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Inessa [10]
2 years ago
15

The question is in the image

Mathematics
1 answer:
Drupady [299]2 years ago
4 0

Answer:

h(t) = -5*t^2 + 20*t  + 2

Step-by-step explanation:

First, we know that the motion equation of the ball will be quadratic, so we write the equation:

h(t) = a*t^2 + b*t + c

Now we need to work with the data in the table.

h(1) = 17

h(3) = 17

h(1) = h(2) = 17

Then we have a symmetry around:

(3 - 1)/2 + 1 = 2

Remember that the symmetry is around the vertex of the parabola, then we can conclude that the vertex of the parabola is the point:

(2, h(2)) = (2, 22)

Remember that for a quadratic equation:

y = a*x^2 + b*x + c

with a vertex (h, k)

we can rewrite our function as:

y = a*(x - h)^2 + k

So in this case, we can rewrite our function as:

h(t) = a*(t - 2)^2 + 22

To find the value of a, notice the first point in the table:

(0, 2)

then we have:

h(0) = 2 = a*(0 - 2)^2 + 22

         = 2 = a*(-2)^2 + 22

            2 = a*(4) + 22

           2 - 22 = a*(4)

            -20/4 = -5 = a

Then our function is:

h(t) = -5*(t - 2)^2 + 22

Now we just expand it:

h(t) = -5*(t^2 - 4*t + 4) + 22

h(t) = -5*t^2 + 20*t  + 2

The correct option is the first one.

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9/10 - 2/5 + 1/3

= 5/6 (Decimal:  0.8333333)


Subtract:
9/10 - 2/5 = 9/10 - 2 . 2/5 . 2
= 9/10 - 4/10 
= 9 - 4/10 
= 5/10 
= 1/2

The common denominator you can calculate as the least common multiple of the both denominators LCM ( 10, 5) = 10


Add: 1/2 + 1/3 = 1 . 3/2 . 3 + 1 . 2/3 . 2 
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= 3 + 2/6 

= 5/6



The common denominator you can calculate as the least common multiple of the both denominators LCM ( 2, 3) = 6

Answer in Lowest term is:  5/6 or Decimal:  0.8333333




Hope that helps!!!




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