Evaluate the integral. (See picture)

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

Rectangle J’K’L’M’ shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applie

7nadin3 [17]

The answer is C. (16, 7)

due to every x is incremented by 10

and every y is incremented by 3

the position of T is (6, 4) so the position of T' becomes (6+10, 4+3) which is (16, 7)

5 0

3 years ago

Solve for 'm': m - 7 = -13 + m

lesya [120]

Answer:

m - 7 = -13 + m

Step-by-step explanation:

8 0

4 years ago

5. Use your answers from Questions 3 and 4 to help you answer this question.

Artist 52 [7]

Answer:

^

Step-by-step explanation:

6 0

3 years ago

State the degree: 11m^3n^2p

Vadim26 [7]

<h3>Answer: 6</h3>

Explanation:

Using the rule that x = x^1, we can rewrite the p as p^1

So 11m^3n^2p is the same as 11m^3n^2p^1

The exponents are: 3, 2, 1

Those exponents add up to 3+2+1 = 6

The degree of a monomial like this is simply equal to the sum of the exponents.

7 0

3 years ago

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