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expeople1 [14]
2 years ago
6

Could i have some really really quick help?

Mathematics
2 answers:
nata0808 [166]2 years ago
8 0

Answer:

1125 m

Step-by-step explanation:

Given equation:

h=-5t^2+150t

where:

  • h = height (in metres)
  • t = time (in seconds)

<u>Method 1</u>

Rewrite the equation in vertex form by completing the square:

h=-5t^2+150t

\implies h=-5t^2+150t-1125+1125

\implies h=-5(t^2-30t+225)+1125

\implies h=-5(t-15)^2+1125

The vertex (15, 1125) is the turning point of the parabola (minimum or maximum point).  As the leading coefficient of the given equation is negative, the parabola opens downward, and so vertex is the maximum point.  Therefore, the maximum height is the y-value of the vertex: 1125 metres.

<u>Method 2</u>

Differentiate the function:

\implies \dfrac{dh}{dt}=-10t+150

Set it to zero and solve for t:

\implies -10t+150=0

\implies 10t=150

\implies t=15

Input found value of t into the original function and solve for h:

\implies -5(15)^2+150(15)=1125

Therefore, the maximum height is 1125 metres.

Irina-Kira [14]2 years ago
5 0
  • h=-5t²+150t

Convert to vertex form y=a(x-h)²+k

  • h=-5t²+150t+1125-1125
  • h=-5t²+150t-1125+1125
  • h=-5(t²-30t+225)+1125
  • h=-5(t-15)²+1125

Vertex at (15,1125)

As a is negative parabola is opening downwards hence vertex is maximum

  • Max height=1125m
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