(Modeling) Mach Number An airplane flying faster than the speed of sound sends out sound waves that form a cone, as shown in the figure. The cone intersects the ground to form a hyperbola. As this hyperbola passes over a particular point on the ground, a sonic boom is heard at that point. If θ is the
where m is the Mach number for the speed of the plane. (We assume m> 1.) The Mach number is the ratio of the speed of the plane to the speed of sound. Thus, a speed of Mach 1.4 means that the plane is flying at 1.4 times the speed of sound.
In each of the following exercises, θ or m is given. Find the other value (θ to the nearest degree and m to the nearest tenth as applicable).
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Trigonometry plus MyLab Math with Pearson eText -- Access Card Package (11th Edition)
- pls exact valuesarrow_forwardFind the polar representations of a point which has -л<О≤л and is symmetrical to the given point with respect to the origin. (√2.- 1/1) π 4arrow_forwardFind the area of a triangle formed by the pole and the two points with polar coordinates. π A 5, - B(10, 2π)arrow_forward
- Plot each point given its polar coordinates. Then, give another pair of polar coordinates for the same point with the opposite radius and angle 0 ≤ 0 < 2π (or 0 ≤ 0 < 360°). (-6, 120°)arrow_forwardFind two additional polar representations of the given point such that one has the same sign as r but the opposite sign of 0, and the other has the opposite sign of r but the same sign as 0. 3, - π 6arrow_forwarde consider the problem -((1+x)))= 0 XE U(0) = 0, 'U(1)=\@Sind the analytical sol and he Find the Variational form and find Matrix A and b? consider the Variational form a (u,v)-(SV) where acu,v) = vdx prove that YVE H. (0,1),i=1, 2, \\-\ a(vi)=-v(x-1)+2V(xi)-(X;+1)] Where Vn is usual basis of hat functions. Consider the Problem Au=f and u= du=0 0 a with bilinear formalu,v) = SAU. AV r Prove that alu, v). V-ellPitic. and aluv) is continuous..arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning