Someone please help me out

Mathematics

1 answer:

Ivan3 years ago

5 0

Answer:

${x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)( {x}^{2} - 1)$

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Slav-nsk [51]

Answer:

a) initial height = 0 m

b) 8 s

c) vertex = (4, 32)

maximum height = 32 m

Step-by-step explanation:

<u>Given equation</u>:

$h=-2t^2+16t$

where:

h is the height of the arrow about the ground (in metres)
t is the time (in seconds)

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

$\implies h=-2(0)^2+16(0)$

$\implies h=0$

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

$\implies -2t^2+16t=0$

Factor out -2t:

$\implies -2t(t-8)=0$

Therefore:

$\implies -2t=0 \implies t=0$

And:

$\implies t-8=0 \implies t=8$

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

$\implies h=-2(4)^2+16(4)$