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3 years ago

About geometry transformation

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

8 0

Answer:

A geometric object is represented by its vertices (as position vectors) A geometric transformation is an operation that modifies its shape, size, position, orientation etc with respect to its current configuration operating on the vertices (position vectors).

You might be interested in

The curve

kherson [118]

Answer:

Point N(4, 1)

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

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

3 years ago

(6x+3) (4x-5) (simp) I try to do this one and got the answer 24x^2-18x-15 but I was told it was wrong

Gemiola [76]

Answer:

(6x+3) (4x-5) = 24x^2 -30x +12x -15 = 24x^2 -18x -15

I get the same answer. I guess we're both wrong?

Or do they want it reduced to:

8x^2 -6x -5

Step-by-step explanation:

8 0

3 years ago

1) What is 2 to the power of 6? 2) What is 17 by the power of 2?

hammer [34]

Answer:

2 to the power of 6 is 32

17to the power of 2 is 289

Step-by-step explanation:

Exponents are just multiplying the same number multiple times. so 2 to the power of 6 is 2*2*2*2*2*2. and 17 to the power of 2 is 17*17 = 289. to the power of is also written with a shift 6. ^

7 0

3 years ago

What is the difference between | -3 | and -3

sineoko [7]

Answer:

Step-by-step explanation:

l -3 l - (-3)

3 + 3

5 0

2 years ago

What is the following qoutient? 3√8/4√6

kogti [31]

Answer:

3 sqrt(3)

----------- or -----------

2 sqrt(3) 2

Step-by-step explanation:

3 sqrt(8)

-----------------

4 sqrt(6)

3 sqrt(4*2)

-----------------

4 sqrt(3*2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

3 sqrt(4) sqrt(2)

------------------------

4 sqrt(3) sqrt(2)

Canceling the sqrt(2) and sqrt(4) is 2

3*2

----------

4 sqrt(3)

-----------

2 sqrt(3)

We can simplify the answer be multiplying by sqrt(3)/sqrt(3)

3 sqrt(3)

----------- * ----------

2 sqrt(3) sqrt(3)

3 sqrt(3)

-----------

2 *3

sqrt(3)

-----------

3 0

3 years ago

About geometry transformation ​

About geometry transformation