Suppose that the length l, width w, and perimeter P of a rectangle are differentiable functions of t. Suppose also that the length is always three times and twenty-two more than the width. Write an equation that relates dPdt to dwdt. Enter your answers using exact values.

Step-by-step explanation:

The perimeter, P, is given by

Since ,

Differentiating P with respect to w,

But

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

the answer will be the last one