A curve has equation xy = 12 + x and a line has equation y = kx

Question:

A curve has equation xy = 12 + x and a line has equation y = kx − 9, where k is a constant.

a. In the case where k = 2, find the coordinates of the points of intersection of the curve and the line.

b. Find the set of values of k for which the line does not intersect 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 03:37 AM

See More Questions

A curve has equation y = f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P.
A curve has equation y = f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P.
A curve has equation xy = 20 and a line has equation x + 2y = k, where k is a constant. a. In the case where k = 14, the line intersects the curve at the points A and B. Find: i. The coordinates of...
In Problems 1158, perform the indicated operation, and write each expression in the standard form a + bi. 2 + i i
Following are the data on study time and score for calculus students from Exercise 4.55. a. Compute SST, SSR, and SSE, using Formula 4.2 on page 167. b. Compute the coefficient of determination, r2....
Reba Dixon is a fifth grade school teacher who earned a salary of $38,000 in 2017. She is 45 years old and has been divorced for four years. She received $1,200 of alimony payments each month from...
The mean annual salary for a sample of electrical engineers is $$86,500$, with a standard deviation of $$1500$. The data set has a bell-shaped distribution. (a) Use the Empirical Rule to estimate...
The following sample data reflect shipments received by a large firm from three different vendors. a. Specify the competing hypotheses to determine whether quality is associated with the source of...
Morten Hansen, in his book Great at Work , challenges the long-held practice and belief by many organizations that in order to succeed and grow the organization, employees need to work longer hours....
Muskoge Company uses a process-costing system. The company manufactures a product that is processed in two departments: Molding and Assembly. In the Molding Department, direct materials are added at...
ABCD is a trapezium with AB parallel to DC and angle BAD = 90. a. Calculate the coordinates of D. b. Calculate the area of trapezium ABCD. B (3, 2) A (13, 17) D C(13,4) X
The line y = x 3 meets the curve y 2 = 4x at the points A and B. a. Find the coordinates of the midpoint of AB. b. Find the length of the line segment AB.
Write up to two lines of code that perform each of the following tasks: a) Specify that class Orange inherits from class Fruit. b) Declare that you are going to override the toString method from...
According to value-chain analysis, a firm Blank______. Multiple choice question. becomes unprofitable when support costs are greater than primary costs creates value to customers when its support...
Aerielle asks her stockbroker to purchase 100 shares of Publix Super Markets, Inc., but he advises her that he cannot do so because Publix is structured as what kind of company?
Write a program that reads two dates entered in the format " day.month.year " and calculates the number of days between them . Enter the first date: 27.02.2006 Enter the second date: 3.03.2006...
The figure shows a robot whose base is 1m away from the base of the table. The table is 1m height and its surface is a square. Frame {1} is fixed on a corner of the table. A 20 cm cube is located on...
Your objective is to write an properly formatted, error-free business document.You may choose your own subject for the communication, keeping in mind to use the proper approach for the intended...
Charlie cares only about the amount of chocolate he eats this year and the amount of chocolate he eats next year. We will use C0 to stand for chocolate this year and C1 to stand for chocolate next...
As you rewrite these sentences, replace the cliches and buzzwords with plain language (if you don't recognize any of these terms, you can find definitions online): a. Being a jack-of-all-trades, Dave...
Given that: a. n = 14 and x = 325.5, find x . b. n = 45 and y = 23.6, find the value of y. c. z = 4598 and z = 52.25, find the number of values in the set of data. d. xf = 86 and x = 7 1/6 = , find...
Identify the mode of x and of y in the following tables. 5 6 -3 -2 -1 7 8. 1 5 6. 4 27 28 29 27 25 4.
The mean mass of 13 textbooks is 875 grams, and n novels have a total mass of 13 706 grams. Find the mean mass of a novel, given that the textbooks and novels together have a mean mass of 716.6 grams.
4 The midterm grades on a chemistry exam, graded on a scale of 0 to 100, were: 62, 64, 65, 65, 68, 70, 72, 72, 74, 75, 75, 75, 76, 78, 78, 81, 83, 83, 84, 85, 87, 88, 92, 95, 98, 98, 100, 100, 740...
Answer any ten questions: (a) If we throw two fair dice, which is more likely: a sum of 11 or a sum of 12? (b) Give a combinatorial explanation of the identity (3)-(8) (E) + (8)(7) + (2)(6). (c) What...
playing the video game Methods of Math Destruction. In order to get to the next level you must discover the access code. The game gives you the following clues: the number is a four digit number all...

A curve has equation xy = 12 + x and a line has equation y = kx

Question:

Step by Step Answer:

a The line equation is y 2x 9 when k 2 To determine the points of intersection we can substitute the ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

Students also viewed these Mathematics questions