Volume = (1/2) (6)(8) (13) = 24 * 13 = 312 ft^3 (good job !!!)
x + xy^2 = 250y
x - xy^2 = - 240y add these
2x = 10y
x = (10/2) y
x = 5y sub this back into the first equation
5y + 5yy^2 = 250y divide though by 5y
1 + y^2 = 50
y^2 = 49 take both roots
y = -7 or y = 7
x = 5(-7) = -35 x = 5(7) = 35
And (x, y) = (0,0) is a trivial solution
So
x = 35, 0 , 35
Selected values of x calculated value
0 0
.25 1
.33 2
.5 4
.72 5
.75 6
1 10
So ..... 7 values
OK......
4^x = 3 ⇒ (4^x)^2 = 3^2 ⇒ (4^x)^2 = 9
So....
4^(2x - 2) =
(4^2)^(x - 1) =
( 4^2)^x / (4^2) =
(4^x)^2 / ( 16) =
9 / 16
Since ZAX is equilateral....then AX = 30 / 3 = 10
And FLAX is a square.....its area = (AX)^2 = (10)^2 = 100
b ( b^4 * b^3)^2 = b^(3x)
b ( b^7)^2 = b^(3x)
b (b^14) = b^(3x)
b^15 = b^3x
15 = 3x
x = 15 / 3 = 5
We have the following relationship
(1/2) length of hypotenuse / 6 = 6 / (1/2) length of hypotenuse
cross - multiply
[ (1/2)lengt of hypotenuse ] ^2 = 6 * 6
[ (1/2) length of hypotenuse ] ^2 = 36 take the postive root of both sides
(1/2) length of hypotenuse = 6
Length of hypotenuse = 2 * 6 = 12
Welcome.....
Ways to roll a "5" =
(1,4) (4,1) (2,3) (3,2) = 4 ways
Ways to roll a "9" =
(4,5) (5,4) ( 6,3) (3,6) = 4 ways
D Each have the same chance of rolling their sum = (4/36) ....the game is fair
