The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 120 cm^2?

The base is decreasing at 2 cm/min.

Step-by-step explanation:

The area (A) of a triangle is given by:

  (1)

Where:

b: is the base

h: is the altitude = 10 cm

If we take the derivative of equation (1) as a function of time we have:

We can find the base by solving equation (1) for b:

Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:

Therefore, the base is decreasing at 2 cm/min.

I hope it helps you!  

the square root of what number? if you add that, then someone will probably answer the question.

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.