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Elena-2011 [213]
1 year ago
11

The graph below shows the speed of a car that is driven through a town and then on a major highway. During which of the followin

g time intervals was the car stopped at a traffic light?

Mathematics
1 answer:
Varvara68 [4.7K]1 year ago
4 0

Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

<h3>When is a car stopped at a traffic light?</h3>

When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.

In this problem, the graph gives the <u>velocity as a function of time</u>, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

More can be learned about the interpretation of the graph of a function at brainly.com/question/3939432

#SPJ1

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Answer:

9x2x1 and 6x3x1

Step-by-step explanation:

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1
IceJOKER [234]

Solution to equationcosxtanx - 2 cos^2 x=-1 for all real values of x is  x=2k\pi + \frac{\pi}{6}  , x=2k\pi + \frac{5\pi}{6} .

<u>Step-by-step explanation:</u>

Here we have , cosxtanx - 2 cos^2 x=-1. Let's solve :

⇒  cosxtanx - 2 cos^2 x=-1

⇒  cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1

⇒  sinx = 2 cos^2 x-1

⇒  sinx = 2 (1-sin^2x)-1

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By quadratic formula :

⇒ sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}

⇒ sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}

⇒ sinx = \frac{-1 \pm3}{4}

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⇒ sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}

⇒ x=\frac{\pi}{6} , x=\frac{3\pi}{2}

But at x=\frac{3\pi}{2} we have equation undefined as cos\frac{3\pi}{2}=0 . Hence only solution is :

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Since , sin(\pi -x)=sinx

⇒ x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}

Now , General Solution is given by :

⇒ x=2k\pi + \frac{\pi}{6}  , x=2k\pi + \frac{5\pi}{6}

Therefore , Solution to equationcosxtanx - 2 cos^2 x=-1 for all real values of x is  x=2k\pi + \frac{\pi}{6}  , x=2k\pi + \frac{5\pi}{6} .

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