The diagram shows the curve and its maximum point M. The shaded region R is enclosed by

Question:

The diagram shows the curveand its maximum point M. The shaded region R is enclosed by the curve, the x-axis and the lines x = 1 and x = p.

i. Find the exact value of the x-coordinate of M.

ii. Calculate the value of p for which the area of R is equal to 1. Give your answer correct to 3 significant figures.

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: Apr 05, 2023 11:07 AM

See More Questions

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
The diagram shows part of the curve y = 2 x 2 ln(x + 1). The shaded region R is bounded by the curve and by the lines x = 0, x = 1 and y = 0. Use the trapezium rule with intervals to estimate the...
The 9-yd-long rectangle below inscribes a perfect semi-circle drawn inside it. Find the area of just one of the two shaded regions that are inside the rectangle and outside the semi- circle. Give...
Ridge Crest Company has beginning Retained Earnings of $39,000, ending Retained Earnings of $41,500, and a net income of $23,500. What was the amount of dividends declared during the year: $15,500...
Use the following balance sheet to answer the questions: a. What is the year-to-year percentage change in the value of the following? Inventory Accounts payable Land Taxes payable Liabilities...
The scatterplot shows reading test scores against IQ test scores for 14 fifth-grade children. There is one low outlier in the plot. What effect does this low outlier have on the correlation? a. It...
Water flows through a 2-in.-diameter pipe with a velocity of $15 \mathrm{ft} / \mathrm{s}$ as shown in Fig. P8.78. The relative roughness of the pipe is 0.004, and the loss coefficient for the exit...
The national mean annual salary for a school administrator is $90,000 a year (The Cincinnati Enquirer, April 7, 2012). A school official took a sample of 25 school administrators in the state of Ohio...
1.If variable manufacturing overhead is applied to production on the basis of direct labor-hours and the direct labor efficiency variance is unfavorable, will the variable overhead efficiency...
When (1 + ax) 2 , where a is a positive constant, is expanded in ascending powers of x, the coefficients of x and x 3 are equal. i. Find the exact value of a. ii. When a has this value, obtain the...
Express in partial fractions. ii. Hence obtain the expansion of in ascending powers of x, up to and including the term in x 2 . 4 + 12x + x (3 - x)(1+2x)
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin. x 2 + x + y 2 + 2y = 0
Differentiate between normalizing and annealing.
An analyst engaged in the tourism industry obtained detailed information on 76 travel packages offered by a Viennese travel agency. The file Travel contains the following variables: - Price (price of...
Differentiate between hardening and tempering.
Give the formula for the money multiplier. In recent years, why has the Fed become less concerned with controlling the money supply?
Define Robot, write the classification based on robot physical configuration, write down the applications of an industrial robot.
A large condenser in a steam power plant dumps 15 MW at 45oC with an ambient at 25oC. What is the entropy generation rate?
Consider a closed, rigid tank with a volume of 0.8L, filled with cold water initially at 27C. The tank is filled such that there are no voids (air pockets) within. The initial pressure within the...
The diagram shows part of the curve y = (x 2) 4 and the point A(1, 1) on the curve. The tangent at A cuts the x-axis at B and the normal at A cuts the y-axis at C. i. Find the coordinates of B and...
The diagram shows part of the curve and a point P(6, 5) lying on the curve. The line PQ intersects the x-axis at Q(8, 0). i. Show that PQ is a normal to the curve. ii. Find, showing all necessary...
The diagram shows parts of the curves intersecting at points P(0, 1) and Q(2, 3). The angle between the tangents to the curves at Q is . i. Find , giving your answer in degrees correct to 3...
Assignment 5B: What's your sign? We can use 2D arrays as a kind of look-up table". This means we can fill it with information, and quickly access relevant data using the index numbers. First, you...
What is the natural rate of unemployment? Provide a detail answer.
Suppose Heat Miser Air Conditioner Company engaged in the following transactions during June of the current year: June 3 Purchased inventory on credit terms of 1/10 net eom (end of month $1,600) 9...

The diagram shows the curve and its maximum point M. The shaded region R is enclosed by

Question:

y= || 1.² 1 + x³ for x > 0,

Step by Step Answer:

i To find the maximum point of the curve y x21 x3 we need to find where the derivat...View the full answer

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

Students also viewed these Mathematics questions