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lianna [129]
3 years ago
9

Your mom's new car gets 32 miles per gallon and gasoline costs $1.99 per gallon. You are going to see Uncle buck for Christmas,

and you will be driving a total of 314 miles. About how much will be the gas for this trip cost?
Mathematics
1 answer:
Mashcka [7]3 years ago
6 0

The gas cost will be $19.53 for this trip.

Step-by-step explanation:

Given,

Distance covered by car per gallon = 32 miles

Cost of one gallon = $1.99

Unit rate in terms of miles;

32 miles = $1.99

1 mile = \frac{1.99}{32}\ Dollars

Therefore,

314 miles = Unit rate of mile * 314 miles

314 miles = \frac{1.99}{32}*314

314\ miles = \frac{624.86}{32}\\\\314\ miles=\$19.526

Rounding off to nearest hundredth;

314 miles = $19.53

The gas cost will be $19.53 for this trip.

Keywords: unit rate, multiplication

Learn more about unit rate at:

  • brainly.com/question/13076219
  • brainly.com/question/13096001

#LearnwithBrainly

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On Saturday, Mark sold gallons of lemonade. On the same day, Regan sold as much lemonade as Mark. How much lemonade, in gallons,
Ira Lisetskai [31]

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gallons.....

Step-by-step explanation:

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3 years ago
CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

y'=\cos^2(x)-\sin^2(x)

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

0=\cos^2(x)-\sin^2(x)

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

\cos(x)=-\sin(x)

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

5 0
3 years ago
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Answer:

A

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Formula: Radius, Height

Exact answer: V≈3.09×108

<u><em>Hope this helps.</em></u>

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