Ben and josh went to the roof of their 40-foot tall high school to throw their math books offthe edge. the initial velocity of ben’s book was 60 feet per second while the initial velocity of josh’s book was 48feet per second. the equation ℎ=−16(++can be used to represent the situation where ℎis the height of the textbook at time seconds, is the initial upward velocity, and is the starting point. whose textbook reaches the ground first and by how many seconds?

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

      Eqn(1).

Where:

: is the height range as a function of time

  : is the initial velocity

    : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

       Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that

Thus Eqn. (2) becomes:

       Eqn.(3)

Josh:

We know that

Thus Eqn. (2) becomes:

      Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at . Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

Using the quadratic expression to find the roots of the quadratic we have:

Since time can only be positive we reject the solution and we keep that Ben's book took seconds to reach the ground.

Similarly solving for Josh we obtain

Thus again we reject the negative and keep the positive solution, so Josh's book took seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

So to answer the original question:

Whose textbook reaches the ground first and by how many seconds?

step-by-step explanation:

in which figure is point g a centroid

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!