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The solution M # 577 is correct. Brilliant!

#M # 578. The edge of a cube is 12 centimeters. Find the volume of the largest sphere that can be carved out from it. (In terms of pi).

]]>**Welcome to the forum!**

In certain parts of the world, grasshoppers are eaten as food. They are often dried, jellied, roasted and dipped in honey or ground into a meal.

Only ever eaten the fried one, and it was delicious.

]]>Here's the proof that I was taught many years ago.

Draw a circle radius R and centre C. Mark points A and B as shown and D so that AD is perpendicular to CB.

Let angle ACB be x in radians.

sin(x) = AD / R

arc length AB / whole circumference = arcAB / 2.pi.R = angle of arc / whole circle angle = x / 2.pi

cancelling the 2.pi gives arcAB / R = x

So sin(x) / x = AD / arcAB

implies sin(x) < x but as x approaches zero AD approaches arcAB so sin(x) / x tends to 1.

Bob

]]>A: Because it was fast food!

* * *

Q: What did Little Caesars say to Wendys?

A: You'll always have a pizza my heart.

* * *

Q: Why is it called "Fast Food"?

A: It's called "fast" food because you're supposed to eat it really fast. Otherwise, you might actually taste it.

* * *

Q: Why is Fast Food increasing illegal immigration?

A: "Fast" food slows you down when it hits your stomach, parks there, and lets the fat have time to get off and apply for citizenship.

* * *

Q: Where do they hold prizefights in Fastfoodland?

A: In an onion ring!

* * *

Q: Why do hamburgers go to the gym?

A: To get better buns.

* * *]]>

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#4661. Find the area of a parallelogram whose length is 30 cm, width is 20 cm, and one diagonal is 40 cm.

]]>Strictly speaking, the Argand diagram is not a graph. As it has 'x' and 'y' coordinates I can see why you might think it was. But it is just a way to represent complex numbers and there is lots of useful maths that stems from it.

A function such as y = 2x + 3 has an input (x) and an output (y). So you can show the effect of the function by plotting a graph.

A function like z = x^2 + y^2 cannot be represented in 2 dimensions, so, if you want a visual representation you have to try and represent the z axis, perpendicular to the other two … usually rising up from the x-y plane. Tricky to show clearly because we are only 3 dimensional beings (as far as I can tell )

So if that was the function of complex numbers of the form x + iy and z was limited to real values that's how you'd have to graph it. But z could also be complex in which case we run out of dimensions to show what is happening. Nevertheless there's a whole area of maths that does consider such functions.

Bob

]]>http://bcs.wiley.com/he-bcs/Books?actio … indow=true

B

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