A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70 cm/s. Find the rate at which the area within the circle is increasing after each of the following. A. After 1 second B. After 5 seconds C. After 6 seconds

(A) 30772cm^2/s

(B) 153860cm^2/s

(C) 184632 cm^2/s

Step-by-step explanation:

We are given

speed of the ripple = 70cm/s

this speed is increasing the radius which means speed = radius /time

radius = speed*time

r= 70t

Now we know the area of the circle

A = π

this area will be increasing as ripples in water will spread out

upon differentiating

dA/dt = 2πr *

dA/dt = 2π*70t*70       ( r= 70t , dr/dt = speed = 70)

dA/dt = 9800π*t

(A) after 1 second

dA/dt = 9800π*1=9800π = 30772cm^2/s

(B) after 5 seconds

    dA/dt = 9800π*5 = 153860cm^2/s

(C) after 6 seconds

 dA/dt = 9800π*6 = 184632 cm^2/s

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

c

step-by-step explanation: