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A rectangular surface of length 3.25 cm and width 5.25 cm lies on the x-z plane at y=0. What is the flux through this surface due to a uniform magnetic field of 0.65 T directed 60° from the +x-axis?
A closely wound 0.20m × .20 m square coil of 100 turns is exposed to an external magnetic field of 0.74 T that is perpendicular to the plane of the coil. The coil is then rotated for 10 s until it makes 60 degrees with the magnetic field. Find the average induced electromotive force during the 10 s interval.
Let f: R->R and g: R->R be defined respectively as follows:
f: x->9-× and g: x->3x+1
Find the domain and range of f and g.
Find f^-1 and g^-1. Using f^-1 and g^-1 you found,
Show that f^-1°g^-1=(g°f)^-1
A function f(x) is defined for the range -2a<=x<=2a by
f(x){2a-x if -2a<=x<0
f(x){2a+x if 0<x<=2a
Sketch f(x) and state the domain and range of f(x)
Explicate a null hypothesis and its alternative hypothesis in (a) words and in (b) symbols for each of the following. Tell whether the test is directional and non-directional.
1. A librarian of a school claims that all their senior high school students read an average of 10 books a month. A random sample of senior high students read an average 12 books. The confidence statement is 95%.
2. According to a factory employer, the mean working time of workers in the factory is 6. A researcher interviewed 50% of the employees and found out that their mean working time is 8 hours. The 𝛼 level is 0.05.
3. A random sample of 200 students got a mean score of 62 in a knowledge test in mathematics. In the standardization of the test, 𝜇=50.
2. A TV set, a stove, a flat iron are connected in series to a 220 V line. The resistance of the TV set is 20 ohms, the stove is 50 ohms and the flat iron is 35 ohms. Find the following;
(a) total resistance
(b) the amount of current flowing in each device
(c) the voltage drop across each device
A car is driven west for a distance of 50 km, then north for 30 km, and then in direction 30° east of
north for 25 km. Determine the total displacement of the car from its starting point by drawing the
vector diagram.
A random sample of 11 observations was taken from normal population. The sample mean and standard deviation are 74.5 and 9 accordingly. Can we infer at 5% significance level that the population mean is greater than 70?
A random of 25 observations was drawn from a normal population. The sample mean and the sample standard deviation are 52 and 15 accordingly. Is there enough evidence at 10% significance level to infer that the population mean is not equal to 50? Estimate the population mean as well.
The potential energy of a system of two atoms is given by the expression, 𝐔 = −𝐀 𝐫 𝟑 + 𝐁 𝐫 𝟖 A stable molecule is formed with release of 10 eV of energy when the interatomic distance is 3 A°. Determine the force needed to dissociate this molecule into atoms and the interatomic distance at which the dissociation occurs
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