ElectricPavlov

Take log of both sides to get

(3-x) LOG 2 = (2x+3) LOG (1/3)      LOG2 =.3010    LOG(1/3) = -.4771

.90308 - .301x = -.9542x - 1.4313     Now just solve for 'x'

2.33438= -.6532x

x= -3.5738

Let's say

Lake Mich = x

Lake Superior  is then 1720 + x

Lake Huron is  x-330

Theay all ad up to 4930

x + (1720+x) + (x-330) = 4930

x = 1180 = Mic

Super = 1720 + 1180 = 2900

Huron = 1180-330 =850

Do not know what format you are looking for, but here are some possibilities:

= (25^1 * y^6)^1/4

= 25^(1*1/4)  *  y^(6*1/4)

=25^(1/4) * y^(6/4)

=(5^2)^1/4 * y^3/2

=5^(2/4) * y^3/2)

=5^(1/2) * y^(3/2)

=sqrt (5) *  y^(3/2) 

=\(\sqrt{5}\)\(\sqrt[2]{y^3}\)

In case you have not yet learned about derivatives (to find the slope):

We can identify the minimum or maximum value of a parabola by identifying the y-coordinate of the vertex. You can use a graph to identify the vertex or you can find the minimum or maximum value algebraically by using the formula x = -b / 2a. This formula will give you the x-coordinate of the vertex.

the parabola equation we had was:

Area = 1/2  px - x^2    

        = -x^2 + 1/2  px         a = -1    b = 1/2  p

the MAXIMUM of the parabolic area equation will be     @  x = -b/2a =  (-1/2p) / 2(-1)  = 1/4 p     and again we have the value of a side which gives maximum area is   x = 1/4 p     so the rectangle is a square....

I would add that  OPPOSITE   and ADJACENT   are NOT the HYPOTENUSE .....

You put in ADJACENT/OPPOSITE     This is COTANGENT

OPPOSITE/ADJACENT  = TANGENT   ( T-O-A)

= 10/19.72  = Tangent  

Try THAT and let me know what you find !

Let

x= one side length

2x= length of TWO sides

P-2x = length of OTHER TWO side

(P-2x)/2 = length of ONE other side

Area = side 1 x side 2

        = x * (P-2x)/2

        = 1/2Px -2x^2/2

        = 1/2 Px -x^2       

This is an upside down 'U' shaped parabola.....we are asked to find the MAXIMUM value of this area equation

   This will be where the slope = 0

   First derivative defines slope          SLOPE= 1/2  P - 2x    Set this equal to ZERO

  1/2 P - 2x = 0  

2x=1/2 P

x = 1/4 P         So the maximum area is acheived when x = 1/4 P   

the SECOND side will be ( P- 2x)/2  = (P- 2(1/4P))/2 = 1/2P / 2 = 1/4P    The same as the FIRST side

  If all of the sides are equal (which we just shown) the rectangle with the biggest area and perimeter P  is a SQUARE !

8^(1/3) = \(\sqrt[3]{8}\) = 2

-Log[OH-] = pOh           pH +pOh = 14   so pOH = 4.45

-log[OH-]= 4.45

[OH] = 3.55 x 10^-5  M

The only place where sin and cosine are equal numerically (absolute value) are at 45  135  225 and 315 degrees ...right?

where they are OPPOSITE in value (so cosx= - sinx)    are in the 2nd and 4th quadrants     135 and 315 degrees = x