(1 pt) A plane with equation 1 (a, b, c > 0) together with the positive...
(c) Each equation below specifies a line or a plane in R3. If possible, express the specified line or plane as a span. Otherwise, justify why it cannot be expressed as a span. i. 2x-yz=4 ii. х+6у—z%3D 0 iii. x+3z = 0 iv. у %3D1 v. x = 0 and z = 0 vi. 2x -y 2 and z =-1 (d) For lines or planes in question 4c that cannot be expressed as spans, express as a translated span
22.M. If c>0 and n is a natural number, there exists a unique positive number b such that b" = c.
1. Floating point arithmetic. The standard formula for solving ax² +bx+c=0 is -b±/b² – 4ac 2a = Fx However, if b² > closest to zero. Why is this, and how can you avoid this problem? Jac| this can give inaccurate results, at least for the root
12. Consider the region bounded above by the function
?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0.
(1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
True/False
(a) If a > 0 and b > 1 then In(a/b) = ln(a)/In(6) ? (b) Suppose a population of rabbits increases proportionally with its size. It takes less time for the rabbit population to grow from 100 rabbits to 150 rabbits, then it takes it to grow from 1000 rabbits to 2500 rabbits. (c) The partial fractions decomposition of a can be written in the form А r2 +- В +1 va du = ln |21/2|+C. «Σε συνειρες
= Consider the equation ax² + 2xy + cy? 1 where a > 0 and ac – 62 > 0. Note that a 6 Y = 1. Consider an invertible linear map y X = 6 с х 1 e и between (x, y) and (u, v) given by = y 0 1 V (a) Choose a value for e (in terms of a, b and c), so that the given equation on the (u, v) LEO plane becomes [u...
Problem4:
25 Ω b 1 = 0, T 80 Ω a 100 Ω + + + 100 V 240 Ω υο 80 μF 275 V Υ 16 mH (b) Find Il(s). Find i(t). (c) Find the zero-input and the zero-state components of iz(t) for t > 0.
3. Given the consumption function C = 0 -by (with a > 0:0 <b< 1): (0) Find its marginal function and its average function. (b) Find the income elasticity of consumption Ecy, and determine its sign, assuming Y >0. (9) Show that this consumption function is inelastic at all positive income levels.
Problem 2 - Point charge and plane (20 pts) A point charge q (q>0) is located a distance d above an infinite conducting plane lying in the x-y plane. The plane is connected to the ground (Fig.1), so that the electric potential V at any point on the plane satisfies V=0. Calculating the electric potential generated by the point charge-grounded plane combination at any point P is more complicated than it looks because the conducting plane pulls some electric charge...