2.8x-1.6y=3.2 -0.7x+1.9y=6.7

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 Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

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

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

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

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

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

Ben:

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

Josh:

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ 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 $h(t)=0$ . 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:

$h(t)=0-16t^2+60t+40=0$

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

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

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

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

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

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

3 0

1 year ago

Nina's monthly budget is $2,250. Every month she makes the following payments: $175 for insurance, $129 for utilities, $283 for

choli [55]

The total costs that Nina would have to pay is the sum of the cost of insurance, utilities, and taxes.
C = $175 + $129 + $283 = $587
The highest house payment she could afford is then the difference between her budget and the costs,
P = $2,250 - $587 = $1663
Thus, the answer would be letter B. House B because all the rest of the monthly payment are way over her budget.

6 0

1 year ago

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Evaluate the integral. ∫50∫25−x2√−25−x2√∫25−x2−z2√−25−x2−z2√1(x2+y2+z2)1/2dydzdx∫05∫−25−x225−x2∫−25−x2−z225−x2−z21(x2+y2+z2)1/2d

Kipish [7]

Is that a valid question?

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2 years ago

Alissa has $360 for guitar lessons. She pays $25 for each lesson. How many lessons has she attended, if she still has $85 left?

bagirrra123 [75]

Answer:

11 lessons

Step-by-step explanation:

360-85=275

275/25=11

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2 years ago

Box A is 567 inches high, 678 inches wide, and 789 inches long. It has a maximum capacity of 1,200 marbles, Box B has three time

kotykmax [81]

Answer:

1701 high

2712 wide

789 long

= 4413

Step-by-step explanation:

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