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# The corners of a square with side 12 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so for

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The corners of a square with side 12 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so formed?

Bala is setting up a factory to manufacture tennis b***s. If he buys a machine that costs Rs. 59728, then he can manufacture a tennis ball for Rs. 3.7. On the other hand, if he buys a machine that costs Rs. 44500, he can manufacture a tennis ball for Rs. 8.4.
How many tennis ball should he make so that his total cost is the same no matter which machine he buys?

Which of the following expressions gives the products of 8 numbers which have the following properties
- The GCD of each pair of numbers in that group is a
- The LCM of the 8 numbers is b

If number in the center is the sum of all other numbers, y= .
If

 x y

=

 9 3

, then identify the incorrect expression from the following.

È

a.
 x + y x - y
=
 12 6

b. 3 y = 9 x
c. 3 x= 9 y d.
 9 3
y - x = 0

Saina is deciding to buy a car. She can choose between a diesel car and a petrol car.
The diesel car costs Rs. 7310 than the petrol car. However, it can travel 15.9 kilometres per litre, whereas the petrol car can only travel 11.3 kilometres per litre.
Also diesel costs Rs. 55.65 per litre, and petrol costs Rs. 58.76 per litre.
If she buys a diesel car, how many kilometres must she drive before the savings in fuel covers the extra price of the diesel car?

Jul 31, 2015

#2
+111360
+15

The corners of a square with side 12 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so formed?

Let S be the side of the octagon......then.....before the corners are to be cut from the square, an isosceles right triangle is formed at each of these vertexes. The hypotenuse of this triangle = S.....and  the other two sides are S/√2 each.

Then, before we make the cuts, the side of the square is composed of lengths of S/√2,  S and S/√2 ...or,  put another way.....

S + 2S/√2  = 12   simplify

S + √2S  = 12      factor

S(1 + √2)  = 12

S = 12/ [ 1 + √2 ]

See the following illustration :

GE, EF = S =  12 / [1 + √2]   ....     CE and FD  = S/√2

Aug 1, 2015

#1
+109496
0

Kes,

Could you please put just one question per post.

Thanks :)

Jul 31, 2015
#2
+111360
+15

The corners of a square with side 12 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so formed?

Let S be the side of the octagon......then.....before the corners are to be cut from the square, an isosceles right triangle is formed at each of these vertexes. The hypotenuse of this triangle = S.....and  the other two sides are S/√2 each.

Then, before we make the cuts, the side of the square is composed of lengths of S/√2,  S and S/√2 ...or,  put another way.....

S + 2S/√2  = 12   simplify

S + √2S  = 12      factor

S(1 + √2)  = 12

S = 12/ [ 1 + √2 ]

See the following illustration :

GE, EF = S =  12 / [1 + √2]   ....     CE and FD  = S/√2

CPhill Aug 1, 2015
#3
+111360
+5

Bala is setting up a factory to manufacture tennis b***s. If he buys a machine that costs Rs. 59728, then he can manufacture a tennis ball for Rs. 3.7. On the other hand, if he buys a machine that costs Rs. 44500, he can manufacture a tennis ball for Rs. 8.4.
How many tennis ball should he make so that his total cost is the same no matter which machine he buys?

Let x  be the number of teniis b***s to make.....then, equalizing the total costs, we have

59728 + 3.7x   =  44500 + 8.4x       simplify

4.7x  =  15228      divide both sides by 4.7

x = 3240  b***s should be manufactured to equalize the cost

Aug 1, 2015
#4
+111360
+5

Saina is deciding to buy a car. She can choose between a diesel car and a petrol car.
The diesel car costs Rs. 7310 than the petrol car. However, it can travel 15.9 kilometres per litre, whereas the petrol car can only travel 11.3 kilometres per litre.
Also diesel costs Rs. 55.65 per litre, and petrol costs Rs. 58.76 per litre.
If she buys a diesel car, how many kilometres must she drive before the savings in fuel covers the extra price of the diesel car?

.................................................................................................................................................

The diesel car costs  55.65/15.9 = 3.5R/km to operate ..... and the petrol car costs  58.76/ 11.3 = 5.2R/km to operate

So  (5.2 - 3.5)x  = 7310    where x is the answer we're looking for

1.7x = 7310    divide both sides by 1.7

x =  4300km

Aug 1, 2015