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3 years ago

Solve for x for Juan’s salary plus $125 is $600.

Mathematics

1 answer:

Solnce55 [7]3 years ago

6 0

X=475

Subtract $600 form both sides
$600-$125=$475 | $600-$600=$0
$475+$125=$475

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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

7 0

3 years ago

A spring exerts a force of 6 N when stretched 3 m beyond its natural length. How much work is required to stretch the spring 2 m

lys-0071 [83]

Answer:

4Joules

Step-by-step explanation:

According to Hooke's law which states that extension of an elastic material is directly proportional to the applied force provide that the elastic limit is not exceeded. Mathematically,

F = ke where

F is the applied force

K is the elastic constant

e is the extension

If a spring exerts a force of 6 N when stretched 3 m beyond its natural length, its elastic constant 'k'

can be gotten using k = f/e where

F = 6N, e = 3m

K = 6N/3m

K = 2N/m

Work done on an elastic string is calculated using 1/2ke².

If the spring is stretched 2 m beyond its natural length, the work done on the spring will be;

1/2× 2× (2)²

= 4Joules

3 0

4 years ago

If the length of AO is three time the length of CO, THE LENGTH OF DC is ...

butalik [34]

The answer is D one third of AB.

8 0

3 years ago

Someone please help I’m begging!! I will mark brainlest!

lara31 [8.8K]

Answer:

Step-by-step explanation:

2(3x^2+23x+14)

2(3x^2+21x+2x+14)

2(3x(x+7)+2(x+7)

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3 years ago

Can somebody help?

Tatiana [17]

Answer:

a its the first one

Step-by-step explanation:

because i did the math and i have dont this question before

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4 years ago

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