NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 229 t + 346 . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? How high above sea-level does the rocket get at its peak?

Step-by-step explanation:

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

to solve the equation can consider the quadratic formula given by

so let our a,b and c be -4.9,229 and 346 Thus substitute:

remove parentheses:

simplify square:

simplify multiplication:

simplify Substraction:

by simplifying we acquire:

since time can't be negative

hence,

at 48.2 seconds splashdown occurs

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

let a and b be -4.9 and 229 respectively thus substitute:

simplify which yields:

now plug in the maximum t to the function:

simplify:

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

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