Mathematics, 26.07.2019 08:30 spalmer8

2. a rocket is launched from a cliff. the relationship between the height of the rocket, ℎ, in feet, and the time since its launch, , in seconds, can be represented by the following function: ℎ() = −162 + 80 + 384. a. sketch the graph of the motion of the rocket. b. when does the rocket hit the ground? c. when does the rocket reach its maximum height? d. what is the maximum height the rocket reaches? e. at what height was the rocket launched?

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The model that represents the relationship between the height of the rocket and time is given by:
h(t)=-16t^2+80t+384
b]When does the rocket hit the ground?
when the rocket hits the ground h(t)=0
thus:
0=-16t^2+80t+384
solving the above quadratic we get:
t=-3 or t=8
since there is not negative time, we conclude that the rocket will hit the ground after 8 seconds.

c] When does the rocket reach its maximum height?
when the rocket riches the maximum time, dh/dt=0
thus differentiating our function and equating it to zero then solve for t we get:
-32t+80=0
t=80/32
t=2.5
thus the rocket reached the maximum height after 2.5 sec

d] The maximum height will be as follows:
time taken to reach maximum height is t=2.5
thus
h(2.5)=-16(2.5)^2+80(2.5)+384
h(2.5)=484 ft
Maximum height is at 484 ft.

e] At what height was the rocket launched?
at the time the rocket was launched, t=0
thus
h(0)=-16(0)^2+80(0)+384
h(0)=384 ft
The rocket was launched at the height of 384 ft

a] The sketch of the function will be:

2. a rocket is launched from a cliff. the relationship between the height of the rocket, ℎ, in feet,

2. a rocket is launched from a cliff. the relationship between the height of the rocket, ℎ, in feet,

Answer from: Quest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

Answer from: Quest

plz yuo

step-by-step explanation:

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