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Given f(x)= identify a function u of x and an integer n not equal to 1 such that f(x)=(x2+3x+1)5/(x+3)5 . Then compute f'(x)
Area of a Segment of a Circle.In a circle of radius 6 centimeters, find the area of the segment bound by an arc of measure 120 degrees
Tangency of three circles.Create two tangent circles with centers A and B. For convenience sake, let circle A have the larger radius.
Let n be a positive integer a) prove that n is divisible by 5 if and only if it ends with 0,5
write down the centre and radius of circle A.Explain why the distance between the centres of circles A and B is 10.
We've got a cylindrical can with height =h and radius =r. It will hold 4L (4,000 cm cubed) of some liquid. The material for the top and bottom costs 2 cents
Write an expression for the slope of the curve at any point (x,y)
Show that if the tangent to y=ekx at (a, eka) passes through the origin then a=1/k.
Revolutions of a tire.Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles
Given a circle, construct a circle with twice its area. I know that the r2 = (x-h)2 + (y+k)2 is the standard equation for a circle.
Functions f, g, and h are continuous and differentiable for all real numbers, and some of their values and values of their derivatives are given by the below
Prove algebraically that the stereographic projection of a circle (C) lying in a sphere (S) is either a circle or a straight line.
Two distinct, nonparallel lines are tangent to a circle. The measurement of the angle between the two lines is 54° (angle QVP).
Use quotient rule to find derivative of this function. f(x) = (20+16x-x^2)/(4+x^2).
Mobius Transformations for Circles.Prove: For any given circles R and R' in C_oo, there is a mobius transformation T such that T(r)=R'.
Find the derivative of each function a. f(x)=x2-6x+3
A brick comes loose from near the top of a building and falls such that its distance s (in feet) from the street (after t seconds) is given by the equation
Right circular cone related rates.Related rates problem on a right circular cone that is increasing its volume at 2 cubic feet/min
Find the derivative by the limit process:
A particle moves along the x-axis so that its acceleration at any time is a(t)=2t-7. If the initial velocity of the particle is 6, at what time t
Equation of the circle.Find the equation of the circle with center at the intersection of 4x + y - 4 = 0 and x - y - 6 = 0 and passing through (-1, -3).
Banking of circular track.The sleepers of a railway track which is turning round a bend of radius 60m are banked
A particle moves along the x-axis so that at any time that t is greater than or equal to zero, its position is given by x(t)= t^3-12t+5.
Use logarithmic differentiation to find dy/dx: y=(x+2)*sqrt[1-x^2]/(4*x^3)
Formula of Circle. A circle is the set of points that lie at a constant distance from one point, the center of the circle.