If a cone has a radius of 6 cm and the height of 18 cm what is it's volume ?

In a random sample of citizens in one town, 21 out of 200 people were left handed. Which of these is the best inference to

Ronch [10]

Answer:

A about ten percent of the town is left handed

Step-by-step explanation:

20 of 200 is ten percent and this town could be an outlier in left handed populations.

6 0

2 years ago

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

The committee is planning a party and 150 guests are expected. Each package of plastic spoons contains 24 spoons.

puteri [66]

Answer:

7 packages

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Please help. Write an

Oliga [24]

Answer:

Step-by-step explanation:

THANKS for the points

5 0

2 years ago

What if this function simplified?

almond37 [142]

Hi!

Let's first expand the cotangent of theta.

You'll probably know that tangent will be "y/x", or $\frac{sin(x)}{cos(x)}$ , and cotangent is the reciprocal of this, meaning that it is "x/y" or $\frac{cos(x)}{sin(x)}$ .