Volume of sphere, V = 4/3 Π r3 Rate of change of volume with respect to time = dV/dt Differentiate expression of V with respect to time(per week) dV/dt = 4/3 x Π x 3r2 = 4Πr2dr/dt radius r...
Volume of sphere, V = 4/3 Π r3 Rate of change of volume with respect to time = dV/dt Differentiate expression of V with respect to time(per week) dV/dt = 4/3 x Π x 3r2 = 4Πr2dr/dt radius r...
Function of instantaneous height with respect to time instantanious distance = 6 + ut - 1/2 gt2 u = initial velocity = 20 ft/sec g = acceleration due to gravity t = time Fucntion of final velocity with respect to time Final velocity...
1 mole of NaCl will have 6.023 x 1023 atoms 8.56 x 1033 moles will have 6.023 x 1023 x 8.56 x 1033 = 51.55688 x 1056 atoms :)
Assume Bert started with x money spent on notebook = 4.75 Remaining money = x-4.75 spent on text book = 1/2 (x - 4.75) remaining money = (x - 4.75) - 1/2(x - 4.75) = 1/2(x - 4.75) spend on sheet music = 4 remaining...
Second plan will fetch him = .25 + .5 + 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.75 second plan would be most profitable. :)
Find slopes of both lines. If product of the slopes is -1 then the line are perpendicular. Slope of line AB = (9-6)/(-4 -1) = -3/5 Slope of line CD = (1-9)/(3-9) = 8/6=4/3 Products of two slopes is not -1 so lines are not perpendicular :)
Assume 100 beans in the soup Lentils = 36/100 x 100 = 36 Green = 33.33/100 x 36 = 12 If green lentils are removed left beans = 100 - 12 = 88 Left beans = 88/100 x 100 = 88% of original beans x = 8...
Amount = principal ( 1+ r)n Amount = 1200 ( 1+ 4.5/100)55-19 = 5852.85
Consider this as a right angle traingle problem. Distance travel by Northbound car represent vertical side of traingle = 12 miles Distance traveled Eastbound car represent base of traingle = x miles Distance between the care is represented...
Find K in both cases. It shoud be same before yielding situation. 1. Stress = 2x9.8N Strain = 17/L k = 2x9.8/(12/L) = 1.6L 2. Stress = 1.4x9.8M Strain =...
When this curve rotates about x axis it will look like a trapeziod with radius of 1 unit (√(2-1))at one end and radius of 4 units (√(5-1)) at another end with height of 3 units (5-2=3_like a chopped off cone. You can use calculus volume of an infinite...
Its a unique point where relative position of distributed mass sums to zero. In other words its a imaginary point where the entire mass of a body or system of bodies is suppose to act. It can be with in a body or outside the body depending on the distribution of mass. In simple...
(f+g)(x) = 5x2 -4x +2 + 4x -6 = 5x2 - 4 (f*g)(x) = (5x2 -4x +2)(4x -6) = 20x3 - 16x2 + 4x - 30x2 +24x - 12 = 20x3 - 46x2 +28x -12 :)
Use 9 years as base year Find increment per year from 9 to 15 years => (46687 - 41350)/6 = 889.5 (A)salary = 41350 + 889.5n where is n is numer of years of experience in addition to 9 years (B) salary in 10 years = 41350 + 889.5x1 = 40,460.5 (C)...
Let money invested i nreal estate be x and moneyinvested in money market = y so money invested in certificates = x + y - 80000 now x + y + (x+y- 80000) = 200000 => 2x + 2y = 280000 => ...
30 degrees or π/6 radian :)
3/(x-8) = 12 3= (x-8)12 3=12x - 96 99=12x x= 99/12 So h(x) = 12 when x = 99/12 :)
Average rate of change of sales per year = change is sales/total years = (15.2 - 8.5)/(2005 - 1995) = 6.7/10=0.67 billion per year :)
33 = 27 :)
C(9,6) = 9!/(6! x 3!) = 9x8x7x6x5x4x3x2x1/(6x5x4x3x2x1)(3x2x1) = 84 :)