Tutor profile: Prashant B.
tanx = root 3 and x is between 180 and 270 find sin(x - 210)
tan(x) = root of 3 it means this angle, x , must be in 1th or 3th quadrant because tangent in these quadrants are positive you know tan(x) = root 3 will tell you the angle, x , must be 60 and also it must be 3th quadrant so x = 180 + 60 = 240 now we need to find sin( x - 210). by plugging 240 in sin ( x- 210 ) we have sin ( 240 - 210) = sin (30 ) = 1/2
Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)= 3x^2+4x+6 at x=3.
f '(y) = limh--> 0 [f(y+h) - f(y)]/h where h is just the change in y. For these small changes in y and x we denote then dy and dx, so you'll see the derivative is dy/dx just the change in y over change in x but at a specific point. f(y+h) = 3(y+h)2 + 4(y+h) + 6 = 3y2 + 6hy + 3h2 + 4y + 4h + 6 f(y) = 3(y)2 + 4(y) + 6 f(y+h) - f(y) = (3h2 + 6hy + 4h) = h(3h + 6y + 4) f '(x) = limh--> 0 [f(y+h) - f(y)]/h = limh--> 0 [h(3h + 6y + 4)]/h h cancels out and you get 3h + 6y + 4 now we take the limit as h approaches 0, plug in h = 0 and you get 6y+4. plug in y = 3 to get 22
if 300 joules of work is performed in 1.00 minutes, what is the power expanded on the object
power = work done/ time Work done = 300 Joules Time = 1 min = 60 sec Power = 300/60 J/s = 5 J/s = 5 Watts I J/s = 1 Watt
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