A line has equation 4x + y + k = 0 and a curve has equation y

Question:

A line has equation 4x + y + k = 0 and a curve has equation y = kx² + 3, where k is a constant.

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

b) Find the equation of the straight line
joining the points on the curve for these
two values of k.

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

Step by Step Answer:

Related Book For book-img-for-question

Complete Pure Mathematics 1 For Cambridge International AS & A Level

ISBN: 9780198427438

2nd Edition

Authors: Jean Linsky, Brian Western, James Nicholson

See More Books

Question Posted: Apr 13, 2023 10:51 AM

See More Questions

A line has equation y = kx + 6 and a curve has equation y = x 2 + 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...
A curve has equation y = 2 3x x 2 . a. Express 2 3x x 2 in the form a (x + b) 2 , where a and b are constants. b. Write down the coordinates of the maximum point on the curve. c. Find the two...
The parallel-plate air capacitor in Fig consists of two horizontal conducting plates of equal area A. The bottom plate rests on a fixed support, and the top plate is suspended by four springs with...
Using the information for Sarot, Inc., in SE 4 and SE 5, compute the current ratio, quick ratio, receivable turnover, days sales uncollected, inventory turnover, days inventory on hand, payables...
Recessions are an economic phenomenon that are often dened as two consecutive quarters of reduced national output. One measure to assess the severity of a recession is the rate of unemployment. The...
On November 23, 2023, Hamlet acquires and places in service a 7-year class asset with a cost of $100,000 (the only asset acquired during the year). Hamlet does not elect immediate expensing under...
The soft-ride suspension system of the mountain bike is pinned at C and supported by the shock absorber BD. If it is designed to support a load of P = 1500 N, determine the factor of safety of pins B...
Richard, age 45, is married with two children in high school. He estimates that his average annual earnings over the next 20 years will be $60,000. He estimates that one-third of his average annual...
Using the Trade Stats Express page and response to the following questions: What are the leading U.S. exports and imports in terms of value? Which trading partners are most important to the United...
Dino Dog Collars uses activity-based costing. Dinos system has the following features: Each collar has four parts, direct materials cost is $ 9.00 per collar, and direct labor cost is $ 4.00 per...
Show that that the straight line with equation 3x y + 8 = 0 is a tangent to the circle with equation x + y 18 x 10y + 16 = 0.
The circles with equations x + y + 6x 10y = 26 and x + y 12x + 4y = k are congruent. a) Determine the value of k. b) Calculate the distance between their centres.
In 2014, Entergy paid a regular quarterly dividend of $.83 per share. a. Match each of the following dates. (A1) Friday, July 25 ........................................(B1) Record date (A2) Monday,...
In Year Lee Incorporated biled its customers $56,800 for services performed. The comparty collected $40,600 of the amount billed Lee incurred $37,100 of other operating expenses on account, and paid...
What do these lasso regression and PCA methodologies have in common?
Figure 3 shows a cantilevered beam (ABC) with modulus E and moment of inertia I. A distributed load of wo spans 1/3rd of its length. The beam is simply supported at point B. Use Castigliano's theorem...
Due to covid-19, do you believe hospitals have changed their tax structure to non-profit to make up for lost revenues during and in the aftermath of covid-19?
On April 1, 2023, Jimmy Kalinowski organized the consulting firm of Uncle Inc., which uses cash basis accounting. The following cash transactions were completed during the month of April: Jimmy...
A $40,000 loan at 6.6% compounded monthly will be repaid by monthly payments over ten years. a. Calculate the interest component of Payment 35. b. Calculate the principal component of Payment 63. c....
Rowland Textile Inc. manufactures two products: sweatshirts and T-shirts. The manufacturing process involves two activities: cutting and sewing. Expected overhead costs and cost drivers are as...
Every year the U.S. Census Bureau releases the Current Population Report based on a survey of 50,000 households. The goal of this report is to learn the demographic characteristics, such as income,...
Contrast the differences between qualitative and quantitative variables?
A community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks how many hours per week...
If an employee contributes $12,000 per year (assume contributions are at the end of each year) to a 401(k) plan (with no fees), and they earn an average rate of return of 8% per year, how much will...
What is the net present value and internal Rate Of Return on this investment from local perspective? Texas Innovation (TI) (U.S.) is considering investing Rs 100,000,000 in India to create a wholly...
Suppose the 2022 adidas financial statements contain the following selected data (in millions). Current assets $6,000 Cash $930 Total assets 10,400 Interest expense 320 Current liabilities 4,400...

A line has equation 4x + y + k = 0 and a curve has equation y

Question:

Step by Step Answer:

a To find the two values of k for which the line is a tangent to the curve we need to find the point...View the full answer

Complete Pure Mathematics 1 For Cambridge International AS & A Level

Students also viewed these Mathematics questions