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2 years ago

What equation represents this sentence?

Mathematics

2 answers:

Firdavs [7]2 years ago

8 0

Answer:

3-n=14

Step-by-step explanation:

Anna007 [38]2 years ago

3 0

Answer:

3-n=14

Step-by-step explanation less than a number!!! If a number is unkown it would be a variable, a letter,

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Determine whether the function shown has an inverse function

pychu [463]

Answer:

yes, it has an inverse

5 0

3 years ago

Read 2 more answers

How can you use a table with equally-spaced inputs to determine whether a relationship is linear? Exponential?

Helen [10]

Nooooooo imneedd piccc

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3 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

3 years ago

What is the distributive property of 5(y-4)

matrenka [14]

5(y - 4) = (5 * y) - (5 * 4) = 5y - 20

8 0

3 years ago

Read 2 more answers

A woman drives an SUV that gets 13 mi/gal (mpg). Her husband drives a hybrid that gets 65 mpg. Every week, they travel the sam

Nady [450]

Answer:

Option 1 will give a better overall mileage.

Step-by-step explanation:

The husband and wife travel the same number of miles each week.

Let's say each one travels x miles in 1 week.

Let e = fuel economy in mpg

Let v = amount of fuel in gallons

Let d = distance in miles

e = d/v

ve = d

v = d/e

Before modifying cars:

Wife:

d = x

e = 13

v = d/e = x/13

Husband:

d = x

e = 65

v = d/e = x/65

Combined fuel they both use in 1 week:

x/13 + x/65 = 5x/65 + x/65 = 6x/65 = 0.0923x

Option 1:

Wife changes to:

d = x

e = 15

v = d/e = x/15

Husband remains the same.

Combined fuel they both use in 1 week:

x/15 + x/65 = 13x/195 + 3x/195 = 16x/195 = 0.08205x

Option 2:

Husband changes to:

d = x

e = 80

v = d/e = x/80

Wife remains the same.

Combined fuel they both use in 1 week:

x/13 + x/80 = 80x/1040 + 13x/1040 = 93x/1040 = 0.08942x

The total fuel used in 1 week by both in terms of the miles, x, driven by both are:

Original case: 0.0923x

Option 1: 0.08205x

Option 2: 0.08942x

The lowest amount of fuel is 0.08205x in option 1.

Answer: Option 1 will give a better overall mileage.

5 0

3 years ago