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kap26 [50]
3 years ago
10

Neil drives at an average speed of 60 miles/hour to reach

Mathematics
1 answer:
nikklg [1K]3 years ago
8 0

Answer:

 480/(x+60) ≤ 7

Step-by-step explanation:

We can use the relations ...

 time = distance/speed

 distance = speed×time

 speed = distance/time

to write the required inequality any of several ways.

Since the problem is posed in terms of time (7 hours) and an increase in speed (x), we can write the time inequality as ...

 480/(60+x) ≤ 7

Multiplying this by the denominator gives us a distance inequality:

 7(60+x) ≥ 480 . . . . . . at his desired speed, Neil will go no less than 480 miles in 7 hours

Or, we can write an inequality for the increase in speed directly:

 480/7 -60 ≤ x . . . . . . x is at least the difference between the speed of 480 miles in 7 hours and the speed of 60 miles per hour

___

Any of the above inequalities will give the desired value of x.

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Answer:

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Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????
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Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do this:

tan (x+y) = \frac{sin (x+y)}{cos(x+y)}   (1)

We also have the following identities:

sin (a+b) = sin (a) cos(b) + sin (b) cos(a)

cos(a+b)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}   (2)

We can divide numerator and denominator from expression (2) by \frac{1}{cos(x) cos(y)} we got this:

tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}

And simplifying we got:

tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}

And that complete the proof.

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1-2cosx = 0
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