Casey has a backyard that is a 50-by-50 foot square. she turned over an irregularly-shaped plot of soil to plan a garden. to find the area of the garden, 1,500 random points are generated and 420 of the points land inside the irregularly-shaped garden. what is the area of the garden?

Area of the garden is 700 square feet.

Step-by-step explanation:

It is given that casey has backyard that is a 50 by 50 foot square. Area of yard is the product of its dimensions. So, the area of yard is

Let the area of the garden be x.

It is given that 420 out of 1500 points land inside the irregularly shaped garden. It means the proportion of these points is equal to the proportion of area.

The value of x is 700. Therefore the area of the garden is 700 square feet.

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