Concept explainers
Arc Length In Exercises 49-54, find the arc length of the curve on the given interval.
Parametric EquationsInterval
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- 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.arrow_forwardA 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.arrow_forwardConsider the parametric curve = cos(t) sin(t) and y sin²(t) on the domain () < t < π. = Find the values of t for which this function has a horizontal tangent line. Find the values of t for which this function has a vertical tangent line. Question Help: Message instructor Submit Questionarrow_forward
- Analytic Geometry: Trace the curve r2 = 4cos4 o tan2 oarrow_forwardUse a graphing utility to graph each set of parametric equations. x = t − sin t, y = 1 − cos t, 0 ≤ t ≤ 2π x = 2t − sin(2t), y = 1 − cos(2t), 0 ≤ t ≤ π (a) Compare the graphs of the two sets of parametric equations in earlier part. When the curve represents the motion of a particle and t is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?arrow_forwardConsider the parametric curve C defined by x = x ( t ) and y = y ( t ) . (a) Explain how to determine the location of the horizontal tangent line(s) of C. (b) Explain how to determine the location of the vertical tangent line(s) of C Use complete sentences to answer this question. All math in your solution must be appropriately typeset.arrow_forward
- 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…arrow_forwardTrace the curve r² = 4cos⁴(theta) tan²(theta).arrow_forwardUsing Derivatives of trigonometrical and inverse trigonometrical functionsarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning