The gas law for an ideal gas at absolute temperature t (in kelvins), pressure p (in atmospheres), and volume v (in liters) is pv = nrt, where n is the number of moles of the gas and r = 0.0821 is the gas constant. suppose that, at a certain instant, p = 8.0 atm and is increasing at a rate of 0.14 atm/min and v = 13 l and is decreasing at a rate of 0.16 l/min. find the rate of change of t with respect to time at that instant if n = 10 mol. (round your answer to four decimal places.)dt/dt = k/min

Step-by-step explanation:

We have to calculate the time derivative of T=PV/nR with P and V variable and n and R constants. This is:

What we have to do is the derivative of a product:

Substituting, we have:

where all these values are given since the time derivatives of P and V are their variation rate, using minutes.

We then substitute everything, noticing that already everything is in the same system of units so they cancel out:

And then just calculate:

answer: 0.64

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)