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3 years ago

Solve for x if 25^x+2=125^3x+4

Mathematics

2 answers:

bogdanovich [222]3 years ago

6 0

This one was pretty tough but Math way helped, you should try it out, it explains the problems so you can learn it. I got x = 0, 5

igomit [66]3 years ago

4 0

What you want to do is write the numbers with similar bases, and then you can cross the bases off. Like this:

25^x+2=125^3x+4
5^2(x+2)=5^3(3x+4)
Now you can cross the similar bases off.
2(x+2)=3(3x+4)
2x+4=9x+12
7x=-8
X=-8/7

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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

Need geometry help ASAP please!

tatiyna

Answer:

1. 121 π unit²

2. 143°

3. 151 unit²

Step-by-step explanation:

Area of a circle is given by the formula A = πr²

where

A is the area,

r is the radius of the circle

From the given diagram, we can see that the radius is 11, hence the area will be:

$A=\pi r^2\\A=\pi (11)^2\\A=121\pi$

The answer is $121\pi$ units^2

The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°

The measure of the central angle of the shaded sector is 143°

Area of a sector is given by the formula $A=\frac{\theta}{360}*\pi r^2$