Kalista practices the piano for at least 8 hours each week. Write an inequality for this situation

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

What is bigger 9/10 or 7/8

Nataliya [291]

You start by cross multiplying:
9 x 8 = 72
This is considered the fraction on the left's value.
You do the same for the other side:
10 x 7 = 70
This is considered the value of the fraction 7/8
72 has a greater value than 70.

Therefore, 9/10 is larger.

4 0

3 years ago

Read 2 more answers

PLEASE HELP!!!!!!!! WILL MARK BRAINLIEST!!!! aLSO 99 POINTS!!!!!!!! If a train is scheduled to go 87 and 1 half miles in 2 and 1

Roman55 [17]

The answer is C. 35 mph

3 0

2 years ago

Read 2 more answers

Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circl

torisob [31]

Please note that pi has just one value. The only difference stems from round-off error when you don't use all of the digits following "3.14159 ... " to represent the value of pi. The formula for circumference is C = 2 pi r, or C = pi d,
where r=radius and d=diameter.

Circle A: Diameter 9 inches and Circumference of 28.26 inches

If the diameter is 9 inches, then C = 28.26 inches = pi (9 inches). Divide 28.26 inches by 9 inches. Note that you MUST round off the ratio (pi) that you obtain, since 28.26 has 4 significant figures and 9 has just one.

28.26
------- = 3.14, but because 9 has just one significant figure, you must round
9 this 3.14 to just 3.

6 0

3 years ago

Question 12 onlyyyyyyyy

netineya [11]

For number 12 you need to make an expression using the information given. a) 25g + 18r + 15b could be the expression.
b) The variables would be 25g for the 25 gold seats, 18r for the 18 red seats and 15b for the 15 blue seats.
c) Plug in the number given according to the variables.
25(100) + 18(250) + 15(200)
2500 + 4500 + 3000
7000 + 3000
$10,000

5 0

3 years ago