A gas station stands at the intersection of a north-south road and an east-west road. A police car is traveling toward the gas station from the west, chasing a stolen truck which is traveling north away from the gas station. The speed of the police car is 90 mph at the moment it is 5 miles from the gas station. At the same time, the truck is 12 miles from the gas station going 70 mph. a. At this time, The distance between the car and truck is decreasing at a rate of mph :
b. Is the distance between the police car and the truck increasing or decreasing?
c. When the truck is 4 miles from the gas station and the police car is 3 miles from the gas station, how fast is the distance between the police car and the truck changing?
d. At the same instant, how fast is the angle changing which has the police car as its vertex?

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step-by-step explanation:

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation: