16. If 2 sin2x - 3 = 3 cos x and 90° < x < 270°, the number of values that satisfy the equation is
use stokes theorem to evaluate the line integral where F= "-y" i +x j and C is the boundary of the ellipse x^2 /a + y^2/b =1 ,z=0
1a.
Show from first principles, i.e., by using the definition of linear independence,
that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix
A with associated eigenvector v = u + iw, then the two real solutions
Y(t) = eat(u cos bt − wsin bt)
and
Z(t) = eat(u sin bt + wcos bt)
are linearly independent solutions of ˙X = AX.
1b.
Use (a) to solve the system (see image)
Reduce the system
(D2 + 1)[x] − 2D[y] = 2t
(2D − 1)[x] + (D − 2)[y] = 7.
to an equivalent triangular system of the form
P1(D)[y] = f1(t)
P2(D)[x] + P3(D)[y] = f2(t)
and solve.
Identify each of the following statements as true or false in relation to confidence intervals (CIs).
Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.
True | False | |
---|---|---|
A 95% CI is a numerical interval within which we are 95% confident that the true mean μ lies. | ||
A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯ lies. | ||
The true mean μ is always inside the corresponding confidence interval. | ||
For a sample size n=29, the number of degrees of freedom is n=30. | ||
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not contain the true mean 𝜇. |
let us also assign to n the orientation in the direction of increasing x value. then compute surface integral over n of the vector field k on plane given by
4. The magnetic field in the certain region is 0.128 T, and its direction is that of the +z-axis in
the figure below. (a) What is the magnetic flux across the surface abcd in the figure? (b) What
is the magnetic flux across the surface befc? (c) What is the magnetic flux across the surface
aefd? (d) What is the net flux through all five surfaces that enclose the shaded volume?
What is the magnitude of the force a + 25 uc charge exerts on a +3.0mc charge 35 cm away
Use the definition of Laplace Transform to determine the Laplace Transforms for
the following time-domain function
f(t)=sin(3t)