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2 years ago

This is VERY URGENT, so 50 points if you answer correctly!

Mathematics

1 answer:

mariarad [96]2 years ago

3 0

Answer:

The circumference is 31.43 cm

The ratio of the circumference to the diameter is equal to 3:1

Step-by-step explanation:

Thed formular for the circumference of a circle is 2 $\pi$ r or $\pi$ d

where d = diameter and r = radius

if d = 10 cm, and $\pi$ = 3.143, then circumference of the circle can be given as

3.143*10 = 31.43 cm

The ratio of the circumference to the diameter can be given as 31.43:10

and that can be given as 3.143:1

or 3:1, for the nearest whole number

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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

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2 years ago

Write an equation of the line that passes through the points (2, -3) and is parallel to the x axis.

podryga [215]

Answer:

y=-3

Step-by-step explanation:

If the line is parallel to the x-axis then it is a horizontal line with slope 0. These lines have form y=b where b is the y-intercept or y value of all points. y=-3 is the line since (2,-3) is on the line.

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2 years ago

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2 years ago

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2 years ago