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Determine the following integral
∫ (1+cos^2 x / 1+cos 2x ) dx
a. 1 / 2 [ tan x + x] + c
b. 1 / 2[1− 1 / cos x ] + c
c. 1 / 2 + c
d. 1 / 2 tan x + x + c
The demand function Q and cost function C(Q) of a commodity are given by the equations
Q=20−0,01P,
C(Q)=60+6Q,
where P and Q are the price and quantity, respectively.
The total revenue function (TR) in terms of P is
a. TR=20−0,01P.
b. TR=P(120−0,01P^2).
c. TR=20P−0,01P^2.
d. TR=P2(20−0,01P^2).
How did Marco Polo’s travel along the Silk Road help increase trade?
A firm has the following total and cost functions:
TR=20Q−4Q^2
TC=16−Q^2,
where Q is the number of unites produced and sold (in thousands). How many units should be produced to maximise the profit?
a.3,3333,333 units.
b.1,7141,714 units.
c.1,3331,333 units.
d.3 3333 333 units.
A 0.415 g sample of KHP will be titrated with a NaOH solution with an assumed concentration of 0.100 M.
Calculate the volume of NaOH that should neutralize the KHP sample.
Complete this table to show the pH and pOH of each solution.
(H+ is short for H3O+)
[H+] [OH−] pH pOH
Solution A 1.0×10−5 5
Solution B 1.0×10−10 10
Solution C 1.0×10−12
Solution D 10
Solution A [OH−]=
M
Solution A pOH=
Solution B [H+]=
M
Solution B pH=
Solution C [OH−]=
M
Solution C pH=
Solution C pOH=
Solution D [H+]=
M
Solution D [OH−]=
M
Solution D pOH=
Calculate the [OH−] and the pH of a solution with an [H+]=4.0×10−13 M at 25 °C .
[OH−]=
pH=
Calculate the [H+] and the pH of a solution with an [OH−]=9.8×10−13 M at 25 °C .
[H+]=
pH=
Calculate the [H+] and the [OH−] of a solution with a pH=3.52 at 25 °C .
[H+]=
[OH−]=
Explain why electron affinity decreases down the group
25.7 ml of 0.487 M HCl and 15.4 ml of 0.765 ml NaOH are mixed.
Determine the mmol of HCl and NaOH in the two solutions that are being mixed.
mmol HCl
mmol NaOH
Which reactant is present in excess?
Is the solution acidic, basic or neutral?
A survey asks a person the percent of time at work they spend working, web-surfing, socializing, eating, and daydreaming. The person should enter the percents as 5 integers that should add to 100. Read 5 integers, and output OK if they sum to 100. Otherwise, output "Total should be 100. Your total: ___".
If the input is 20 30 10 10 30, the output is: OK
If the input is "80 10 10 10 5", the output is:
Total should be 100. Your total: 115
#340153 on Dec 2023