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1.) A motor has 5 speeds varying from 29 rpm to 464 rpm in a Geometric Progression.
(a)Calculate the common ratio
(b)Make a table of the speeds.
2.)
a.)Solve by calculating a value for the following Maclaurinseries when
π₯=3to 3 decimal places.
π(π)=π/π
b.)Solve using power series prove:
π /π π(π^π)=π^x
You have carried out an experiment to investigate the effect of the
length of a pendulum on the time-period of oscillation. Theory says
that the pendulum should follow the rule
π»=ππ βπ³/π
Where T is the time-period
L is the length of the pendulum
G is the acceleration due to gravity
Accurately solve using routine/non-routine operations and evaluate using non-routine sequence and series operations, the approximate percentage error in the time-period calculation if your measurement of length is 3% high and G is measured 2% too smal
Direction: Answer the following and illustrate each under the normal curve:
1. Compute the probability area to the left of z = -1.25.
2. Compute the probability area above z = 1.
3. Find the probability area between z = -0.25 and z = 1.5.
4. Find the 90th percentile of a normal curve.
5. Compute the upper 5% of the normal curve.
MID_TERM ASSIGNMENT 1. Evaluate the integral β« (πΜ ) ππ π π+π π a) Along the line π = π π b) Along the real axis from 0 to 2 and then vertically 0 to 2+i 2. Use Cauchyβs Integral Formula to evaluate β« ππ π πͺ ππβππ+π , where C is the circle |π β π| = π π 3. Evaluate β¬ βπ π + π π πΉ π ππ π; over the region R in the y-z planr bounded by π π + π π = π 4. Evaluateβ (ππ + π)π π π½ ; where V is closed by the cylinder π = π β π π ;and the planes x=0;y=0;y=2 and z=0
MID_TERM ASSIGNMENT
1. Evaluate the integral β« (πΜ ) ππ π π+π π a) Along the line π = π π b) Along the real axis from 0 to 2 and then vertically 0 to 2+i
2. Use Cauchyβs Integral Formula to evaluate β« ππ π πͺ ππβππ+π , where C is the circle |π β π| = π π
3. Evaluate β¬ βπ π + π π πΉ π ππ π; over the region R in the y-z planr bounded by π π + π π = π
4. Evaluateβ (ππ + π)π π π½ ; where V is closed by the cylinder π = π β π π ;and the planes x=0;y=0;y=2 and z=0
The following sample observations were randomly selected:
X. 4. 5. 3. 6. 10
Y. 4. 6. 5. 7. 7
determine the correlation coefficient and the coefficient of determination
Check whether the series sum_(n=1)^(oo)(nx)/(n^(4)+x^(3)) x in 0 alpha is uniformly convergent or not
2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is MPa. The decision for the extension of the contract with the manufacturer depends on the engineer . Test the hypothesis whether there is no significant difference between the two means using a twotailed with a = 0.01
- A meeting of envoys was attended by 4 koreans and 2 filipinos. If there envoys were selected at random one after the other , determine the values of the random variable F representing the number of Filipinos.
2. During a sale at a menβs store, 16 white sweaters, 3 red sweaters, 9 blue sweaters, and 7 yellow sweaters were purchased. If a customer is selected at random, find the probability that he bought,
a. A blue sweater. (3 marks)
b. A yellow or a white sweater. (3 marks)
c. A red, blue or a yellow sweater. (3 marks)
d. A sweater that was not white (3 marks)
