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]
3 years ago
5

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

Mathematics
1 answer:
monitta3 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
in one year angelicas height went from 60 inches to 63 inches. What as the percent of increase in angelicas height?
SpyIntel [72]
5% total increase, as 3 to 60 is 1/20 (5%)
7 0
4 years ago
Interior and Exterior Angle polygons. I need help to find the measure of a regular decagon. To find each interior angle and to f
Nadusha1986 [10]
<h3>Answer:</h3>
  • interior: 144°
  • exterior: 36°
<h3>Step-by-step explanation:</h3>

It may be easiest to remember that the sum of exterior angles of any convex polygon is always 360°.

Your decagon has a sum of exterior angles that is 360°. Since it is a regular 10-sided polygon, each one is 1/10 that value: 36°.

The measure of each exterior angle is 36°.

The measure of an interior angle is the supplement of the exterior angle. Each interior angle of the regular 10-sided polygon will be ...

... 180° -36° = 144°

The measure of each interior angle is 144°.

_____

A formula often used for the sum of the measures of the interior angles is ...

... interior angle total = (n -2)×180°

For a 10-sided figure, the interior angle total is ...

... (10 -2)×180° = 1440°

When this sum is divided into 10 equal angles, the measure of one interior angle is ...

... 1440°/10 = 144° . . . . . agrees with the above computation

The exterior angle measure is the supplement of this:

... 180° -144° = 36° . . . . . exterior angle measure; agrees with the above computation

5 0
4 years ago
bill has to figure out the area of his square yard. He knows that one side of his yard is equal to the length of his garage. The
Blababa [14]
The area is 256, since the yard is square, all sides are the same length. We're then given the length, being that it is equal to the side of the garage. (16) We multiply 16 by 16, and voila
6 0
3 years ago
Read 2 more answers
Lacy walks 3 miles in one hour. How many feet does Lacy walk in 30 minutes
Juliette [100K]
First we have to convert 1 mile into feet, then divide by two to find how many feet she walked in a half an hour.

There are 5280 feet in a mile.
5280/2640

The correct answer is 2640.

Hope this helped! Please comment or DM me if you have any questions or still need help. :)
5 0
3 years ago
124\7 93 <br> Which one is bigger?
Alchen [17]

Answer:

93 is bigger cause if u divide 124 by 7 u get 17

4 0
4 years ago
Other questions:
  • Brandon is half as old as his brother Ryan.Ryan is one eight the age of his fatherb if their father is 2 years old. How old are
    7·1 answer
  • Bengus the expert blacksmith forged 16 swords from copper, 25 swords from iron, and 20 swords from mythril.
    12·2 answers
  • Dimitri is helping to plan the school talent show. Each performer for the talent show has 6 66 minutes for his or her performanc
    5·1 answer
  • Arielle earned 84 last week and spent 10.50 going to the movies. What percent of the money earned did ar
    8·1 answer
  • 10 Points!! Please Help!
    14·1 answer
  • 1453897 what is the place value of 4
    12·1 answer
  • Choose the correct correspondence<br> D &lt;-&gt;<br> Options <br> 1.R<br> 2.K<br> 3.O
    15·2 answers
  • Hiii i need help with this!
    12·1 answer
  • 1 point
    14·1 answer
  • PLEASE HELP ME!! I WILL GIVE BRAINLIEST TO THE FIRST TO HELP ME, AS WELL AS 5 STARS AND A THANK YOU!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!