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vova2212 [387]
3 years ago
15

A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear gr

aph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the total distance the car travels in this 30 second interval? Your must show your work but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.
I think I need to find the velocity equation then take the absolute value of the integral from 0 to 30, but I'm not sure how to find the velocity equation.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
8 0
From an acceleration-time graph, you can work out the area under the graph to find the velocity. There are two triangles on the graph as shown below. The total area of the triangles are

\frac{(10)(10)}{2}+ \frac{(20)(20)}{2}=250 ft/sec^{2}

Hence, the distance is 250×30=7500 ft

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Please help? I’m super lost...
babunello [35]

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function.  Watch and see.

a.  sin2\theta =-\frac{\sqrt{3} }{2}

Take the inverse sin of both sides.  When you do that, you are left with just 2theta on the left.  That's why you do this.

sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )

This simplifies to

2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2.  Those are:

2\theta =\frac{5\pi }{6} and

2\theta=\frac{7\pi }{6}

Divide both sides by 2 in both of those equations to get that values of theta are:

\theta=\frac{5\pi }{12},\frac{7\pi }{12}

b.  tan(7a)=1

Take the inverse tangent of both sides:

tan^{-1}(tan(7a))=tan^{-1}(1)

Taking the inverse tangent of the tangent on the left leaves us with just 7a.  This simplifies to

7a=tan^{-1}(1)

We look to the unit circle to find which values of <em>a</em> give us a tangent of 1.  They are:

7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}

Dibide each of those equations by 7 to find that the values of alpha are:

\alpha =\frac{5\pi}{28},\frac{\pi}{28}

c.  cos(3\beta)=\frac{1}{2}

Take the inverse cosine of each side.  The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems.  That simplifies to:

3\beta=cos^{-1}(\frac{1}{2})

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

3\beta =\frac{\pi}{6},3\beta  =\frac{5\pi}{6}

Divide each of those by 3 to find the values of beta are:

\beta =\frac{\pi }{18} ,\frac{5\pi}{18}

d.  sec3\alpha =-2

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

\frac{1}{cos(3\alpha) } =\frac{-2}{1}

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

cos(3\alpha)=-\frac{1}{2}

Now we will take the inverse cos of each side (same as above):

3\alpha =cos^{-1}(-\frac{1}{2} )

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

3\alpha =\frac{7\pi}{6},3\alpha  =\frac{11\pi}{6}

Dividing both of those equations by 3 gives us

\alpha =\frac{7\pi}{18},\frac{11\pi}{18}

And we're done!!!

8 0
2 years ago
What is the constant of proportionality in the equation 9y = 45x?
Mars2501 [29]
Divide by the coefficient of y.
  y = (45/9)x
  y = 5x

The constant of proportionality is 5.
3 0
3 years ago
Read 2 more answers
You need to write an essay that has at least 500 words. You have written 285 words so far. Write and solve an inequality that re
BabaBlast [244]

Answer:

The minimum number of words left to write is 215

Step-by-step explanation:

Let

w -----> the number of words left to write

we know that

The number of words left to write plus the words written so far must be greater than or equal to 500 words

Remember that the word "at least" means "greater than or equal to"

w+285\geq 500

Solve for w

Subtract 285 both sides

w\geq 500-285\\w\geq 215

The minimum number of words left to write is 215

4 0
3 years ago
Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a 20\%20%20, perc
motikmotik

Answer:

false

Step-by-step explanation:

Based on the information provided we can say that this is false. Since it is a board game and no actual information regarding each players position in the game has been presented, then each player has an equal chance of winning each game. Therefore since there is a total of 3 players the percent chance of winning each game for each player is 33% (100 / 3 = 33)

6 0
3 years ago
Brainliest + Points<br><br> Help please and explain!
Olin [163]

ADD = 300

ITI = 323

ON - 33 (Almost a 6 at the end!)

4 0
3 years ago
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