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We've never figured that out.....she's from Australia....but....those Aussies can be sneaky.....!!!

https://web2.0calc.com/questions/help_66955

4) A 3cm*4cm*5cm rectangular metal block was put into a well that took the shape of a right circular cylinder. When the block was submerged, the water level in the container had increased by 0.5 centimeters. What is the base area of the well in square centimeters?

V prism =  3 * 4 * 5  =  60cm^3

V of cylinder  without prism =  pi * r^2 * h

V of cylinder with prism added  = pi* r^2 (h + .5)

V of cylinder with added prism - V of cylinder without prism  = volume of prism 

[ pi * r^2*(h + 5cm)]  - [ pi * r^2 * h]  =  60 cm^3

pi^r^2 *h  + pi*r^2 * .5cm  - pi * r^2 * h   = 60 cm^3

pi* r^2 * .5 cm    =  60 cm^3

r^2  =    60cm^3 / [.5 cm pi]

r^2  = 120cm^2 /  pi

pi * r^2  = 120 cm^2   =  base area of well

Nickolas, i dont hink you would be willing enough to solve for it if u wanted to.

Jklol. Luv u

Here's a fast way to solve this type of problem    :

2[ Rate a * Rate b ]

________________   =  Avg rate

  Rate a + Rate b

2[ 60* b ]

_________  =   45

    60 + b 

120b = 45 [ 60 + b]

120b = 2700 + 45b

75b = 2700

b = 36

Use Graphing Calculator to get the two values for a:

a = 1   and    a = ≈0.29560

Set the equations equal

-2x + 5  = -x^2 + 3x + 1        add x^2 to   and subtract 3x + 1  from  both sides

x^2 -5x + 4  = 0       factor

(x -4)(x - 1)  = 0          set both factors to 0  and solve for x and we have that

x = 4     or    x = 1

Maybe:

∛-512² = 64 
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = -8
Power: (-8) ^ 2 = 64

∛-512² = -32-55.4256258i = 64 × ei (-120°) 
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4-6.9282032i
Power: (4-6.9282032i) ^ 2 = (4-6.9282032i) * (4-6.9282032i) = 16-27.712812i-27.712812i-47.999997 = -32-55.4256258i

∛-512² = -32+55.4256258i = 64 × ei 120° 
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4+6.9282032i
Power: (4+6.9282032i) ^ 2 = (4+6.9282032i) * (4+6.9282032i) = 16+27.712812i+27.712812i-47.999997 = -32+55.4256258i

OK....try the others

Ya-a-a-a-h     CPhill gave you that one   Haha.....   keep going !    He gave you the second one too....

Area of parallelogram  = height * width

height = EG   = 16

width  = AB =  DC  = 27

So

16 * 27  =

432 units^2

I did respond....you never posted what you thought the answers were.......

These are always a little difficult....you just have to translate words to math expressions

Some number increased by two....let the number = b

Increasing this by 2 must be  b + 2

A variable decreased by 2.....let the variable  = x

Decreasing this by 2 must be   x - 2

Product of an unknown variable and 2 ...."product"  means "multiply"

So....we're multiplying an unknown variable by 2.....do you see the correct answer, Nickolas???

Quotient of some number and 2...."quotient" means "divide"

Which one of the answers looks like division ????

Unknown variable squared......we have ....(some variable)^2

Which one is this???

Nickolas....if you cannot get ANY of these......or at least TRY, after all of your postings and all of the answers given to you, you are in a course that is too advanced for you....you may need to back down a couple of course levels and re-tool before taking on this level.  

To be nit-picky ......    we should have   [-8, -4)  U  (0, 8]

[ At x  -4, the function isn't increasing or decreasing.....same at x = 0 ]