Explanation Note that if an equation of the line is y = m x + c then the slope of the line is given by m . Use the parametric equation and deduce the equation in the xy- plane to calculate the slope. Use y = − 2 + 6 t to calculate the value of t in terms of y as shown below. y = − 4 − 5 t 2 y = − 8 − 5 t 2 t = 2 y + 8 − 5 Substitute the value of t in the value of x and simplify as, x = 1 + 2 t 3 = 6 + 2 ( 2 y + 8 − 5 ) 3 =

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 10.1, Problem 40E

To determine

To find: Slope of the line and a point on the line represented by the parametric equation x=1+2t3,y=−4−5t2 and also draw the corresponding graph.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.1, Problem 39E

Chapter 10.1, Problem 41E

Students have asked these similar questions

3. Find the derivative of each function. Label with appropriate derivative notation showing both dependent and independent variables. f(t)=4t(2t⭑+4)³ a. f(t)=4t (2t+4)³ (Answer must be factored.) b. y= 3 1 (2x³-4) 6

4.3 The Chain Rule 1. {Algebra review} Let f(x)=2x²-5 x and g(x)=6x+2. Find f[g(−5)]. 2. {Algebra review} Write h(x)=√√8x-3 as the composite of two functions f(x) and g(x). (There may be more than one way to do this.)

4.4 Derivatives of Exponential Functions 1. Find derivatives of the functions defined as follows. a. g(t)=-3.4e b. y=e√x c. f(x)=(4x³+2)e³* d. y=- x²

Chapter 10 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 10.1 - Explain how a pair of parametric equations...Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Give parametric equations that generate the line...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Explain how to find points on the curve x = f(t),...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Slope of the line and a point on the line represented by the parametric equation x = 1 + 2 t 3 , y = − 4 − 5 t 2 and also draw the corresponding graph.

Solution Summary: The author explains that the slope of the line is -154 and the point lies on it.

Concept explainers

Videos

To find: Slope of the line and a point on the line represented by the parametric equation x=1+2t3,y=−4−5t2 and also draw the corresponding graph.

Want to see the full answer?

Chapter 10 Solutions