(5a^2 - b^2) - (4a^2 + 3b^2) - (a^2 - 7b^2)

Answer: 3.675 seconds

Step-by-step explanation:

Hi, when the object hits the ground, h=0:

h=−16t^2+48.6t+37.5

0=−16t^2+48.6t+37.5

We have to apply the quadratic formula:  

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

Feel free to ask for more if needed or if you did not understand something.  

The object to hit the ground takes 3.675 seconds.

An initial velocity of 48.6 feet per second

When the object hits the ground, h=0:

h=−16t²+48.6t+37.5

0=−16t²+48.6t+37.5

We have to apply the quadratic formula:  

For: ax²+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Substituting with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

For such more questions on object

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The co-ordinate points of B is (3,1)

What is midpoint in a line ?

A midpoint in a given line segment divides the line segment in two equal parts.

In the given question

AB is a line segment.

Point A has co-ordinates (-1,5) and midpoint M has co-ordinates (1,3).

Assuming point B has co-ordinates (x,y)

We know midpoint formula is give by

M of x  = (x₁ + x₂)/2 and M of y = (y₁ + y₂)/2

∴ 1 = (-1 + x₂)/2

 2 = - 1 +x₂

 x₂ = 3

And

3 = ( 5 + y₂)/2

6 = 5 + y₂

y₂ = 1

So the co-ordinate points of B(x₂,y₂) = (3,1)

Learn more about midpoints here :

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Answer:

(3,1)

Step-by-step explanation:

let B be (x,y)

m(1,3)=midpoint

A(-1,5)=(x1,y1)

B(x,y)=(x2,y2)

(1,3)= x1+x2/2          y1+y2/2

(1,3)= -1+x/2           5+y/2

so,

-1+x/2=1              5+y/2=3

-1+x=2                 5+y=6

x=3                      y=1

therefore the co ordinates of B(x,y) are (3,1)

The answer is x=-1, x=8