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3 years ago

Why is 8:6 equivalent to 4:3 and 16:12

2 answers:

6 0

8:6 is equivalent to 4:3 because 8 divided 2 is 4 and 6 divided by 2 is 3. 8:6 is equivalent to 16:12 because 8 x 2 is 16 and 6 x 2 is 12

ki77a [65]3 years ago

3 0

8:6 is equivalent to 4:3 because if you divide the 8:3 by 2 then you would get 4:3 . And if you multiply the 8:6 by 2 then you would get 16:12

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Help with some algebra please?

kipiarov [429]

Vertex form is f(x) = a(x - b)^2 + c where the vertex is (b, c) and a is some constant.

So for the first part we have f(x) = a(x + 6)^2 - 1

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9a - 1 = 0 , a = 1/9

The other 3 are derived in the same way.
so required equation is f(x) = (1/9)(x + 6)^2 - 1

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3 years ago

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3 years ago

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TEA [102]

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3 years ago

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