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iVinArrow [24]
2 years ago
10

A rock is launched from a cannon. After 1 second, the rock is 58 feet in the air; after 2 seconds, it is 112 feet in the air. Us

ing the quadratic function, find the height, in feet, of the rock after 10 seconds in the air
Mathematics
1 answer:
max2010maxim [7]2 years ago
8 0

Answer:

Step-by-step explanation: This is the quadratic function:

h(x)=ax²+bx+c

We have two points:

(1,58)

(2,112)

Now, we calculate this quadratic funtion.

we assume that h(0)=0

Therefore:

a(0)²+b(0)+c=0

c=0

(1,58)

a(1)²+b(1)=58

a+b=58  (1)

(2,112)

a(2)²+b(2)=112

4a+2b=112

2a+b=56  (1)

With the equations (1) and (2) we make a system of equations:

a+b=58

2a+b=56

we can solve this system of equations by reduction method.

-(a+b=58)

2a+b=56

---------------------

a=-2

-2(a+b=58)

2a+b=56

-------------------

      -b=-60  ⇒  b=60

The function is:

h(x)=ax²+bx+c

h(x)=-2x²+60x

Now find the height, in feet, of the rock after 10 seconds in the air.

h(10)=-2(10)²+60(10)

h(10)=-200+600=400

Answer: 400 ft.

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Step-by-step explanation:

aₙ = a₁ + (n - 1) × d  

aₙ = the nᵗʰ term in the sequence

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Using the above formula to solve the first part, we have :

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Step-by-step explanation:

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