Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

A 92.0 kg football player at 6.50 m/s North collides with an 85.0 kg football player running at 6.00 m/s south. The 92.0 kg foot

s2008m [1.1K]

Answer:

-1.13 m/s

Step-by-step explanation:

Parameters given:

Mass of first footballer, M = 92 kg

Initial velocity of first footballer, U = 6.5 m/s (taking North to be the +ve y axis)

Mass of second footballer, m = 85 kg

Initial velocity of second footballer, u = -6.0 m/s (taking South to be the -ve y axis)

Final velocity of first footballer, V = 2.0 m/s

We need to find the final velocity of the second football (v)

Applying the principle of conservation of momentum, we have that, in a system:

Total Initial Momentum = Total Final Momentum

(M * U) + (m * u) = (M * V) + (m * v)

(92 * 6.5) + (85 * -6) = (92 * 2) + (85 * v)

598 - 510 = 184 + 85v

88 = 184 + 85v

88 - 184 = 85v

-96 = 85v

=> v = -96 / 85

v = -1.13 m/s

The final velocity of the 85 kg player is -1.13 m/s i.e 1.13 m/s South

5 0

2 years ago

Charlie bought a pair of shorts at the store when they were having a 45% off sale. If the regular price of the pair of shorts wa

spayn [35]

Answer:

$13.20

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expressi

myrzilka [38]

Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86

To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)

7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8

This implies that the company will need to sell at least 106 items to make a profit.

The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106

The solution to the inequality is as follows

Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695

Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66

Profit ≥ (695 - 694.66)
Profit ≥ 0.34

The company must sell at least 106 items to make a profit.

7 0

2 years ago

Read 2 more answers

Maggie has exactly $20 to buy decorations for the dance. Streamers cost $2 per roll and balloons are $1.50 per package. Which se

IgorC [24]

Answer:

streamers are closest to her budget.

Step-by-step explanation:

because if you want to buy balloons then you would have to buy 13.3 3 is infinite, but if you bought streamers then you would only buy 10.

6 0

2 years ago

A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he s

fredd [130]

Assuming the man works 8 hours straight without breaks:

25% is the same as 1/4 of something.

So, we just have to figure out what 1/4 (one quarter) of 8 equals.

You can think of it as a pizza cut into 8 slices. One slice is equivalent to one hour for the patrolman.

If we take away 1/2 (half) of the pizza, we have 4 slices, right? Since we start with 8 slices, half of that equals 4 slices. In other words, 50% (half) of the pizza = 4 slices.

Now, 25% (one quarter) of the pizza will equal half of what is left:

If we know that 50%=4 slices (or 4 hours), then 25% must be 2 slices (or 2 hours).

That's it! 25% of 8 hours = 2 hours.

***So, the patrolman spends 2 hours each day completing paperwork.***

Lets check our work:
We know 8 hours (or 8 slices)= 100%
(We know this because
8 slices = 1 whole pizza, or 100% of a pizza. Similarly,
8 hours = 1 whole shift or 100% of the man's shift ).

So

25% + 25% + 25% + 25% = 100%

If 100% of the mans shift = 8 hours:

2+2+2+2 = 8

It checks out!

Hope this helps!

4 0

2 years ago