Flying against the wind, an airplane travels 3850 km in 7 hours. Flying with the wind, the same plane travels 4350 km in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?

The rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr

Explanation:

Let Va = the velocity of the airplane

Let Vw = the velocity of the wind

When flying with the wind:

(Va+Vw)*(5 hours) = 4350

5Va + 5Vw = 4350

5Vw = 4350 - 5Va

Vw = 870 - Va

When flying against the wind:

(Va-Vw)*(7 hours) = 4200 km

7Va - 7Vw = 4200

Substitute 870-Va for Vw and solve for Va:

7Va - 7(870-Va) = 3850          

7Va -6090 + 7Va = 3850

14Va = 9940

Va = 710 km/hr

Rate of wind:

Vw = 870 - Va

     = 870 - 710

     = 160 km/hour

Therefore, the rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr

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.

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step-by-step explanation:

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