Sin - 22.5 degrees =

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

2 years ago

Fun question: how can you make 11 out of 4 sevens?

Vladimir [108]

Answer: (7+1/7) *(7+7)

Step-by-step explanation:

7 0

2 years ago

What number goes on top and how do you solve it.

vekshin1

So basically, each number is equal to the two numbers below it added together.

See, 7 = 3+4, 8 = 5 +3, etc.

So, the top would be 16 + 17.

16 + 17 = 33

So 33 goes on top.

4 0

3 years ago

LXISSUU Simplify -8-1+4.2 Enter your answer in the box

jekas [21]

Answer:

-4.8

Step-by-step explanation:

4 0

3 years ago

What 2 numbers can be added to make 16 as well as multiplied to make -36

Sladkaya [172]

Answer:

18 and -2

Step-by-step explanation:

Let x = 1st no.

y = 2nd no.

(1) x + y = 16 (2) xy = -36

y = 16 - x x(16 - x) = -36

$16x - x^{2} = -36\\x^{2} - 16x - 36 = 0\\$

(x - 18)(x + 2) = 0

x = 18 or x = -2

y = 16 - 18 = -2

y = 16 -(- 2) = 16 + 2 - 18

The two numbers are 18 and -2

3 0

3 years ago