[Ananya]

Diameter of a cylindrical water tank is 1.4m , and radius of a cylinder is half of its diameter .

Therefore, radius of cylindrical water tank = 1.4/2 = 0.7m .

Height of the cylindrical water tank is 2m.

Capacity of the cylindrical water tank can be calculated by the formula :

( π r^2h )

Where, r is the radius of cylindrical water tank and h is the height of the cylindrical water tank .

• r^2 = 0.7 * 0.7 = 0.49m^2

• Capacity of cylindrical water tank=

π *( r^2 )*h

= (22/7)*(0.49)(2)

= (22)(0.07)(2)

=(44)(0.07)

= 3.08m^3

• 1m^3 = 1000litre

To convert metre cube into litre , we have to multiply it by 1000 .

Therefore, capacity of cylindrical water tank is 3080litres.

[Ananya]

To prove :

(Sin^4(θ) – cos^4(θ) + 1)(cosec^2(θ) =2

Left hand side :

(Sin^4(θ) – cos^4(θ)+1)(cosec^2(θ))

=> We can write sin^4(θ) as (sin^2(θ))^2

and cos^4(θ) as (cos^2(θ))^2 .

=> ((Sin^2(θ))^2 -(cos^2(θ))^2 +1)(cosec^2(θ))

=> Now we will use the following identity: (a^2 – b^2) = (a+b)(a-b) in our equation

=> ((Sin^2(θ)-cos^2(θ))(sin^2(θ) + cos^2(θ) ) + 1)(cosec^2(θ))

=> We know that :

(sin^2(θ) + cos^2(θ))= 1 ,

Therefore,

((Sin^2(θ)-cos^2(θ)).1 +1)(cosec^2(θ))

=> We can write it as ↓

=> (Sin^2(θ) +1- cos^2(θ))(cosec^2(θ))

=> We can write sin^2(θ) as

(1- cos^2(θ)) as we know sin^2(θ)+cos^2(θ) = 1

sin^2(θ) = 1- cos^2(θ) —{eq a}

=> (sin^2(θ) + sin^2(θ))(cosec^2(θ)). {using eq a}

=> (2sin^2(θ))(cosec^2(θ))

=> Using the relation between cosec(θ) and sin(θ)

We know sin(θ)=1/(cosec(θ) or

Cosec(θ)=1/(sin(θ)

Squaring both side

cosec^2(θ)=1/(sin^2(θ)). —eq 1

=> (2sin^2(θ))/(sin^2(θ)). {using eq 1}

=> 2

Hence proved

[Ananya]

The slope intercept form of line is y=mx+c

Where m is slope and c is intercept with y axis

Here , m = 19 and c =3

Therefore required slope intercept form is

y= 19x + 3

• This reply was modified 1 year, 9 months ago by  Ananya.
• This reply was modified 1 year, 9 months ago by  Ananya.