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3 years ago

I don't know how to do this please help explain how to do it aswell as give the answer so i understand

Mathematics

1 answer:

Zinaida [17]3 years ago

4 0

We are given:

The function: y = -16t² + 64

where y is the height from ground, t seconds after falling

Part A:

when the droplet would hit the ground, it's height from the ground will be 0

replacing that in the given function:

0 = -16t² + 64

16t² = 64 [adding 16t² on both sides]

t² = 4 [dividing both sides by 16]

t = 2 seconds [taking square root of both sides]

Part B:

for second droplet,

height from ground = 16 feet

time taken = t seconds

acceleration due to gravity = 10 m/s²

initial velocity = 0 m/s

h = ut + (1/2)at² [second equation of motion]

16 = (0)(t) + (1/2)(10)(t²)

16 = 5t²

t² = 16/5

t = 1.8 seconds (approx)

Therefore, the second droplet takes the least amount time to hit the ground

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$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

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$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

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$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

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