Hi. Please help me with the following two mathematical questions.

Question

1) Solve the following equations using inverse operations.

i) 3x-7=7+x

ii) 3[(6x-2)/4 (Separate)+ 1 ] = 33

2) A cylindrical (cylinder) water tank of diameter 2.2m and height of 3m is full of water. The water flows out of the base into a rectangular prism 7m long and 3m wide.

a) Find the volume of the water in the cylindrical water tank in:
i) cubic metres
ii) litres 

b) Let the height of the rectangular prism be hm. Find the volume of the rectangular prism (box) in terms of h. Do this by writing the formula for the volume of a rectangular prism and substituting in the two known values and h.

c) What would the minimum height (h, to the nearest cm) of the rectangular prism have to be if it is to hold all the water. 

Thanks so much!!

Answer 1

I am not sure what you mean by "inverse operations", unless you mean additive inverses and multiplicative inverses.  So that is how I will proceed.

 

3x-7=7+x

 

Additive inverse:

3x - 7 - x = 7 + x - x

2x - 7 = 7

 

2x - 7 + 7 = 7 + 7

2x = 14

 

Mult inverse:

(2x)/2 = 14/2

 

X = 7

 

 

3 ((6x-2)/4) + 1 = 33

 

Mult inv:  (mult both WHOLE SIDES by 4 to "get rid of" 4 in denom

 

3 (6x-2) + 4 = 132

 

Add inv:

3 (6x-2) + 4 - 4 = 132 - 4

3 (6x - 2) = 128

 

 

Mult inv:  divide both sides by 3

 

6x - 2 = 128/3

 

Add inv:

6x - 2 + 2 = 128/3  + 2

6x = 128/3 + 6/3

6x = 134/3

 

Mult inv:  mult both sides by (1/6) to isolate x.

 

x = (134/3) (1/6) = 134/18

 

This reduces to

 

x = 67/9

 

 

 volume in cylinder

V = (pi) (r^2) (h)

V = (pi) (1.1)^2 (3)

V = 3.63 (pi) m^3

 

To convert to liters:

 

1 m^3 = 1000 liters

So 3.63 (pi) (1000) = 

 

3630(pi)   liters.

 

 Vol of rect = l w h

 

 

Vol = (7) (3) (h)

 

Vol of cyl = Vol of box

 

3.63 (pi) = 21 h

 

Isolate h

[3.63 (pi)]/21. =  h

 

Rearrange and reduce

 

h = [1.1 (pi)]/7  meters