Engineers are designing a rollercoaster that at one point goes underground

Here the function is 

E(t) = t^2 - 10t + 16 

using middle term splitting method 

E(t) = t^2 - 8t - 2t + 16 

E(t) = t(t-8) -2(t-8) 

E(t) = (t-8)(t-2) 

For  t > 8 or t < 2  rollercoaster is above the ground 

and when  2<t<8 rollercoaster  is below the ground 

Rollercoasters generate speed by converting gravitational potential energy into kinetic energy by taking the cart to the top of a large hill and letting it go. The conversion of a perfectly efficient system would be like so:

PE = KE

and using the formulas for potential and kinetic energy:

mgh = 1/2mv^2.

However, the efficiency of this system is 50%, meaning that the kinetic energy obtained from this conversion would appear as so:

PE=0.5 KE

mgh=0.5(1/2mv^2)

mgh=1/4mv^2.

The masses cancel out, leaving:

gh=1/4v^2

The goal is to achieve 65 m/s, and with Earth’s innate gravity of 9.806 m/s^2, we have:

gh=1/4v^2

(9.806)h=1/4(65)^2

h=107.71 meters

The height of the first hill must be 107.7 meters to generate a speed of 65 m/s with a conversion efficiency of 50%.

Hope this helps!

Rollercoasters generate speed by converting gravitational potential energy into kinetic energy by taking the cart to the top of a large hill and letting it go. The conversion of a perfectly efficient system would be like so:

PE = KE

and using the formulas for potential and kinetic energy:

mgh = 1/2mv^2.

However, the efficiency of this system is 50%, meaning that the kinetic energy obtained from this conversion would appear as so:

PE=0.5 KE

mgh=0.5(1/2mv^2)

mgh=1/4mv^2.

The masses cancel out, leaving:

gh=1/4v^2

The goal is to achieve 65 m/s, and with Earth’s innate gravity of 9.806 m/s^2, we have:

gh=1/4v^2

(9.806)h=1/4(65)^2

h=107.71 meters

The height of the first hill must be 107.7 meters to generate a speed of 65 m/s with a conversion efficiency of 50%.

Hope this helps!

c. between his own choices

Explanation:

Based on the scenario given in the question, we can say that Harry is acknowledging the dependencies that exist between his own choices.

We make choices when we have different alternatives and due to the scarcity of resources. In this case, Harry has to make a choice between the alternatives that he has and he has to make a decision regarding that.

c. between his own choices

Explanation:

Based on the scenario given in the question, we can say that Harry is acknowledging the dependencies that exist between his own choices.

We make choices when we have different alternatives and due to the scarcity of resources. In this case, Harry has to make a choice between the alternatives that he has and he has to make a decision regarding that.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg