Question The graphs of y = 1 − x2 and y = x4 − 2x2 + 1 intersect at three points. However, the area between the curves can be found by a single integral. Explain why this is so, and write an integral that represents this area.

Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded above by the curve \( y=x^{2} \), below by the \( x \)-axis, and on the right by the line \( x=2 \), about the line \( x=-1 \). \[ \mathrm{V}= \] (Type an exact answer, using \( \pi \) as needed.) Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded above by the curve y=x2, below by the x-axis, and on the right by the line x=2, about the line x=−1. V= (Type an exact answer, using π as needed.)

11.60 Consider the flow of air through the piping system shown in Fig. P11.60. If the system is choked, determine the location where the Mach number is 1. Calculate the pressure ratio pb/Po, that causes choking in this system. 100 in 100 in Pв PO то 4 1.5 in diameter 1 in diameter Short nozzle 0.0030 in 1.5 in pipe 0.0035 in 1 in pipe

The worldwide market share for the Chrome web browser was 56.43% in a recent month. Suppose that you decide to select a sample of 100 students at your university and you find that 60 use the Chrome web browser. a. Use the five-step p-value approach to determine whether there is evidence that the market share for the Chrome web browser at your university is greater than the worldwide market share of 56.43%. (Use the 0.05 level of significance.) b. Suppose that the sample size is n = 600, and you find that 60% of the sample of students at your university (360 out of 600) use the Chrome web browser. Use the five-step p-value approach to try to determine whether there is evidence that the market share for the Chrome web browser at your university is greater than the worldwide market share of 56.43%. (Use the 0.05 level of significance.) c. Discuss the effect that sample size has on hypothesis testing. d. What do you think are your chances of rejecting any null hypothesis concerning a population proportion if a sample size of n = 20 is used?

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 26 lb and b = 12 lb. Round your answers to one decimal place.) Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 26 lb and b = 12 lb. Round your answers to one decimal place.)

Harley-Davidson is known for its strong brand name and loyal following and yet by 1980 Harley was on the verge of bankruptcy. Why was Harley in deep trouble even with such a strong brand name? a) Harley-Davidson cannot compete in foreign markets b) Competitors beat Harley on reliability and cost c) All of the above d) Harley-Davidson bikes are technologically inferior COURSE: STRATEGIC BUSINESS DECISIONS

Suppose that a wind is blowing in the direction S45°E at a speed of 30 km/h. A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 200 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.)