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**Mathegocart**- Replies: 0

You are a pilot of a medical evacuation helicopter. At 5:30 am, you receive word that a passenger on a ship fell ill and needs to be airlifted as quickly as possible to the nearest hospital, which is where you and the helicopter are located. The cruise ship is 400 miles away from you, where the nearest hospital is found. The ship is making it's way at 10 mph to your port. Your helicopter only has 6600 pounds of fuel, and it burns 1,200 pounds of fuel every hour when it is airborne. Airlifting a passenger takes 30 minutes. Federal law mandates that pilots most retain an hours worth of fuel at all times. If your helicopter travels at 150 miles per hour, at what time must you leave the ship to get to the ship as quickly as possible?

This was one of my practice HW problems and the answer is apparently not 5:30.AM

Could someone give me a detailed explanation on why this isn't 5:30 AM and what the answer is?

THOUGHT PROCESS;

The helicopter can obviously not travel for more than 5 hours since it must maintain an hours worth of fuel.

Now the heli and boat have a 400 mile distance between eachother.

x = time since 5:30 AM

y = time after 5:30 AM when starting the helicopter

now the helicopter's traveled distance is 150(x-y), and the boat's distance is 10x. Summing these expressions, we get 160x-150y = 400, which is (16/15)x- 40/15.

Getting to the ship as quick as possible is minimizing both x and y, and I got 2.5,0.

So is it 8:00 AM?

thickhead wrote:

6 also is a solution, and 6 is not a cube. = 20

bobbym wrote:

Hi;

Both answers are reasonable solutions, also thickhead has a good soultion as well.

thickhead wrote:

Thickhead, could you explain the process on the inequality? I used a bit of Cauchy Schwarz on this.

bobbym wrote:

Hi;

Correct.

**Mathegocart**- Replies: 13

1.Express

as the product of 2 factors, where neither of them is 1.

2. Express as the product of 2 factors, where neither of them is 1. Do not express these 2 factors explicitly.

3. What does equal?

4. Find all integers where n! is a multiple of n^2.

5. If 3 numbers are chosen at random from first 1000 natural numbers,what is the probability that the three numbers are in G.P.? All numbers are distinct.

6. prove that is true for all non negative integers.

bobbym wrote:

Hi;

I do not agree.

Why assume x > y? The problem does not state that. And why combinations? x and y are two different variables, so order should count. I think that EVW has the correct two answers for the problem as stated.

Please Mathegocart be more specific which answer, he has 3 different answers, is the one you think is correct.

Where did that little guy go?

That was quite late at night for me, I believe now that EVW's answers are right.

thickhead wrote:

That is correct, thickhead. Congratulations.

bobbym wrote:

I think √ and x² are copied from top of this page and not LaTex.

That is precisely the point.

True but I was too lazy to put LATEX on the top. I will now.

Penguins are hard workers so they can not claim they are lazy. So what is it for 3? With replacement or not?

I meant to say without. Penguins are busy animals, surely.

thickhead wrote:

I think √ and x² are copied from top of this page and not LaTex.

True but I was too lazy to put LATEX on the top. I will now.

**Mathegocart**- Replies: 3

Kai rides his bike up the hill to school and back every day. If he travels twice as fast downhill as up, and it takes 30 minutes round trip how far away is it from his school?

I don't believe that there is a solution with the given information.

bobbym wrote:

Hi;

For 3) with replacement or without? Also, you mean

We are going to have to teach you some latex. It is pronounced lah - tek?! Now ain't that just as weird as a two headed squirrel? Us bumpkins say lay-tex like the sap they make rubber from.

Bobbym, modus means method, and I already know LATEX.

**Mathegocart**- Replies: 1

Which of these points are closest to the origin?

A.(-1,-1)

B.(.5,.5)

C.(.5,-.5)

D.(0,-1)

E(0,.5)

There is only 1 answer, apparently.

Wouldn't B and C be the nearest to the origin(having distance .25?)

**Mathegocart**- Replies: 17

1. We have a unit square [0,1],[0,1]. I pick 2 random numbers from this unit square with uniform distribution. What is the average length between these two numbers? What is the median length? What is the modus??

2. Find the sum of the reciprocals of the triangular numbers.

3. I choose 2 integers from the set [1,100]. What is the probability that

4.Does there exist a function f:R→R such that for every real number x? Prove whether or not this exists.

