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3 years ago

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Two trains 300 miles apart are heading toward each other on the same track. The first one travels at 100 miles per hour and the

second at 50 miles per hour. As the trains depart, a jet-powered drone flying 200 miles per hour leaves the first train and heads for the second. Upon reaching it, the drone instantaneously turns around and heads back towards the first. The drone continues back and forth in this manner. How far in miles will the drone fly before being crushed between the two trains?

1 answer:

Setler [38]3 years ago

8 0

Answer:

400

Step-by-step explanation:

u = 50 km/hr

v = 100 km/hr

d = 300 km

b = 200 km/hr

= b*d/(u+v)

= 200* 300/(50+100)

= 400

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Answer:

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$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

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------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

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$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

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