CalculatorUser

I finished part of my essay so I decided to take a little break with math.

So the center of the circle is E.

1. We draw EA, which is the radius of the circle.

2. Now we connect the center to the midpoint of AD.

3. We set the hypotenuse of the triangle equal to X.

4. We know that the longer leg of the triangle is 5

5. We draw a line from center E to the midpoint of BC.

6. We know that is a radius. So the length of that is also X.

7. Since the side of the square is 10, we know that the line from center E to the midpoint of AD is 10-x

8. Using the pythagorean theorem, you set up the equation

\(5^2+(10-x)^2=x^2\)

9. Solve for X.

10. Use the circle formula to find the area of the circle using your value of X. Then  you have the answer.

Not giving my answer, but when I solved it, I got a decimal (or fraction).

Well Im going to give ya my method:

The diagonal of the square is equal to the diameter of the circle around it.

The Diameter of that circle is equal to the side length of the square around it.

So you just keep calculating. Quite a tedious problem, once you know the method.

Find units digit of each term

1^5 is 1

2^5 is 2

3^5 is 3

See the pattern here?

Its 1 + 2 + 3... 121 + 122 + 123

So (123)*(124)/2 = 7626.

The units digit of that number is \(\boxed{\sqrt{6}}\)

My strategy:

After analyzing the two equations, we can conclude that A and B must be perfect square integers.

As both of their square roots end up forming integers after being added by eachother.

So I would guess and check from there.

They both should be less than 121 because the largest integer in the equations is 11.

So I would guess all perfect squares from 1 to 121.

Not the best strategy...

Rip but my parents are forcing me to do orchestra nuuuuuuuuuuuuuuuuuuuuuuu

going off your answer, if the frog DID reach the top the moment it goes over the well top, regardless how much it falls:

the well is 20m deep, the frog jumps 5m. So the frog needs to reach 20 - 5 = 15m.

jumps 5m and falls 4m, so it jumps 5 - 4 = 1m

15m/1m=15

the frog reaches the top on the 15th day

thanks nirvana

yes! remember that! very important.

We classify the types of equ-triangles starting with biggest to smallest.

The biggest is obviously the equ-triangle with a side length of 5, the smallest equ-triangle has a side length of 1.

Count the number of equ-triangles for each class. The first one has already been filled out for you.

Now once you complete the table, just find the total up the number of equ-triangles for the table.

Calcuser not logged in

you need 23 energy... you get one energy every 5 minutes....

23 * 5 = 115

115 minutes