A sample of gas has a volume of 5.35 L at 1.346 atm. What will the volume (L) of the gas be if the pressure is at 924 torr? 760 torr = 1atm
This is a gas law problem. List the knowns V1 = 5.35 L V2 = ? P1 = 1.346 atm P2 = 924 torr = 1.216 atm n1 = n n2 = n R1 = R R2 = R T1 = T T2 = T (P1)(V1)/nRT = (P2)(V2)/nRT The denominators on both sides cancel out (P1)(V1) = (P2)(V2) Now plug in the values and solve for V2 (1.346 atm)(5.35 L) = (1.216 atm)(V2) V2 = (1.346 atm)(5.35 L)/(1.216 atm) (the unit "atm" cancels out here) V2 = 5.92 L This makes sense because according to Boyle's Law, the volume of a gas is inversely proportional to pressure, so if the pressure decreases than the volume increases.
Given the function f(x) = (tan(x^3 + 4x^2 - 7))^5 Find f'(x)
The chain rule, power rule, and must be used several times for the solution. For the first part of the solution, let tan(x^3 + 4x^2 - 7) = u so f(x) = u^5 and f'(x) = (5u^4)(u') Next, let x^3 +4x^2 - 7 = v so u = tan(v) and u' = (sec(v))^2(v') and f'(x) = (5u^4)((sec(v))^2)(v') Next, find v' v = x^3 +4x^2 - 7 v'= 3x^2 + 8x Lastly, substitute back in all of the values f'(x) = (5(tan(x^3 + 4x^2 - 7))^4)((sec(x^3 +4x^2 - 7))^2)(3x^2 + 8x)
Simplify the expression: 8(x + 3y - 2z) - (1/2)(z - 7y + 2x - 64) + 90
Given the expression: 8(x + 3y) - (1/2)(z - 7y - 64) + 90 Multiply through the parentheses: 8x + 24y -16z - (1/2)z + (7/2)y - x + 32 + 90 Combine like terms (cross multiply to get a common denominator for fractions): (8x - x) + ((48/2)y + (7/2)y) - ((32/2)z + (1/2)z) + (32 +90) = 7x + (55/2)y - (33/2)z + 122