3 years ago

Please help on this I will mark brainlist!!!

Mathematics

1 answer:

ad-work [718]3 years ago

3 0

9d=h

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A plane intersecting a double-napped cone is perpendicular to the central axis. Which conic section is formed?

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Philip shoots an arrow from the top of a hill into the ground. the flight of the arrow can be modeled with the quadratic functio

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(a)Time taken to reach the ground, x=6 seconds

(b)Maximum height of the arrow during its flight =101.25 feet

Step-by-step explanation:

Given the quadratic function which models the flight of the arrow:

$y=-5x^2+15x+90$

Where:

y represents the vertical height of the arrow, in meters; and
x represents the time, in seconds.

(a)Positive Zero

$-5x^2+15x+90=0\\-5(x^2-3x-18)=0\\-5(x^2-6x+3x-18)=0\\-5(x(x-6)+3(x-6))=0\\-5(x+3)(x-6)=0\\x+3=0\:or\:x-6=0\\x=-3,x=6$

In 6 seconds, the arrow will hit the horizontal plane, i.e. the ground.

(b)

$y=-5x^2+15x+90\\y-90=-5(x^2-3x)\\y-90-5(\frac{9}{4}) =-5(x^2-3x+(\frac{3}{2} )^2)\\y-101.25=-5(x-\frac{3}{2} )^2\\y=-5(x-\frac{3}{2} )^2+101.25$

Comparing with the vertex form:

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

Our vertex, (h,k)=(1.5, 101.25)

Maximum Value of y=101.25

The maximum value of y represents the maximum height of the arrow during its flight, which is 101.25 feet.

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4 years ago