Aladder 10 ft long rests against a vertical wall. let theta be the angle between the top of the ladder and the wall and let be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta=pi/3?

5 ft/s

Step-by-step explanation:

Let L be the length of the ladder. The relation between the angle and distance X is:

X = L * sin θ      the change of X will be:

dX/dt = L * cos θ    If we evaluate the expression when θ = π/3, we get the change of X:

dX/dt = 10 * cos(π/3)

dX/dt = 5 ft/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:

ok then what happened.