Convert the rectangular Point (8,0) in polar point.
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- II. Determine the equation of the family of curves as described then find thedifferential equation by eliminating the arbitrary constants. Draw the figure showingthe family of curves. 2. Circles tangent to the x-axis.as engineer design a cooling tower in the shape of hyperboloid of one sheet. The horizontal cross sections of the cooling tower are circular with 10m.The cooling tower is 40m tall with maximum cross-sectional radius of 15m. (A) Construct a mathematical equations for this cooling tower. (B) If x=a cos(u) cosh(v) ,y=b sin(u) cosh(v) and z= csinh(v), show that (x,y,z)lies on your equation in Q1(A). (C) A colleague at the same institution want to construct the cooling tower using an hyperbolic cylinder, give reasons for your result in Q1(A) as the best model for the design of cooling tower.Q4: Find parametric equations for the line through (7,2,-4) parallel to the z-axis. Let z=-4+t. x___, y____, z_____, −∞<t<∞ (Type expressions using t as the variable.)
- I've attached the question, along with my attempt at a solution. Is my example right? The first term is what I chose for a removable singularity at 1, the second term for a pole of order 5, and the last as an essential singularity at 0. The part I'm not completely sure about is if the residue of the function is 14. I know that removable singularities have a residue of 0, and that the essential singularity has a residue of 1. Then I figured I needed to get a function with a residue of 13 in order to have a total residue of 14. Can you verify/correct my work? Or provide a different solution? Thank you.If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)} is differentiable at x. What rule is this? A. Sum Rule B. Power Rule C. Product Rule D. Chain Rule It represents the distance of a point from the y-axis. A. polar distance B. ordinate C. coordinate D. abscissamulivariate constrained optimizations: second order conditons Given the constraint, find the stationary points for the following function and evaluate the second order conditions. Use the Lagrange technique. Show all steps. z=28x-2x2+6xy-5y2+10y subject to 2x+10Y=250
- II. Determine the equation of the family of curves as described then find thedifferential equation by eliminating the arbitrary constants. Draw the figure showingthe family of curves. 1. Parabolas with axis parallel to the x-axis with focal distance “a” fixed.2. Circles tangent to the x-axis.3. Straight lines with sum of x and y intercept equal to a constant “k”.calc 3 Use Green's Theorem to evaluate ∫C F·dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = ‹y - ln(x2 + y2), 2arctan(y/x)›C is the circle (x - 5)2 + (y - 3)2 = 16 oriented counterclockwise.Suppose a city of 225290 people is experiencing a viral outbreak. Public health officials have determined that a SIR model is a good model for this outbreak. They have calculated that the parameter a is approximately 2.3 x 10^-7 and the data on the virus indicates that it takes approximately 25 days to recover from infection. After infection and recovery, a person becomes immune. At day 32 there are 4421 people infected, 421 people have recovered, and 224418 people are still susceptible. Use Euler's method to predict the susceptible, infected, and recovered the population on day 33. a)233624 susceptible,8802 infected, and 468 recovered b)233624 susceptible,406 infected, and 8740 recovered c)233624 susceptible,426 infected, and 8760 recovered d)224396 susceptible,406 infected, and 488 recovered e)224396 susceptible,426 infected, and 468 recovered solve step by step
- 4.2-2 continuation of the problem Deduce that x is a regular mapping if and only if EG - F2 is never zero. (Thisis often the easiest way to check regularity. We will see, beginning in the nextchapter, that the functions E, F, G are fundamental to the geometry ofsurfaces.)a. Show that if the position x of a moving point is given by a quadratic function of t, x = At2 + Bt + C, then the average velocity over any time interval [t1, t2] is equal to the instan-taneous velocity at the midpoint of the time interval. b. What is the geometric significance of the result in part (a)?