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mixas84 [53]
3 years ago
10

Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following func

tions, h(t) represents the height of the ball above the ground, in feet, with respect to time, t, in seconds, after the ball was thrown. Which of the following functions models the amount of time the ball is in the air?
h(t)= -4(t-1)^2 +3
h(t)= -16(t-1)^2 -4
h(t)= -16(t-1)^2 +12
h(t)= -16(t-1)^2 +28
Mathematics
1 answer:
lbvjy [14]3 years ago
8 0

Answer:

Your answer will be the third function

Step-by-step explanation:

The base function you need to know is h(t)= 1/2at^2

Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12

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PRETTY PLEASE HELP!! ILL GIVE BRAINLIEST! it’s due tonight :(
Marianna [84]

Answer:

a = 8 m

Step-by-step explanation:

Since, given is an isosceles right triangle.

So, by Pythagoras theorem:

{a}^{2}  +  {a}^{2}  =  {(8 \sqrt{2} )}^{2}  \\  \\ 2 {a}^{2}  = 128 \\  \\  {a}^{2}  =  \frac{128}{2}  \\  \\  {a}^{2}  = 64 \\  \\ a =  \sqrt{64}  \\  \\ a = 8 \: m

5 0
3 years ago
Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi
kompoz [17]

Answer:

The general solution is

y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

     + \frac{x^2}{2}

Step-by-step explanation:

Step :1:-

Given differential equation  y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

(D^4 -2D^3+D^2)y = e^x+1

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

                         m^4 -2m^3+m^2 = 0

                         m^2(m^2 -2m+1) = 0

(m^2 -2m+1) this is the expansion of (a-b)^2

                        m^2 =0 and (m-1)^2 =0

The roots are m=0,0 and m =1,1

complementary function is y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x

<u>Step 2</u>:-

The particular equation is    \frac{1}{f(D)} Q

P.I = \frac{1}{D^2(D-1)^2} e^x+1

P.I = \frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}

P.I = I_{1} +I_{2}

\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}

\frac{1}{D} means integration

\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx

applying in integration u v formula

\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx  } )\, dx

I_{1} = \frac{1}{D^2(D-1)^2} e^x

\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))

\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

I_{2}= \frac{1}{D^2(D-1)^2}e^{0x}

\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x

again integration  \frac{1}{D} x = \frac{x^2}{2!}

The general solution is y = y_{C} +y_{P}

         y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

      + \frac{x^2}{2!}

3 0
3 years ago
_____________________________
ValentinkaMS [17]

Step-by-step explanation:

hope it is helpful to you

7 0
3 years ago
Use (r,16) to solve y=2x-4
damaskus [11]
(x,y) = (r,16)

With this knowledge, plug in r for x, and 16 for y

16 = 2(r) - 4

Isolate the r, add 4 to both sides

16 (+4) = 2r - 4 (+4)

20 = 2r

Divide 2 from both sides

20/2 = 2r/2

r = 20/2

r = 10

hope this helps
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Answer:

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Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spacfund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.

Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spac

Step-by-step explanation:

fund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.

Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spac

8 0
2 years ago
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