A line has equation y = kx + 6 and a curve has equation y = x

Question:

A line has equation y = kx + 6 and a curve has equation y = x² + 3x + 2k, where k is a constant.

i. For the case where k = 2, the line and the curve intersect at points A and B. Find the distance AB and the coordinates of the mid-point of AB.

ii. Find the two values of k for which the line is a tangent to the curve.

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 And A Level Mathematics Pure Mathematics 1 Coursebook

ISBN: 9781108407144

1st Edition

Authors: Sue Pemberton, Julian Gilbey

See More Books

Question Posted: Mar 09, 2023 05:44 AM

A line has equation 2x + y = 20 and a curve has equation where a is a constant. Find the set of values of a for which the line does not intersect the curve. 18 x-3 y = a +-
At which points on the curve y = 1 + 40x3 3x5 does the tangent line have the largest slope?
2. A line has equation y=r-0.5 a. Pick five distinct x-values, use the equation to compute the corresponding y-values, and plot the five points obtained. b. Give the value of the slope of the line;...
Economic crises tend to occur sporadically virtually every decade and in various countries ranging from Sweden to Argentina, from Russia to Korea, and from Japan to the United States. Each crisis is...
A company produces cans of stewed tomatoes with an advertised weight of 14 oz. The standard deviation of the weights is known to be 0.4 oz. A quality-control engineer selects a can of stewed tomatoes...
Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film: a. Within the dorm...
The rigid beam is supported by a pin at A and two steel wires, each having a diameter of 4 mm. If the yield stress for the wires is y = 530 MPa, and E st = 200 GPa, determine (a) the intensity of...
Harte Systems, Inc., a maker of electronic surveillance equipment, is considering selling to a well-known hardware chain the rights to market its home security system. The proposed deal calls for the...
The following data (in thousands) were taken from recent financial statements of Under Armour, Inc.: December 31 Current assets Current liabilities Year 2 Year 1 $ 159,002 $ 115,644 38,971 28,839 a....
a. Complete the traffic table in Figure 3-13. b. In Figure 3-12, add 392 Mbps of traffic for Seattle-Ogden communication. Using a picture like the one in the figure, show your work. c. Do it again...
Find the real solutions of the equation (3x 2 + 5x 7) 4 = 1.
The path of a projectile is given by the equation where x and y are measured in metres. a. Find the range of this projectile. b. Find the maximum height reached by this projectile. y =(3)x. 49x 9000
Imagine that a person you admire is coming to speak on campus. You have been selected to introduce the speaker to your entire graduating class. Of course, you want to ensure you have accurate...
that Given that two random vectors x and z are jointly Gaussian, show 2Pyy-1/2-(y-y) Py(y-y) 2P21/2e-(2-2) P (z-z) where y = [x ZTT p(x|z) = p(x,z) p(z) is Gaussian with mean and covariance given by...
MANAGERIAL ACCOUNTING IB CHAPTER 20 QUIZ Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Seven Seas Company operated at 100% of capacity during its...
According to Dalton's atomic theory a b no two atoms of given element are exactly alike. only compounds are made of atoms. d atoms cannot be subdivided, created, or destroyed. atom is composed of...
23) A company might choose to allocate corporate costs to various divisions within the company for what four purposes? Give an example of each. 24) An electronics manufacturer is trying to encourage...
During 2010, Vaughn Corporation sold merchandise costing $1,500,000 on an installment basis for $2,000,000. The cash receipts related to these sales were collected as follows: 2010, $800,000; 2011,...
In the last 30 years, the wage difference between high school and college graduates has grown dramatically. At the same time, the fraction of adults over age 25 that have college degrees has risen...
Beginning with a country that has a trade deficit, demonstrate graphically what will happen to a countrys potential output with globalization if that countrys costs of production fall. Explain your...
Research shows that 17% of children are absent from school on at least five days during winter because of ill health. A random sample of 55 children is taken. a. Find the probability that exactly 10...
The following table shows the probability distribution table for the random variable Q. a. Find the value of x. b. Evaluate Var(Q). Camb P(Q= 3 x-2 x+1 18 x- 3 2.
A fair six-sided die is numbered 1, 1, 2, 3, 5 and 8. The die is rolled twice and the two numbers obtained are added together to give the score, X. a. Find E(X). b. Given that the first number rolled...
Describe the current global business trend wherein countries are reducing trade between themselves to develop capabilities/supply chains in their own country. Provide 3 examples of companies or...
In 2015, the weather conditions were better than normal, leading to higher rainfalls filling up the rivers (which is good for salmon breeding). Moreover, the cooler weather led to higher growth of...
in java please. you will carry out a binary classification task, code and a report on this. The data come from photos, and your task is to come up with a machine learning method for classifying the...

A line has equation y = kx + 6 and a curve has equation y = x

Question:

Step by Step Answer:

i When k 2 the line and the curve have equations y 2x 6 y x2 3x 4 To find the points of intersection ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

Students also viewed these Mathematics questions