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at a basketball game, members of the spirit club use a t-shirt cannon to launch team t-shirts to spectators in the stands. the equation below describes the height, h, of the t-shirt, t seconds after it is shot from the cannon c feet above the ground, at an initial velocity of v.
h = -16t 2 + vt + c
solve the equation for initial velocity, v. the cannon launched a t-shirt from an initial height of 5 feet. after 3 seconds the shirt has reached a height of 131 feet. use your equation from #1 to find the initial velocity of the t-shirt. show your work. what does the equation from #1 tell you about the value of the velocity, v, when t = 0? explain.

The required formula is . The initial velocity is 90 ft/s. At t=0, the value of v is undefined.

Step-by-step explanation:

The equation below describes the height, h, of the t-shirt, t seconds after it is shot from the cannon c feet above the ground, at an initial velocity of v.

We need to solve this equation for v.

Subtract c from both sides.

Add 16t² on both sides.

Divide both sides by t.

        .... (1)

Therefore the required formula is .

We need to find the velocity for

Initial height c = 5 feet

Time t = 3 sec

Height h = 131 feet

Substitute c = 5, t = 3 and h = 131 in equation (1).

Therefore the initial velocity is 90 ft/s.

Substitute t=0 in equation (1).

At t=0, the value of v is undefined.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

10 you would take 50/ .2

step-by-step explanation: