An auto mechanic charges (c) an initial fee of 50$ and then 40$ per hour. The graph of this model would be

Mathematics

1 answer:

barxatty [35]2 years ago

8 0

I believe the answer is option A. I’m very very sorry if this is wrong. Good luck with your studies!

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If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

Step 2: Differentiate

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

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

Unit: Differentiation

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3 years ago

X-2y=4 How to solve this

WARRIOR [948]

Since x does not contain the variable to solve for, move it to the right side of the equation by subtracting x from both sides
.−2y=−x+4
divide each term by −2 and simplify.
 the answer is y=x/2−2

slope= 1/2
y-intercept = -2

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What is the distance between each data point and the regression line called; tatistics for people who (think they) hate statisti

Nadusha1986 [10]

The vertical distance from the data points to the line are called the residuals.

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Round 2,583,999 to the nearest hundred thousand. I feel like the answer is 2,500,000 but the big numbers make me think it could

Lelechka [254]

Answer:

Its 2,600,000

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