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Locus of a point-Determining the equation of a curve.A curve is traced by a point P(x,y) which moves such that its distance from the point A
Finding Curvature. Compute the curvature k(t) of the curve r(t) = 2t i + 4sint j +4cost k
Calculate the area under the curve y=1/(x^2) above the x-axis on the interval [1, positive infinity].
Tangent Normal and curvature of parametric plane curves.Find unit tangent and normal vectors at the given point:
Operations supply management - learning curve. A time standard was set at 0.20 hour per unit based on the 50th unit produced.
Charecteristics of a curve.Find the unit tangent and principle normal vectors at an arbitrary point h(s)
Curve on a Spherical Surface. Curve C defined by x=sin(2t), y=1-cos(2t), z=2cos(t) where t lies between (or equal to) -pi and pi.
The monopolist has a constant marginal and average total of $50 per unit. Calculate the monopolist 's profit.
The particle flies off on tangent at t0 = 2 and moves along the tangent line to its trajectory with the same velocity that it had at time 2.
Prove the following product rule for vector derivatives given the functions: vec{A} = 2x x-hat + y y-hat + 4z z-hat
Arc Length and Tangent.The equation R(t)=sint(i)+cost(j)+logsect(k) (0 less than or equal to t and t is less than pi/2)
Water is poured into a conical funnel at a rate of 1 cm3/s. The readius of the top of the funnel is 10 cm and the height of the funnel is 20 cm
Z scores and p values. Fill in the answers for each table below. Please report your z scores to two decimals and your p values to three decimals.
Evaluate the following logarithms. a)log22log55
For the following function find the value of the derivative at the specific point given using:
Determine dy/dx for each of the following relations.
Explain why the firm's short run production has only one 'rational' stage of production
Find the exact length of the curve defined by y=2[(sqrt(x))^(3)]-1=2x^(3/2)-1 from x=0 to x=2.
If f'(a) = 0 and f"(a) = 0, then the function f does not have an extreme point at x = a.
Gaussian Curvature of the Unit Sphere. Compute the curvature of the unit sphere in R^3.
Curve Fitting and Input and Output Files. This is a three dimensional version of the two dimensional curve fitting problem associated with determining
Suppose f(x) = ln(2 + cos x) on the interval (0, 2pi).
Early one morning it began to snow at a constant rate. At 7 AM a snowplow set off to clear a road. By 8 AM it had traveled 2 miles but it took two more hours
Value Curve and Swing Weights in Excel.Generate a value curve using Excel for the following problem:
The resale value of a certain industrial machine decreases at a rate that depends on its age. When the machine is t years old, the rate at which its value