Heyy. So here's the deal. Can't figure these questions out, need some help.


81. a rectangular garden is 10ft longer than it is wide. its area is 875ft². what are its demensions?

82. a rectangular bedroom is 7ft longer than it is wide. its area is 228ft².what is the width of the bedroom?

87. a box with a square base and no top is to be made from a square peice of cardboard by cutting 4-in. sqaures from each corner and folding up the sides. the box is to hold 100in². how big a peice of cardboard is needed?

88. a cylindrical can has a volume of 40∏cm³ (∏=pi) and is 10cm tall. what is its diameter?

91. A salesman drives from Ajax to Barrington, a distance of 120 mi, at a steady speed. he then increases his speed by 10mi/h to drive 150 mi from barrington to collins. if the second leg of his trip took 6 min more time than the first leg, how fast was he driving betweem Ajax and Barrington?

Please show work so I can understand the answer better. Much appreciated (:

81. well if the rectanguar garden is 10 ft longer than it is wide and it is are is 875ft^2 and you need to know it's dimensions then you should probably cut 875 in half and add 10 to one of the numbers and subtract 10 from the other, that should give you an answer

82. *(see 81.)

87. well you can get a piece of cardboard that is around 500ft, then cut the 4in squares and fold them as needed, all the excess cardboard can be used to help your classmates with there problems as it's always a good think to assist your peers, maybe some day they can help you

88. specify type of can?

91. He was driving about 12mph faster on the way back.

im glad to help you friend =) it's always a good think to peer your help as they may some day help you.

LERN

81. This is supposed to be done In the form of a Quadratic Equation.

So let Width = X and the Length = X +10

If you multiply these together you get: X

² +10X = 875

Now you make the equation = to 0 by moving the constant over.

X

² +10x - 875 = 0

Now you simply Factor out to get two values of X which will be your length and Width

(X+35)(X-25) = 0 (this part takes some trial and error on your calculator but keep in mind one number will be 10 higher than the other)

And there you have you have your Width = 25 and your Length = 35. Keep in mind you cant have negative lengths so consider them both positive.

82. you can do in the same way.

87. This one is pretty simple. It tells you that the base is a square but it didnt necessarily say the shape was a cube, so you can assume that to get to 100in³ you know that one of the dimensions is 4in. Divide 100 by 4 so give you the area of the base. Which is 25, and now, because its a square, you can square root it to find the other dimensions. 5 by 5. You would have to specify what you mean by how big the cardboard is but im going to assume it means when its flat. Well it says you dont need a lid so you have

5in by 5in which is 25in² You only need this once

The sides are given to us at 4in² and we need 4 of them meaning you have another 16in²

Add them together to give you your answer of 41in²

88. Similar problem above They give you a cylinder with a volume of 40πcm³ and a height of 10cm.

We immediately know that 10cm is one dimension so we can divide that from the volume. Giving us 4πcm²

Now this is the area of the base and what we need to do is Figure out what the radius is. This can be done

by rearranging the formula for the area of a circle which is πr².

This means that 4πcm² = πr²

The pi's cancel eachother out giving you 4cm² = r²

You square root both sides giving you r = 2cm and you know that the Diameter is twice the size of r so the answer is d = 4cm

I only went through the entire steps because in other questions it may not be this simple. The important think is knowing the steps. The diameter wont necessarily be the same as r² like in this example.

91. Okay this one is just a matter of looking at the wording and finding the appropriate equation from it. But the first rule you need to take into accont is that Speed x time = distance

So for the first part of the question we have 2 unknown variables X and Y where X represents the speed m/h and Y represents the time taken in hours. So from the rule above we can conclude that X x Y = 120miles

For the second part of the question we do the same but it is a bit more tricky. Just remember to convert the 6minutes into hours which is 0.1hrs. The second equation is (X+10)x(Y+0.1) = 150miles

Now you have to use the formula above to solve this one so make Y the subject of the formula. Y = 120m/X

Now we put this into the second formula and you get this equation (X+10)(120mil/x + 0.1) = 150miles

Now the multiplying out and simplifying of this will take forever so im going to skip a few steps.

You should get to a point where your equation looks like this: 0.1X+1200/X = 29 Multiply all of it by X and then 10 and bring it all to one side You should get: X²-290X+12000 = 0

Now as in previous examples you solve it. (X - 50)(X - 240) = 0

X = 50miles/hr or X = 240miles/hr

I checked both answers by putting them back into the formula and they are correct. Both of those speeds satisfy the conditions of the question.

Sorry for being late to the party but I feel the post before mine didnt really help mathematically. So I felt I should post anyway. Someone else might see and find it useful anyway. I hope I helped, good luck

Local Moderators :  Close as this has not been posted in for like almost a year.