Question

In: Math

For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table.

For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table.

Solutions

Expert Solution

Consider a set of parametric equations as follows,

x(t) = 4 - t ...... (1)

y(t) = 3t + 2 ...... (2)

 

t x(t) = 4 - t y(t) = 3t + 2
0 4 – 0 = 4 3 × 0 + 2 = 2
1 4 – 1 = 3 3 × 1 + 2 = 5
2 4 – 2 = 2 3 × 2 + 2 = 8
3 4 – 3 = 1 3 × 3 + 2 = 11
4 4 – 4 = 0 3 × 4 + 2 = 14

 

From the table, for 1 unit decrease in x, the variable y increases by 3 units. Hence, above equation is a linear equation with slope

m = change in y/change in x

    = 3/(-1)

    = -3

 

Since, the slope-point form of a straight line,

y – y1 = m(x – x1) ...... (3)

 

Substitute m = -3 and (x1, y1) = (4, 2), the Cartesian equation of above line will be,

  y – 2 = (-3)[x – 4]

  y – 2 = -3x + 12

3x + y = 14

 

Therefore, the Cartesian form of above parametric equations is 3x + y = 14.


Therefore, the Cartesian form of above parametric equations is 3x + y = 14.

Related Solutions

1a. Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) =...
1a. Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = cos(t) + 1 y(t) = 7 sin2(t) 1b. A dart is thrown upward with an initial velocity of 68 ft/s at an angle of elevation of 52°. Consider the position of the dart at any time t. Neglect air resistance. (Assume t is in seconds.) Find parametric equations that model the problem situation. x(t) = y(t) = 1c. A dart is thrown upward with...
rewrite cartesian equation r=(sinTHETA)/(2cos^2THETA)
rewrite cartesian equation r=(sinTHETA)/(2cos^2THETA)
Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant-...
Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant- coefficeint equation by substituting x = e^t. b) Solve it when x(1)=0, x'(1)=1.
Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equation of x-y form (cartesian equation). Thank you
Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equation of x-y form (cartesian equation). Thank you
For the following exercises, write a logarithmic equation corresponding to the graph shown. Use y = log2 (x) as the parent function.
For the following exercises, write a logarithmic equation corresponding to the graph shown.Use y = log2 (x) as the parent function.
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)?
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.
Two linearly independent solutions of the following equation (1 − x) y″  +  x y′  − ...
Two linearly independent solutions of the following equation (1 − x) y″  +  x y′  −  y  =  0 are  y1(x)  =  4ex and  y2(x)  =  8x. (a) Find the Wronskian W(y1, y2) of y1 and y2. (b) Using the method of variation of parameters, find a particular solution of (1 − x) y″  +  x y′  −  y  =  2(x − 1)2 e −x
Rewrite the following statements to use only one if statement. if x < y if z < 10
Rewrite the following statements to use only one if statement.if x < yif z < 10w = x*y*zendend  
For the following exercises, each graph is a transformation of y = 2x. Write an equation describing the transformation.
For the following exercises, each graph is a transformation of y = 2x. Write an equation describing the transformation. 
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT