can't figure out how to set up some problems...

[dkboone22]

1. assume that the amount of money deposited in a bank by depositors is proportional to the square of the interest rate the bank pays on deposited money. the bank then invests this money at a 12% simple interest rate. find the simple interest rate the bank should pay depositors to maximize the banks profit

2. a lighthouse is located on a small island 3 km away from the nearest point "P" on a straight shoreline and its light makes two revolutions per minute. how fast (in km/hr) is the beam of light moving along (away from "P") down the shoreline when it is 1.5 km from "P"?

3. a concical, paper cup is made by cutting a sector from a circular piece of thin, waxed cardboard and bounding the edges of the sector together. what size should we make the angle (measured in degrees) of the sector to create a paper cup from a circular piece of thin metal that has a radius of 12 centimeters to maximize the volume of the resulting conical cup? what is the maximum volume for this cup?

4. the minute hand on a watch is 8mmm long and the hour hand is 4 mm long. how fast is the distance between the tips of the hands changing at one o'clock?

5. a steel girder, 27 ft long, is moved horizontally along a passageway 8 ft wide and into a corridor at right angles to the passageway. how wide must we make the corridor for the girder to go around the corner when the width of the pipe is zero? if the pipe is 1 ft in diameter, then how wide must we make the corridor?


any help with any of these would be greatly appreciated...thank you

 

[stapel]

Are you unable even to get started on any of these?

 

[HallsofIvy]

These are Calculus problems in the end, but setting them up is simply algebra- at least try and we will give suggestions.

 

[JeffM]

1. assume that the amount of money deposited in a bank by depositors is proportional to the square of the interest rate the bank pays on deposited money. the bank then invests this money at a 12% simple interest rate. find the simple interest rate the bank should pay depositors to maximize the banks profit

2. a lighthouse is located on a small island 3 km away from the nearest point "P" on a straight shoreline and its light makes two revolutions per minute. how fast (in km/hr) is the beam of light moving along (away from "P") down the shoreline when it is 1.5 km from "P"?

3. a concical, paper cup is made by cutting a sector from a circular piece of thin, waxed cardboard and bounding the edges of the sector together. what size should we make the angle (measured in degrees) of the sector to create a paper cup from a circular piece of thin metal that has a radius of 12 centimeters to maximize the volume of the resulting conical cup? what is the maximum volume for this cup?

4. the minute hand on a watch is 8mmm long and the hour hand is 4 mm long. how fast is the distance between the tips of the hands changing at one o'clock?

5. a steel girder, 27 ft long, is moved horizontally along a passageway 8 ft wide and into a corridor at right angles to the passageway. how wide must we make the corridor for the girder to go around the corner when the width of the pipe is zero? if the pipe is 1 ft in diameter, then how wide must we make the corridor?


any help with any of these would be greatly appreciated...thank you

We do not like to see more than one problem per thread. In the future, please respect that preference.

With respect to the first problem, the first thing to do in any word problem is to label your unknown or unknowns with a definition in writing. In a problem of differential calculus, identify what is to be optimized and what is to be found: those represent the unknowns relevant to solving your problem. So let x = rate offered, y = dollars received, and z = profit realized. The second thing to do is to express the relationship or relationships among your unknowns in mathematical terms using the labels assigned. What are the relationships implied or explicitly given in this problem that may be relevant to a solution?

PS You can use this method to solve almost any word problem.