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3 years ago

At Smith’s Bike Rentals, it cost $27 to rent a bike for 6 hours. How many dollars does it cost per hour of bike use

Mathematics

2 answers:

lilavasa [31]3 years ago

8 0

Answer:

$4.50 per hour

Step-by-step explanation:

Step 1: 27 divided by 6 is 4.50

Step 2: Double check your work by multiplying 4.50 times 6 to make sure you get 27

Delicious77 [7]3 years ago

5 0

To find how much it would cost for one hour you would need to divide 27 by 6.

27/6 = 4.5

Therefore it costs $4.5 to rent the bike per hour

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Phoenix [80]

Answer:

Vertical asymptote: x=2

Horizontal asymptote: y=5

Step-by-step explanation:

Hi there!

The parent function for a rational function has a horizontal asymptote at y=0 and a vertical asymptote at x=0.

First, we want to perform long division on 5x/x-2. Please check the image attached.

The result is $5+\displaystyle\frac{10}{x-2}$ .

Here are the transformations of a rational function:

$f(x)=\displaystyle\frac{a}{b(x-h)}+k$

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According to $5+\displaystyle\frac{10}{x-2}$ , we applied a horizontal translation of 2 units right and a vertical translation of 5 units up. Therefore, our asymptotes are now x=2 and y=5.

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2 years ago

What is the antiderivative of sin^2(x)cos^2(x)?

marin [14]

Answer:

$\frac{x}{8}-\frac{\sin(4x)}{32}+C$

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

$\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.$

And so inverting these,

$\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x)$ .

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

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So then,

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