5. Find all numbers x for which the equation where 3^x + 3^-x = 3.

I need serious help on number 3

**Mathegocart**- Replies: 4

1. A train travelling 30mph reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to clear the tunnel, how long is the train in feet?

first 2/60 = 1/30 of an hour, thus the train travels 1 mile. Thus the tunnel is 1 mile. 5280 miles divided by 9 = 586.6666 reperating, so the train is 586.6 feet.

2. If x - y + 2z, and x+z = y + t, and y + t+z, how many z's = x?

3. a athelete running 100 meters or 200 meters does not reach top speed until 40 miles. In a 200 meter race a certain runner's time is 5.4 secs and his time for 100 meter s is 10 secs.Assuming he maintains full speed from 40 meters to the end of the reae, what would be his time for 200 meters?

**Mathegocart**- Replies: 3

In the following sequence of numbers. each number has one mode 1 thean the preceding number. 1,11,111,1111,11111.... Which is the tens digit of the sum of the first 30 digits in the sequence?

**Mathegocart**- Replies: 2

1. Separate the product of the product of 999 and 7163 into sums that add to 999

example: 5 x 999 = 4995, 4 + 995 = 999.

2. Bobbym and Agnishom both leave Mathocity on their cars at the same time. Bobbym travels at a constant speed of 12 miles per hour and Agnishom at a constant 8 Miles per hour. Bobbym arrives at Sophopolis 2 hours before agnishom. How many miles is it from Mathocity to Sophopolis?

3. Find a 6 digit number whose numbers are l distinct such that when it is multiplied by 1, 2, 3 ,4, 5 or 6, the product contains the same set of digits.

4. When the Bobbym family went on vacation, mr bobbym traveled 4/9 of the distance at 40mph, 7/18 of the distance at 70mph, and the final 3- miles at 60mph. If there WERE NO STOPS, the entire trip took them X hours. find X.

5. Bobbym's water bill for every 30 days is $16. For the next 30 days the sprinklers were on everyday for 15 minutes 4 times per day.. His water bill then increased to 184. For the next 3 days he will have his sprinkers on every other day and ONLY ONCE for 15 minutes. His water bill for these 30 days should be...

2A x AB = 1971, A =B, find a + b.

6.(1-1/3)(1-1/4)...(1-1/50) =?

7. (2^100 + 3^100) modulus 5 = ?

8. (20-19+18....+2-1)/(19-18....+3-2+1) =?

**Mathegocart**- Replies: 25

1. A circular track is 1000 yards in circumference. Cyclists A B and C start at the same place and time at the following rates per minute, respectively, 700 YARDS, 800 yards, and 900 yards. What is the LEAST number of minutes it takes for all 3 to be back again?

thickhead wrote:

Hi mathegocart,

your Q(3) and and Q(4) There is no clarity about the questions and also about our answers whether right or wrong.

They are both correct.

bobbym wrote:

Hi;

I got your answer for 1).

Is it 105?

**Mathegocart**- Replies: 4

1) The average weight for the 5 starting persons on the HS team was reported as 150 pounds(total:750). One of the 5 weights has been recorded incorrectly. It should have been 175 pounds. Now the average weight of the 5 persons is correctly reported as 164 pounds. What weight was recorded instead of 175 pounds?

My Logic:

so the incorrect total was 150 * 5 = 750, and the correct total was 164 * 5 = 820. Because 820 - 750 = 70, the difference in the totals is 70, the weight that was incorrectly recorded was 175 - 70 = 105.

2)A clock is divided in 12 equal parts and each of these are split into 5 equal smaller parts. Normally the hour moves on the smaller parts while the minute moves 12 of the small parts. The clock pictured below shows 3 PM. From this moment on, the hour hand moves correctly, but the minute hand only moves *10* of these smaller parts as the hour hand moves. Eventually the minute hand will be in the correct position and the clock will give the correct time. What time will it be when this FIRST occurs?

3) Using only the digits 1,2,3,4 with repetition allowed, how many 3 digits number can be made that sum up to 9

144,234,243,324,342,333,414,441,423,432,.

so there are 10.

4)MR DEE spent 1/4 of his life in England; 1/3 of his life in France, 7 years in germany, half the remainder of his life in russia, and half as long in the US has he spent in France. If he was born in 1908, when did he die?

Good job all.

Both answers seem to be wrong. I have tried 148 and 4 as answers too.

**Mathegocart**- Replies: 5

How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a 4 x 4 square array of dots like the one shown below?

Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths.