A curve has parametric equations The point P on the curve has parameter p. It is given

Question:

A curve has parametric equations

The point P on the curve has parameter p. It is given .that the gradient of the curve at P is −0.4.

a. Show that

b. Use an iterative process based on the equation in part a to find the value of p correct to 3 decimal places. Use a starting value of 1 and show the result of each iteration to 5 decimal places.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Mar 24, 2023 02:10 AM

See More Questions

Show that if b = a/4 in Problem 61, the parametric equations of the hypocycloid may be simplified to x = Î± cos3 t, y = Î± sin3 t This is called a hypocycloid of four cusps....
A point P on the rim of a wheel of radius a is initially at the origin. As the wheel rolls to the right along the x-axis, P traces out a curve called a cycloid (see Figure 18). Derive parametric...
In Question 24 of the extended activities regarding the ELISA test data, you found that the probability that a randomly selected person who tests positive for HIV (the first time) actually has the...
Find the struggles faced by business (printed t-shirts) with suppliers? Explain what would be the communication plan for each stakeholder and how you'll implement the decision you have taken?
The Top 25 global research organizations include companies such as The Nielsen Company, the Ipsos Group, and Harris Interactive. Data about global research revenues (in US$ millions) and the number...
a) Lisa promises to give Billy as a gift, her laptop. The laptop is valued at $1000. Billy accepts. Is there a legally enforceable contract. Give your reasons. b) If Lisa sells her laptop to Billy...
What other unforeseeable events contributed to making Xeroxs executives unwilling to take any new risks precisely at the time the Alto was ready to be released? Imagine the value of cornering the...
Make a briefing for division managers showing the advantages and disadvantages of e-learning and how to blend it with other teaching techniques. Use websites, including www.astd.org.
9. What were the companys predetermined overhead rates in the Molding Department and the Fabrication Department? (Round your answers to 2 decimal places.) A.) How much manufacturing overhead was...
Zheng Corporation had the following selected transactions in the month of March. The company adjusts its accounts monthly. 1. Th e company has an 8%, $12,000 bank loan payable due in one year....
In the diagram, A, B and C are points on the circumference of the circle with centre O and radius r. The shaded region, ABC, is a sector of the circle with centre C. Angle OCA is equal to radians....
Explain how an increase in the rate of inflation might affect (a) real interest rates and (b) nominal interest rates.
Problem 8-19 (Algo) Cash Budget; Income Statement; Balance Sheet [LO8-2, LO8-4, LO8-8, LO8-9, LO8- 10] Minden Company is a wholesale distributor of premium European chocolates. The company's balance...
Consider the unsteady flow of a fluid in the x direction through a control volume. The linear momentum of the fluid within the control volume is a function of time given by 200ti slug*ft/s, where t...
For a continuous uniform distribution with u = 0 and o = 1, the minimum is - V3 and the maximum is V3. For this continuous uniform distribution, find the probability of randomly selecting a value...
Marc Goudreau, administrator of Clearwater Hospital, was puzzled by the prior month's reports. "Every month, it's anyone's guess whether the lab will show a profit or a loss. Perhaps the only answer...
A system consisting of a gas consisting of O2 (32 Da), H2 (2 Da), and Ar (40 Da) molecules and a billiard ball is at some temperature . Relative to O2, the billiard ball is 1.0 E+26 times as massive...
During June, Plowers Company accumulated 2,400 hours of direct labor costs on Job 30 and 3,000 hours on Job 32. The total direct labor was incurred at a rate of $22 per direct labor hour for Job 30...
Determine by direct integration the values of x for the two volumes obtained by passing a vertical cutting plane through the given shape of Fig. 5.21. The cutting plane is parallel to the base of the...
Find the first three terms, in ascending powers of x, in the expansion of (2 3x) 4 (1 + 2x) 10 .
a. Write down the expansion of (x + y) 5 . b. Without using a calculator and using your result from part a, find the value of correct to the nearest hundred. (101), 4
An arithmetic progression has first term a and common difference d. The sum of the first 100 terms is 25 times the sum of the first 20 terms. a. Find d in terms of a. b. Write down an expression, in...
Create a Data Table to depict the future value when you vary the interest rate and the investment amount. Use the following assumptions: Interest Rates: Investment Amounts:-10.0% $10,000.00 -8.0%...
Isaac earns a base salary of $1250 per month and a graduated commission of 0.4% on the first $100,000 of sales, and 0.5% on sales over $100,000. Last month, Isaac's gross salary was $2025. What were...
Calculate the price, including both GST and PST, that an individual will pay for a car sold for $26,995.00 in Manitoba. (Assume GST = 5% and PST = 8%) a$29,154.60 b$30,234.40 c$30,504.35 d$28,334.75...

A curve has parametric equations The point P on the curve has parameter p. It is given

Question:

1 === , y = √t + 1 X t

Step by Step Answer:

ANSWER To find the gradient of the curve at P we differentiate both sides of the given equations wit...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions