{r} + 2 \cdot A_{c}

A_{tot} = 4 \cdot (10)\cdot x + 2\cdot x^{2}

El cual corresponde con la opción 1.

4 0
3 years ago
Niki makes the same payment every two months to pay off his $61,600 loan. The loan has an interest rate of 9.84%, compounded eve
mars1129 [50]
After a series of calculations, I found out that the interest he has to pay in total would be <span>$117,484.77.

You might use my answer in reviewing by using your solution also.

I hope my answer has come to your help. God bless and have a nice day ahead!
</span>
6 0
3 years ago
Read 2 more answers
Find the area of the shaded regions. Give your answers as a completely simplified exact value in terms of pi (no approximations)
KonstantinChe [14]
Answer = 7pi
Go in go knbjjjjb bxh b

7 0
3 years ago
Find the domain of: y = 3x + 1
Vedmedyk [2.9K]

y = 3x + 1

It's a linear function. The domain of linear function is the set of all real numbers.

D=\mathbb{R}=(-\infty,\ \infty)

6 0
3 years ago
Other questions:
  • una madre compra a su hija una caja de bombones favoritos la caja tiene forma de prisma triangular de 21 cm de largo y 12 cm de
    9·1 answer
  • the beginning balance of the monthly bank statement for Ignatius' checking account was 124.82, and the ending balance was 659.27
    11·1 answer
  • Is This Answer Correct (A)
    12·1 answer
  • Solve the following equation:<br> 6X – 2 = -14
    9·2 answers
  • Please help quickly thanks :)
    8·1 answer
  • Jeremiah opened a savings account with a one-time deposit of $500. His savings account will pay a 5% simple interest per year. H
    11·2 answers
  • Find the LCM of 220,440,660 by common division method​
    15·1 answer
  • PLEASE HELP FAST <br><br>WILL MARK BRAINLIST
    13·1 answer
  • 3n+7−2 i need help on this i just don't get it and this is combining like terms
    7·2 answers
  • Please help me with this
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!