The parametric equations x = : e2t cos t, y = e2t sin t define a curve in the parametric interval –0
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![Question 8
The parametric equations x =
e2t cos t, y
e2t sin t define a curve in the parametric interval -o <t <∞.
A. Find an equation in polar coordinates for the curve.
B. Find the length of the curve from t = 0 to t = 27.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c4a66ef-c9c6-4abf-a644-7d4d1711fffc%2F29ecbf12-d727-4794-a820-ca41b71d7bac%2Fjbi136w_processed.png&w=3840&q=75)
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.The path of a projectile that is launched h feet above the ground with an initial velocity of vo feet per second and at an angle 0 with the horizontal is given by the parametric equations shown below, where t is the time, in seconds, after the projectile was launched. x= (vo cos 0) t, y=h+ (Vo sin 0) t-16t2 Use a graphing utility to obtain the path of a projectile launched from the ground (h=0) at an angle of 0 = 65° and initial velocity of v = 130 feet per second. Use the graph to determine the maximum height of the projectile and the time at which it reaches this height, as well as the range of the projectile and the time it hits the ground. Choose the correct graph of the path of the projectile. OA. Q G OB. ○ C. O D. Q Q E G [0,1000]x[0,300] [0,1000] x [0,300] [0,1000]x[0,300] What is the maximum height of the projectile? feet (Type an integer or decimal rounded to the nearest tenth as needed.) At what time does the projectile reach this maximum height? seconds (Type an integer or…Consider the parametric equation What is the length of the curve for 0 = 0 to 0 = ³/? x = 8(cos 0 + 0 sin 0) y = 8(sin 0 - 0 cos 0)
- Graph the curve with parametric equations x = sin(t), y = 2 sin(2t), z = sin(3t). And Find the total length of this curve correct to four decimal places. Calculus 3A wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 790 cm long, and 250 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale). P 790 cm 250 cm Write parametric equations for the position of the point P as a function of t, time in seconds after the ball starts rolling up the ramp. Both x and y are measured in centimeters. I = y = You will have a radical expression for part of the horizontal component. It's best to use the exact radical expression even though the answer that WAMAP shows will have a decimal approximation.A curve has parametric equations given below: x = 2 cot(t), y =2 sin?(t) 0• Find the equation of the tangent line to the curve described by the parametric equation described below at the given point. ta + 2, t3 +t (3, –2)Graph the pair of parametric equations for 0 ≤t≤ 2. Describe any differences in the two graphs. (a) x = 8 cost, y = 8 sin t (b) x = 8 cos 6t, y = 8 sin 6t ... (a) Graph the first pair of parametric equations x=8 cost, y = 8 sin t. Use the graphing tool to graph the function. Click to enlarge graph CILDHelpMatch equation graph with its parametric equation. Not all equations will be used. All graphs shown for -5Please help me.Part I: PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric equations given. Plot the curve and draw the tangent line and locate the point of tangency. y = 11+ t², x = 4t - 3 DIESEE MORE QUESTIONSRecommended textbooks for youAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage