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Consider two bonds, HI and LI. The HI bond has a 10% coupon rate and the LI bond has a 5% coupon rate. Both bonds pay interest annually and are priced to yield 10%. Suppose the following interest scenarios are possible at the point in time when both bonds have five years remaining to maturity:
possible interest rate 5%,10,15
possibility of interest rate 10%, 50,40
Required:
a. Calculate the expected value for each bond.
b. Calculate the standard deviation of possible values for each bond.
c. Which bond is riskier? Why?
A rain drop of mass 3gm starts to fall from rest under the effect of gravity from a height of
100m. There is an air drag acting on the rain drop, the drag force is given by the equation,
F = bv.
Here, b = 2 × 10−3kgs−1 s
(a) Determine the governing differential of the system.
(b) Build a SIMULINK model of the system using transfer functions.
(c) Show velocity vs time graph with and without the effect of air drag on the same
plot.
(d) Show height vs time graph with and without the effect of air drag on the same
plot.
(e) From your graphs, determine the approximate time required for the rain drop to
reach the ground.
Two shafts A and B are connected by rolling cones and turn in the same direction. Shaft A makes 300 rpm while shaft B makes 100 rpm. Calculate the cone angle of each cone and the diameter of each base if the base of cone B is 2 in. from the vertex. θ = 30°
Two shafts, having axes in the same plate intersecting at an angle of 45°, turn in opposite senses at 30 rpm and 90 rpm. Draw a pair of cone to be located on these shafts and turn in pure rolling contact. Diameter of base of smaller cone is 1 in. Calculate the cone angles.
Two solids of right section 2 and 4 are in pure rolling contact between the circular arcs. What is the angular speed ratio for the position shown? Determine the size of the angles , β, and Ø in degrees, and of the radii x and y in inches.
If F is Lipschitz function and g(x) is monotonically increasing on [a,b] then fog is bounded variation
Consider the function
F(x)= xsin(π/x) 0<x≤1
0 x=0
Show that f(x) is continuous but not of bounded variation
Consider the markets for film-streaming services, TVs and cinema tickets.
a For each pair, identify whether they are complements or substitutes.
– film-streaming services and TVs
– film-streaming services and cinema tickets
– TVs and cinema tickets
b Suppose a technological advance reduces the cost of manufacturing TVs. Draw a diagram to
show what happens in the market for TVs.
c Draw two more diagrams to show how the change in the market for TV screens affects the
markets for film-streaming services and cinema tickets.
Find the real root of the equation 𝑥𝑒𝑥=2 correct upto two decimal places using the method of false position.
The plates of a parallel – plate capacitor uses a disk with a radius of 10mm. The separation distance between the plates is 100 nm and between the plates is a sheet of mica. What is the capacitance of the capacitor?
#340153 on Dec 2023