I WILL MARK BRAINLIST

Find the slope of the line that passes through (1, 8) and (10, 1).

leonid [27]

Answer:

$m = \frac{1 - 8}{10 - 1} = - \frac{ 7}{9} \\$

Slope(gradient)=

$-\frac{7}{9}$

Good luck!

Intelligent Muslim,

From Uzbekistan.

8 0

2 years ago

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Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

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

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

2 years ago

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I need help please I suck at math

Scrat [10]

It’s b I’m positive because I did 1.25 to the power of 3 and put that into fractional form

3 0

2 years ago

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You buy a 1:1000 scale model of the Statue of Liberty during a trip to New York City. The height of the model is 9.3 centimeters

yanalaym [24]

The Statue of Liberty is 93 meters tall. If you have a model that is 9.3 centimeters and is 1/1000 the size of the actual Statue, then you would multiply the model by 1000 to get 9,300 centimeters. To get this number in meters, you would divide your result by 100. This would give you 93 meters.

Sorry if the explanation is worded poorly, the answer is 93 meters.

7 0

3 years ago

Need help, all work needs to be provided as well, 100pts, and brainliest . please no incorrect answers and/or trolls.

LiRa [457]

Tell me if this is fine. I wasn't able to edit the document you gave me, so i made one on my own. If you require a full graph, comment, and ill make it again. (I put 2, select the best one)

3 0

3 years ago

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