CALCULUS RELATED RATES: A 20 foot ladder is leaning against a wall. The base of the ladder is placed 6 feet from the bottom of the wall. The base of the ladder slips away from the wall at a constant rate of 2 feet/sec. Find the velocity of the top of the ladder as it slider down the wall 3 seconds after it begins to fall.

2.17ft/s

Step-by-step explanation:

Look at the sketch of ladder at the beginning and after 3 seconds it starts to fall,

Distance of ladder from the wall 3 seconds after ladder starts to fall                                       =  Initial distance+  Velocity× time

= 6 + 2×3

= 12ft

Use trignometry to find out the speed of the top of ladder

cosθ= 12/20

θ= 0.825 rad

tan θ= v/2

v= 2.17ft/s

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.