To determine Find the values of x and y and slope of the curve for x 3 + 2 t 2 = 9 , 2 y 3 − 3 t 2 = 4 , t = 2 . Explanation Given data: x 3 + 2 t 2 = 9 (1) 2 y 3 − 3 t 2 = 4 (2) t = 2 Formula used: Consider the Parametric Formulas. d y d x = d y / d t d x / d t (3) Calculation: Rearrange equation (1) as follows. x 3 = 9 − 2 t 2 Substitute 2 for t as follows. x 3 = 9 − 2 ( 2 ) 2 = 9 − 2 ( 4 ) = 9 − 8 = 1 Simplify the equation as follows. x = 1 3 = 1 Rearrange equation (2) as follows. y 3 = 4 + 3 t 2 2 Substitute 2 for t as follows. y 3 = 4 + 3 ( 2 ) 2 2 = 4 + 3 ( 4 ) 2 = 4 + 12 2 = 16 2 Simplify the equation as follows. y = 8 3 = 2 Find d x d t . Differentiate equation (1) with respect to t . d d t ( x 3 + 2 t 2 ) = d d t ( 9 ) d d t ( x 3 ) + 2 d d t ( t 2 ) = d d t ( 9 ) 3 x 2 d x d t + 2 ( 2 t ) = 0 3 x 2 d x d t + 4 t = 0 d x d t = − 4 t 3 x 2 Find d y d t . Differentiate equation (2) with respect to t

14th Edition

ISBN: 9780134654874

Author: WEIR

Publisher: VST

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 11.2, Problem 15E

To determine

Find the values of x and y and slope of the curve for x3+2t2=9, 2y3−3t2=4,t=2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.2, Problem 14E

Chapter 11.2, Problem 16E

Students have asked these similar questions

1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]

(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]

Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find lim→-4 1 [2h (x) — h(x) + 7 f(x)] : - h(x)+7f(x) 3 O DNE

Chapter 11 Solutions

EBK THOMAS' CALCULUS

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Finding Cartesian from Parametric...

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.