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r-ruslan [8.4K]
3 years ago
14

Plz help ill give u brainlist

Mathematics
1 answer:
monitta3 years ago
4 0
A² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
b = √3 
b  1.73 (nearest hundredth)

Answer: b =  1.73

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

\sin(\alpha) =  \dfrac{\text {opp}}{\text{hyp}}

\sin(\alpha) =  \dfrac{\text {1}}{\text{2}}

\alpha =  \sin^{-1} \bigg ( \dfrac{1}{2}  \bigg)

\alpha = 30 \textdegree

Answer: 30°

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

\cos(\beta) = \dfrac{\text {adj}}{\text{hyp}}

\cos(\beta) = \dfrac{\text {1}}{\text{2}}

\beta = \cos^{-1} \bigg ( \dfrac{1}{2} \bigg)

\beta = 60 \textdegree

Answer: 60°
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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:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. 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:

<u>Step 1: Define</u>

<em>Identify</em>

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

<u>Step 2: Differentiate</u>

  1. [Function] Derivative Rule [Product Rule]:                                                   \displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  2. 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)]
  3. Basic Power Rule:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  4. 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
2 years ago
Arithmetic and Geometric Sequences (Context)
V125BC [204]

The formula for compound interest

A = P( 1 + r/n) ^ (nt)

A is the amount in the account at the end

P is the principal balance or the amount initially invested

r is the annual interest rate in decimal form

n is the number of times it is coupounded per year

t is the number of years

A = 1800 ( 1+ .0375/1) ^ (1*6)

A = 1800 ( 1.0375)^6

A = 2244.92138

Rounding to the nearest cent

A = 2244.92

7 0
1 year ago
Please help! Help is appreciated! :)
-Dominant- [34]
Your answer to the question is A
4 0
3 years ago
A mint produces 150,000 souvenir coins each year. In a random sample of 400 coins, 3 have a misprint. Predict the number of coin
Tema [17]
150,000 / 400 = 375. 375(3)= 1,125 misprints per year. hope this helps!
5 0
3 years ago
Solve the inequality:<br> 4 +5t &lt; 19
iogann1982 [59]
4 + 5t < 19
Subtract 4 from both sides
5t < 19 - 4 or 5t < 15
Divide both sides by 5
t < 3
4 0
3 years ago
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