Volume of a cylinder: v=πr to the power of 2 h;solve for h

V = π * r2 * h, and r + h = 12

You have 2 independent variables, so use both equations to develop a formula for V. It seems best to use substitution for h, to keep the equation relatively simpleSo:

r + h = 12

rearrange to get: h = 12 - r

Substitute in the 1st equation to get:

V = π * r2 * (12 - r)

Expand:

V = 12πr2 - πr3

To find a maximum (or minimum), the typical method is to find the 1st derivative and set it equal to zero.

V' = 24πr - 3πr2

Set equal to 0 and solve for r:

24πr - 3πr2 = 0

8r - r2 = 0

r = 0, 8 (Interpretation: 0 gives you the minimum volume, and 8 gives you the maximum)

Step-by-step explanation:

hope this will help you

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

1) is right

step-by-step explanation: