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3 years ago

8

Josh Lisa and Vicki are one fourth of their own pizza each pizza was the same size but josh are 1 slice Lisa ate 2 slices and Vi

cki ate 3 slice how is this possible

1 answer:

ANEK [815]3 years ago

4 0

Josh ate 1/4
Lisa ate 2/8
Vicki ate 3/12

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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:

<u>Algebra I</u>

Factoring

<u>Calculus</u>

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:

<u>Step 1: Define</u>

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

<u />

<u>Step 2: Integrate Pt. 1</u>

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

<u>Step 3: Identify Variables</u>

<em>Set up u-substitution for the arctan trig integration.</em>

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

<u>Step 4: Integrate Pt. 2</u>

[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

Write an equation and solve.<br> How opd am I if 400 reduced by 2 times my age is 244?

seropon [69]

Answer:

78

Step-by-step explanation:

x = your age

400 - 2x = 244

subtract 400 from both sides of the equation:

-2x = -156

divide both sides by -2:

x = 78

4 0

3 years ago

Read 2 more answers

Can someone help me out plz ??!

scoray [572]

Answer:

≈ 62.8

Step-by-step explanation:

Using the equal ratios of

$\frac{areaof circle}{areaofsector}$ = $\frac{circleangle}{sectorangle}$ , that is

$\frac{100\pi }{sector}$ = $\frac{2\pi }{\frac{2\pi }{5} }$ = 5, thus

5 × sector = 100π ( divide both sides by 5 )

sector = 20π = 20 × 3.14 = 62.8 units²

7 0

3 years ago

for Anthony's birthday his mother is making cupcakes for his 12 friends at daycare the recipe calls for three and one third cup

charle [14.2K]

You subtract in this number sentence

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3 years ago

If a line with a slope of -2 crosses the y-axis at (0,3). What is the equation of the line?

baherus [9]

It technically would be y=3x-3 in the y=mx+b formula, but it could also be rewritten 3x-y=3. Hope this helps!

3 0

3 years ago