Two jet planes simultaneously started travelling in opposite directions from the same airport. four hours later they were 3800 miles apart. if one plane traveled 80 miles per hour faster than the other, what was the speed of each plane? a tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. after walking for a while, he gets tired and decides to get a taxi. the taxi gets him to the top travelling at a constant speed of 50 mph. if the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?

Step-by-step explanation:

let the speed of one plane=x

speed of other plane=x+80

time=4 hrs

then 4x+4(x+80)=3800

4x+4x+320=3800

8x=3800-320

or 8x=3480

x=435

speed of one plane=435 m/h

speed of other plane=435+80=515 m/h

2.

Let he walks x hrs

then he take a taxi for 2-x hrs

4x+(2-x)50=31

4x+100-50x=31

-46x=-69

so he walks 3/2 hrs=1.5 hrs

travels by taxi=2-1.5=0.5 hrs

distance traveled by taxi=0.5×50=25 miles

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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