Happy B-Day to Jack & Coke

[Jack & Coke]

correct!

In the figure below (see attachment), the rectangle at the corner measures 2 cm x 4 cm. What is the radius of the circle in cm?

[Blazestorm]

I'm guessing the diameter is 20cm... so the radius is 10cm?

[Jack & Coke]

correct!

Equation 1
x^2 + y^2 = r^2


Equation 2
r = 4 + x
r = 2 + y

or

x = r - 4
y = r - 2

Sub Eq 2 into Eq 1

(r-4)^2 + (r-2)^2 = r^2

r^2 - 8r + 16 + r^2 - 4r + 4 = r^2

r^2 -12r + 20 = 0

(r-10)(r-2)=0

r = 10


r = 2 does not work




NEW ONE (easy)


A cylinder 105 cm high has a circumference of 20 cm. A string makes exactly 7 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?


(as an example, the attached pic shows 4 complete turns)

[Benfica4ever]

Happy B-Day

[Jack & Coke]

ty maybe I should make a new thread where I challenge you guys to answer questions...?

[Blazestorm]

300cm?

[Mango]

These equations bring back memories of my Computer Science days....ugghhhh

Happy Belated B-day J&C!!!!

[Jack & Coke]

Answer = 175 cm

Blazestorm,

Originally posted by Jack & Coke


Previous Question:

A cylinder 105 cm high has a circumference of 20 cm. A string makes exactly 7 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?

Answer:

105 cm / 7 = 15 cm (each segment)

If you "unroll" the cylinder, you have a rectangle that is 15 cm x 20 cm (each segment).

The diagonal for this segment = (15^2 + 20^2) ^ .5 = 25 cm

Since we have 7 segments, we have 25 x 7 = 175 cm (Answer)






New one...

If the difference of two numbers is 10 and their product is 18, what is the sum of their squares?




p.s. thanks SprayingMango

[1stdeadeye]

The answer is 212!

Please give us a hard one, like: Who's on First?

[Jack & Coke]

Incorrect

Originally posted by 1stdeadeye
The answer is 212!

Please give us a hard one, like: Who's on First?

212 is incorrect...

[Jack & Coke]

Regarding: If the difference of two numbers is 10 and their product is 18, what is the sum of their squares?


No solution yet?

[Blazestorm]

the sum is somewhere around 64-65

I found out that 2.35 and 7.65 were very close, but I'm not good with math so yah... I don't know any equation stuff yet. But lemme know jack

[Jack & Coke]

Let a = one number
Let b = the other number

equation 1:

a-b = 10 "...difference of two numbers is 10..."

equation 2:

ab = 18 "...their product is 18..."


the square of equation 1:

(a-b)^2 = 10^2

a^2 - 2ab + b^2 = 100

a^2 + b^2 = 100 + 2ab

a^2 + b^2 = 100 + 2(18) (substitute equation 2)

a^2 + b^2 = 100 + 36

a^2 + b^2 = 136 "...the sum of their squares..."

The answer is 136.

We actually did not have to find out what a and b are. We just needed to know their product.




New one...

If you were to construct a 8 x 8 checkered square (i.e., a 8 x 8 chess board), how many squares would there be in total?

[Cryer]

Originally posted by Jack & Coke

If you were to construct a 8 x 8 checkered square (i.e., a 8 x 8 chess board), how many squares would there be in total?

65? no that not right...

[penguinpunk555]

and they say paintballers are a whole bunch of mindless rambos who dont know anything we should show them this