a square garden with a side of 150m has a square swimming pool in the very center with a side length of 25m calculate the area of the garden

21,875 sqm

Step-by-step explanation:

Step 1:

   Find the gross area of the garden.

   Square 150m = 22,500 sqm.

Step 2:

   Find the area of the pool.

   Square 25m = 625 sqm.

Step 3:

   Subtract the area of the pool from the gross area of the garden

   to find the net area of the garden.

   22,500 - 625 = 21,875 sqm.

Warning:

   Do not subtract the side length of the swimming pool from the side length

   of the garden before squaring.

See below

Step-by-step explanation:

Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.

if v(t) is the speed at time t after being dropped, v'(t) is the acceleration at time t, so the the initial value problem for the downward velocity is

v'(t) = 10 - 0.1v(t)

v(0) = 0 (since the object is dropped)

The equation v'(t)+0.1v(t)=10 is an ordinary first order differential equation with an integrating factor

so its general solution is  

To find C, we use the initial value v(0)=0, so C=-100

and the solution of the initial value problem is

what is the terminal velocity?

The terminal velocity is

How long before the object reaches 90% of terminal velocity?

90%  of terminal velocity = 90 m/sec

we look for a t such that

How far has it fallen by that time?

The distance traveled after t seconds is given by

So, the distance traveled after 23.026 seconds is