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3 years ago

What is the value of x if f(x) = 76

Mathematics

1 answer:

GaryK [48]3 years ago

3 0

Answer:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x

No solution

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Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

2 years ago

7(x+2)=2x-1 solve for the variable

Len [333]

Answer:

x = - 3

Step-by-step explanation:

Given

7(x + 2) = 2x - 1 ← distribute parenthesis on left side

7x + 14 = 2x - 1 ( subtract 2x from both sides )

5x + 14 = - 1 ( subtract 14 from both sides )

5x = - 15 ( divide both sides by 5 )

x = - 3

7 0

3 years ago

URGENT HELP! Graph and indicate the 3rd Critical Point

atroni [7]

6 is the critical point

4 0

3 years ago

Question 2 says: With out multiplying, determine the sign of the product

DiKsa [7]

Count the negative signs, if you get an odd number of negative signs, the product is a negative. If you get an even number of negative signs, the product is a positive.
in this case, there are two negatives, the the product is a positive number

3 0

3 years ago

9 + 5 + 5+1 = 20 What is the average value?

Bezzdna [24]

Answer:

The average value is 5.

Step-by-step explanation:

9 + 5 + 5 + 1 = 20, divide 20 by 4 (the amount of numbers that are being added), you have your average.

6 0

3 years ago

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