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3 years ago

For the following right triangle, find the side length x

Mathematics

2 answers:

Aleks [24]3 years ago

7 0

Answer:

x = 25

Step-by-step explanation:

b² + h² = x²

24² + 7² = x²

576 + 49 = x²

625 = x²

√625 = √x²

25 = x

alexdok [17]3 years ago

3 0

Step-by-step explanation:

x² = 7² + 24²

x² = 49 + 576

x² = 625

x = 25

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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

3 years ago

What is the area of the sector of the circle below, if the radius is 5 m. and the central angle < AOB measures 88 °. (round a

MariettaO [177]

Answer:

b 19.2

Step-by-step explanation:

a = $\pi$ $r^{2}$ for a circle. We do not want to find the area for a whole circle. We only want to find the area for part of a circle. a hole circle is 360 degrees.

a = $\frac{88}{360}$ $\pi$ $r^{2}$

a = $\frac{88}{360}$ $\pi$ ( $5^{2}$ )

a = 19.2 rounded.

8 0

1 year ago

Read 2 more answers

It costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expres

Nataly [62]

Answer = $160

Using the formula 100+4n, we need to substitute 15 with n. Therefore making the formula, 100 + 4×15. 4×15 = 60. 60+100= $160.

-Hope it helps!

8 0

3 years ago

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Ali had his car repaired at Ace Auto. He was charged AED 50 per hour of labor plus AED 150 for parts. His total bill for the rep

AnnZ [28]

Step-by-step explanation:

x = hours Ali was charged for

150 + 50 x = 375

- 150 -150

50x = 225

÷ 50. ÷50

x = 4.5 hours