Question

1).factorise..
64m^3-125n^3
2).In a hot water heating system ,there is a cylindrical pipe of length 28m n diameter 5m. find the total radiating surface in the system..
3).If x+1/x=7 find x^3+1/x^3
4). the inner diameter of a circular well is 3.5 it is 10m deep find. it's inner csa, and the cost of plastering this csa at the rate of Rs. 40/m^2
5). find the value of (256)^0.16*(256)^0.09
plz answer my questions... if u know then only...

Answer 1

(1) 

64m^3 - 125n^3

4^3m^3 - 5^3n^3

We know that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

(4m - 5n)(5^2n^2 + 4 * 5nm + 4^2m^2)

(4m - 5n)(25n^2 + 20nm + 16m^2).



(2) 

Given height = 28cm.

Given Diameter = 5m.

Then the radius r = 5/2

                              = 2.5cm.

                              = 0.025m.


Now,


The total radiating surface in the system = 2pirh

                                                                    = 2 * 22/7 * 0.025 * 28

                                                                    = 2 * 22 * 0.025 * 4

                                                                    = 4.4m^2.


Therefore the radiating surface in the system = 4.4m^2.


(3) 

Given x + 1/x = 7

On cubing both sides, we get

(x + 1/x)^3 = (7)^3

x^3 + 1/x^3 + 3 * x * 1/x(x + 1/x) = 343

x^3 + 1/x^3 + 3(7) = 343

x^3 + 1/x^3 + 21 = 343

x^3 + 1/x^3 = 343 - 21

x^3 + 1/x^3 = 22


(4) 

Given that the diameter of the circular well = 3.5m.

Then the radius of the circular well r = 3.5/2

                                                              = 1.75m.

Given Depth of the well = 10m.

We know that Curved surface area of cylinder = 2pirh

                                                                              = 2 * 22/7 * 1.75 * 10

                                                                              = 110m^2.

Given the cost of plastering per m^2 = 40

Therefore the plastering 110 m^2 = 110 * 40

                                                        = 4400.


Hence the cost of plastering = 4000. 


(5)

(256)^0.16 * (256)^0.09

(256)^0.16 + 0.09

(256)^0.25

(4^4)^0.25

(4^4)^1/4

(4)^4 * 1/4

(4)^1

4.


Hope this helps!

Answer 2

Answer:

Step-by-step explanation:

64m^3-125n^3

(4m)^3-(5n)^3

Identity is x^3 -y^3=(x -y) (x^2+xy+y^2)

So,

(4m)^3-(5n)^3=(4m-5n)(16m^2+4m*5n+25n^2)

=( 4m- 5n)(16m^2+20mn-25n^2)