(a) On a separate sheet of paper, sketch the parameterized curve x=tcost, y=tsint for 0≤t≤4π. Use...

(a) On a separate sheet of paper, sketch the parameterized curve x=tcost, y=tsint for 0≤t≤4π. Use your graph to complete the following statement:

At t=6t=6, a particle moving along the curve in the direction of increasing t is moving _________ and _____________

(b) By calculating the position at t=6 and t=6.01, estimate the speed at t=6.
speed ≈___________

(c) Use derivatives to calculate the speed at t=6 and compare your answer to part (b).

speed ≈___________

Expert Solution

milcah answered 2 years ago

y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0, x and y are real numbers

utility function u(x,y;t )= (x-t)ay1-a x>=t, t>0, 0<a<1 u(x,y;t )=0 when x<t does income consumption curve...

utility function u(x,y;t )= (x-t)ay1-a x>=t, t>0, 0<a<1 u(x,y;t )=0 when x<t does income consumption curve is y=[(1-a)(x-t)px]/apy ?(my result, i used lagrange, not sure about it) how to draw the income consumption curve?

1. Use the guidelines of this section to sketch the curve. y = x(x − 4)^3...

1. Use the guidelines of this section to sketch the curve. y = x(x − 4)^3 . Provide answer to parts below–you may need another piece of paper. (Note: Domain is all Reals; No Symmetry; No Asymptotes. A. Intercepts B. Intervals of Increase or Decrease C. Local Max or Min Values D. Concavity and points of Inflection E. Sketch the graph. Thank you!

Sketch the curve given by the parametric equation x= tan(t) , y=sec (t) for -pi/2 <...

Sketch the curve given by the parametric equation x= tan(t) , y=sec (t) for -pi/2 < t < pi/2. Eliminate the parameter "t" and find the Cartesian form of this curve. What type of curve is this? What curve would be good if "t" belong to the interval (pi/2, 3pi/2)?

Solve the following differential equations: 1.) y"(x)+ y(x)=4e^x ; y(0)=0, y'(0)=0 2.) x"(t)+3x'(t)+2x(t)=4t^2 ; x(0)=0, x'(0)=0

Solve the following differential equations: 1. x"(t)+ x(t)=6sin(2t) ; x(0)=3, x'(0)=1 2.y"(t)- y(t)=4cos(t) ; y(0)+0 ,...

Solve the following differential equations: 1. x"(t)+ x(t)=6sin(2t) ; x(0)=3, x'(0)=1 2.y"(t)- y(t)=4cos(t) ; y(0)+0 , y'(0)=1

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts. Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

On a separate sheet of paper, draw a Lorenz Curve for the United States, using the...

On a separate sheet of paper, draw a Lorenz Curve for the United States, using the 2017 values for income quintiles. Label each kink point carefully, and draw the diagonal equality Lorenz Curve. Calculate the Gini Coefficient, and show your work. This is a long and tedious math problem, where you find the areas of triangles, rectangles and trapezoids over and over to get the areas needed for the formula. 2017: Shares of aggregate income Quintile Share of income Cumulative...

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1...

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1 , x'(0)=0

Sketch the region bounded above the curve of y=(x^2) - 6, below y = x, and...

Sketch the region bounded above the curve of y=(x^2) - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integrals and evaluate the integral.

Question