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3 years ago

WILL MARK BRAINLIST!! SOS MATH. Look at picture

Mathematics

1 answer:

Aleks [24]3 years ago

5 0

Answer:

Yes, the transformation is a 270° clockwise rotation

Step-by-step explanation:

(-3, 4) ,( -4, 7) and (-2,7) transformed to (-4, - 3), (-7, -4) and (-7, -2).

Rule for 270° clockwise rotation:

(x, y) --> (- y, x)

A transformation that doesn't change the size or shape of an object.

So answer is:

Yes, the transformation is a 270° clockwise rotation

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Graph a line that contains the point ( 3 , -6) and has a slope of 1/2

irina [24]

You need to physically draw that on a graph

3 0

3 years ago

What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?

scoray [572]

Answer:

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to c} x = c$

Special Limit Rule [L’Hopital’s Rule]:
$\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]:
$\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$
Derivative Rule [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

Identify given limit.

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}$

Step 2: Find Limit

Let's start out by directly evaluating the limit:

[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}$

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

[Limit] Apply Limit Rule [L' Hopital's Rule]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}$
[Limit] Differentiate [Derivative Rules and Properties]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}$
[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}$

∴ we have evaluated the given limit.

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Learn more about limits: brainly.com/question/27807253

Learn more about Calculus: brainly.com/question/27805589

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

Unit: Limits

3 0

1 year ago

Verify: cos(2A)=(cotA-tanA)/cscAsecA

kolbaska11 [484]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cot A = $\frac{cosA}{sinA}$ , tanA = $\frac{sinA}{cosA}$ , cscA = $\frac{1}{sinA}$ , secA = $\frac{1}{cosA}$

Consider the right side

$\frac{cotA-tanA}{cscAsecA}$

= $\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }$

= $\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }$

= $\frac{cos^2A-sin^2A}{sinAcosA}$ × sinAcosA ( cancel sinAcosA )

= cos²A - sin²A

= cos2A

= left side ⇒ verified

5 0

3 years ago

Madeline is working to teach her 4-year-old daughter, eliza, how to count. she places ten buttons in one row with very little sp

Lelechka [254]

Answer: This is an example of Centration.

Centration refers to the tendency to focus on only one aspect of a situation, problem or object. For example: a child may complain that there is little ice cream left in a big bowl. The child will be satisfied if the ice cream is transferred to a little bowl, even though nothing is added, because he only considers how full the bowl appears to be.

6 0

3 years ago

The perimeter of an isosceles triangle is 71 centimeters. The measure of one of the sides is 22 centimeters. What are all the po

Paha777 [63]

An isosceles triangle has 2 sides the same length and 1 side of a different length

so if the 22 is the identical length then you would have another side of 22
and the 3rd side would be 71 - 22 -22 = 27 cm
so you could have 22 and 27

if the 22 is the odd length side then you would have 71 - 22 = 49 / 2 = 24.5
so you could have 24.5 and 24.5

3 0

3 years ago