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Dennis_Churaev [7]
3 years ago
9

What is 33.3 as a whole number?

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
7 0
If you mean by rounding, then it is 33

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A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is lo
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y=-\frac{8}{15}x^2+8x

Step-by-step explanation:

Consider the equation that shows flea's motion is y=ax^2+bx+c.

Since the origin is located at the point from where the flea jumped,

So, y=ax^2+bx+c  passes through (0,0).

That is, (0,0) must satisfy y=ax^2+bx+c,

0=a(0)^2+b(0)+c

\implies c =0

Now, it travels 15 cm horizontally from where it started.

That is, y=ax^2+bx+c  passes through (15,0).

0=a(15)^2+b(15)+c

0=a(225)+b(15)   (Because c=0)

225a+15b=0  ...... (1)

Again, it jumps from the ground to a height of 30 cm,

So, the y-coordinate of vertex of y=ax^2+bx+c is 30.

Now, the x-coordinate of vertex of the quadratic function must be half of the distance from its starting point to final point.

That is, x-coordinate of the vertex = \frac{15}{2} = 7.5,

Thus, vertex = (7.5, 30)

(7.5, 30) must satisfy y=ax^2+bx+c

That is, 30=a(7.5)^2+b(7.5)+c

30=56.25a+7.5b

56.25a+7.5b=30                ...... (2)

Equation (1) - 2 × equation (2),

225a - 112.5a = -60

112.5a = -60

\implies a = -\frac{60}{112.5}=-\frac{8}{15}

From equation (1),

225(-\frac{8}{15})+15b = 0

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15b=120

b=8

Substitute the values of a, b and c in the quadratic equation y=ax^2+bx+c,

y=-\frac{8}{15}x^2+8x

Which is the required quadratic equation.

6 0
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