Tutors Answer Your Questions about Rectangles (FREE)
Question 649421: 1. Find the dimensions of the rectangle whose perimeter is 40 inches and whose area is a maximum.
2. An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
3. A closed box, whose length is twice its width, is to have a surface area of 192 square centimetres. Find the dimensions of the box when the volume is maximum.
4. What is the least amount of material needed to make an open right cylindrical can of volume 8 cubic inches?
5. Find the dimensions of the right circular cone whose volume is 3000 cubic centimetres if its lateral area is a minimum.
6. Find two numbers whose sum is 10 and the sum of the squares is a minimum.
7. Divide 20 into two parts such that the product of one part and the square of the other is maximum.
8. The electrical potential at a point (x,y) on the line extending from (0, 3) to (2, 0) is given by . At what point on this segment is the potential a minimum?
9. A man wishes to heat his basement by plugging a long extension chord connected to a number of heaters into a 120-volt socket at the house. The power P in watts radiated by the 30-omhs heater is given by , where n is the number of heaters plugged in. What would be the maximum amount of heat?
10. The power P generated by a 120-volt generator of internal resistance 5 ohms is given by watts, where is the current in amperes. For what current does the generator produce maximum power?
Click here to see answer by lynnlo(4155)  |
Question 649421: 1. Find the dimensions of the rectangle whose perimeter is 40 inches and whose area is a maximum.
2. An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
3. A closed box, whose length is twice its width, is to have a surface area of 192 square centimetres. Find the dimensions of the box when the volume is maximum.
4. What is the least amount of material needed to make an open right cylindrical can of volume 8 cubic inches?
5. Find the dimensions of the right circular cone whose volume is 3000 cubic centimetres if its lateral area is a minimum.
6. Find two numbers whose sum is 10 and the sum of the squares is a minimum.
7. Divide 20 into two parts such that the product of one part and the square of the other is maximum.
8. The electrical potential at a point (x,y) on the line extending from (0, 3) to (2, 0) is given by . At what point on this segment is the potential a minimum?
9. A man wishes to heat his basement by plugging a long extension chord connected to a number of heaters into a 120-volt socket at the house. The power P in watts radiated by the 30-omhs heater is given by , where n is the number of heaters plugged in. What would be the maximum amount of heat?
10. The power P generated by a 120-volt generator of internal resistance 5 ohms is given by watts, where is the current in amperes. For what current does the generator produce maximum power?
Click here to see answer by ralhp09(3) |
Question 253415: 4. If the perimeter of a rectangle is 8√2 cm, what is the smallest possible value of the length of one of its diagonals in cm?
I've tried:
let length be l, width be w, and diagonal be d
let l be x, then w will be:
(8√2-2x)/2 = 4√2-x
d^2=l^2+w^2
=x^2+(4√2-x)^2
=x^2+(32-8√2x-x^2)
=32-8√2x...
Click here to see answer by ralhp09(3) |
Question 654843: sonja needs to borrow $2,251 to pay for her college classes. Sallie Mae is offering her a 4.5% simple interest loan with an interest charge of $405.18 over the life of the loan. How many years is Sallie Mae giving her to pay back the loan with interest?
Click here to see answer by josmiceli(9669)  |
Question 654892: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. How long will it take the object to reach a height of 144 feet?
Click here to see answer by DrBeeee(378) |
Question 654900: I would just like to have it explained to me in words how to get the expression for this question. I would love the answer yes, but I want to know how to get it.
Yardbird Landscaping has 40 m of fencing with which to enclose a rectangular garden. If the garden is x meters long, express the garden's area as a function of the length.
Thanks for the help.
Click here to see answer by ewatrrr(10682)  |
Question 655241: Please help me with this!
A rectangle is 2 feet wide and 3 feet long. Each side is increased by the same amount to give a rectangle with twice the area of the original one. Find the dimensions of the new rectangle. (Hint: Let x feet be the amount by which side is increased.)
Thank You!
Click here to see answer by lwsshak3(6491) |
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