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Check whether or not the function f, defined on R by
f(x) = { 3x^2sin(1/2x), when x≠0
{ 0 ,when x=0
is derivable on R. If it is, is f' continuous at x=0? If f is not derivable , then define a derivable function on R
Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant?
Consider a hollow spherical conductive shell of radius (R) 0.2 m with a fixed
charge of +2.0 x 10-6 C uniformly distributed on its surface.
a. What is the electric field at all points inside the sphere? Express your answer as
a function of the distance r from the center of the sphere. (2 points)
b. What is the electric field outside the sphere? Express your answer as a function
of the distance r from the center of the sphere. (2 points)
c. What if the sphere is a solid conductive sphere? What is the electric field at all
points inside the sphere? Express your answer as function of the distance r from
the center of the sphere
Propane, C3H8, is a fuel commonly used for cooking on gas grills and for heating in rural areas where natural gas is unavailable. Propane reacts with oxygen gas to produce heat and the products carbon dioxide and water. This combustion reaction is represented by the unbalanced equation
C3H8(g) + O2(g) → CO2(g) + H2O(g)
Give the balanced equation for this reaction, and state the meaning of the equation in terms of numbers of molecules and moles of molecules.
A family has four children find the probability that the family has equal number of sons and daughter.
It is claimed that last year, 65% of the people believed that there was an improvement in the country’s economy.
Suppose this year, only 270 out of the 450 people randomly selected believe that there is an improvement in the country’s
economy. Does this indicate that there is a decrease in the number of people who believes that there is an improvement in
the country’s economy? Use 0.05 significance level.
(Use critical value method)
A History teacher claims that the average height of Filipino males is 163 centimeters. A student taking up Statistics
randomly selects 20 Filipino males and measures their heights. Their heights in cm are shown below.
163 164 165 177
167 163 159 169
159 160 163 163
165 169 163 165
162 174 163 167
Do the collected data present sufficient evidence to indicate that the average heights of Filipino male is different
from 163 cm? Use 0.05 level of significance and assume that the population follows a normal distribution.
(Use critical value method)
The cashier of a fastfood restaurant claims that the average amount spent by customers for dinner is P 120. 00. A sample
of 50 customers over a month period was randomly selected and it was found out that the average amount spent for dinner
was P 112. 50. Using a 0.05 level of significance, can it be concluded that the average amount spent by customers is more
than P 120. 00? Assume that the population standard deviation is P 6.50.
(Use the critical value method)
80% area below it
8. Calculate the missing cell potential. 2.20 V 0.77 V -0.44
FeO4
2- Fe
3+ Fe
2+ Fe
E
o Will Fe
3+ disproportionate. Give reasons.
#340153 on Dec 2023