PLEASE ANSWER QUICKLY

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

monitta

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

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

Algebra I

Functions
Function Notation
Coordinates (x, y)

Calculus

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:

Step 1: Define

Identify

Point (0, 18)

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

Step 2: Find General Solution

Use integration

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

Step 3: Find Particular Solution

Substitute in point [Function]: $\displaystyle 18 = \frac{0^2}{16} + C$
Simplify: $\displaystyle 18 = 0 + C$
Add: $\displaystyle 18 = C$
Rewrite: $\displaystyle C = 18$
Substitute in C [Function]: $\displaystyle y = \frac{t^2}{16} + 18$

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

Unit: Integration

Book: College Calculus 10e

4 0

3 years ago

3h-2(4h-5)=10-5h A-0 B-4 C-infinity many solutions D-no solutions

Crank

Answer:

Step-by-step explanation:

3h - 8h + 10 = 10 - 5h

-5h + 10 = 10 - 5h

10 = 10

infinitely many solutions

7 0

3 years ago

A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is tr

DedPeter [7]

For this case we observe that the lines AB (red) and CD (purple) are cut at one point.
We observe that the slopes of both lines are different (they are not reciprocal opposites).
Therefore, the lines are not perpendicular.
Answer:
AB and CD are intersecting lines but are not perpendicular.
See attached image.

4 0

3 years ago

Read 2 more answers

Gina will package the trail mix into single servings. To do this, she needs to know the total volume of 1 serving.

mafiozo [28]

Answer:

150 cups and batch is 1 cup

Step-by-step explanation:

The total amount of snack mix for one recipe would be. 1. 1. 1 ... servings is 150 cups, and 1 batch is 10 cups, then she will need to bake 15 batches.

36 pages.

7 0

3 years ago

HELPPPPPPPPPPPPPPPP

Natasha_Volkova [10]

Answer:

it is A hope this helps

Step-by-step explanation:

7 0

3 years ago