plz tell me the method to solve this problem n solve it step by step.its urgent?

Question

power cable is to be run from a power plant on the river bank 900m wide to a factory that is located 3000m downstream to the opposite bank.if the cost of laying cable under water is Rs 5 per metre and that is laying overhead is Rs 4 per metre .find the point downstream where the cable is to cut accros the river.

Answer 1

It always helps to put things in equations first.

Here we have to go 3000 m down and 900 across, and have to minimize cost.

So, if we put "x" as the length of the cable on land, we have
(x*4) cost on land
SQRT((3000-x)^2+900^2)*5 cost under water

The total cost is thus
(x*4)+SQRT((3000-x)^2+810000)*5 and we need to minimize that.

A bit of algebra:
4 x + 5 SQRT(9810000-6000x+x^2) = total cost

Since we have to minimize cost, we can take the derivative of the equations and find where it equals zero (do I have to explain why the minimum value will have a zero derivative?)

4 + 5/(2*SQRT(9810000-6000x+x^2)) * (-6000+2x) = 0
4 + (5x - 15000)/SQRT(9810000-6000x+x^2) = 0
4 = (15000 - 5x)/SQRT(9810000-6000x+x^2)
16 = (15000 - 5x)^2 / (9810000-6000x+x^2)
16 = (225e6 - 150e3 x + 25x^2)/(9.81e6 - 6e3 x+x^2)
156.96e6 - 96e3 x + 16 x^2 = 225e6 - 150e3 x + 25x^2
-69.04e6 + 54e3 x - 9x^2 = 0

You solve this quadratic equation (find the roots) and there are 2 roots: one at 4152.774 (which is obviously not the right one as you'd be past the factory already) and one at 1847.226, which is the solutions sought.

So, you lay 1847 m of cable on land, and the rest (1463 m approximately) across water, at an angle.

Answer 2

I agree with vincent reasoning but to simplify math we would choose y as the distance from the factory to the point exactly opposite to the point of cut across, that is the cable run (3000-y) on the plant side over head then it cut across inclined directly toward the factory. the distance frm this point to the factory on the bank is y, but the cable will run diagonaly for a distance of sqrt(900^2+y^2)
now the total cost is
C=4*(3000-y)+5*sqrt(900^2+y^2)
differentiate wrt y and eqate to zero
dC/dy=-4+5*(1/2)*2*y/sqrt(900^2+y^2)=0
5y/sqrt(900^2+y^2)=4
5y=4sqrt(900^2+y^2)
square both sides
25y^2=16(900^2+y^2)
25y^2-16y^2=16*900^2
9y^2=16*900*900
y^2=16*900*100
y=4*3*100=1200m

Answer 3

Makes no sense...

Find the point downstream where the cable is to cut across the river??

The cable can cross the river anywhere, unless it is more narrow somewhere else.

What are you asking? What does where it crosses have anything to do with math, how much the cost is, whether it is over or under the water... makes no sense.

Answer 4

a million) It took 10 minutes to go 9 gaps and you prefer to renowned the time it takes to go 14 gaps. you prefer gaps cases minutes according to hollow, or 14 * 10 / 9 that's approximately 15.4. 2) permit the size of the bridge be X. The cow traveled x/2-4 ft in one direction in the comparable volume of time by way of fact the practice moved from everywhere it began to a million foot before the commencing up of the bridge. If the cow had run far off from the practice, then whilst the practice became a million foot before the commencing up of the bridge, the cow could have nonetheless traveled x/2-4 ft. for this reason, the cow could have been 9 ft far off from the top of the bridge. for this reason, the practice can go the bridge in the comparable volume of time by way of fact the cow can shuttle 8 ft. From this, you may not tell the size of the bridge. to illustrate, think the cow became trotting alongside at 10 miles according to hour. by way of fact the practice became shifting 9 cases swifter, the bridge could be 72 ft long. on the different hand, think the cow became galloping at 18 miles according to hour. Now the practice is 5 cases swifter than the cow and the bridge is 40 ft long.

Answer 5

No sense! I think the first thing you must do before trying to solve any problem is reading the questions very carefully.

I agree... Big fat F.

Answer 6

Use pythagoras' theory.

Also: do your homework earlier than the day before it's due.

Answer 7

I think your going to get a BIG FAT (F) on your home work this week

Answer 8

If its cheaper overhead then isnt that your answer?