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Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not
Given: A = 100m, 30°NofE; B⃑ = 80m, 30°WofNandC = 40m, 55°SofW
a) Write each vector in Figure on the right in terms of
the unit vectors î and ĵ.
b) Use unit vectors to express the vector C , where
C = 3.0A − 4.0B⃑ .
c) Find the magnitude and direction of C .
Show your solution:A soda mint tablet contains NaHCO3 as an antacid. One tablet requires 30.5 mL of 0.135 M HCI for complete reaction. Determine the number of grams of NaHCO3 that one tablet contains. The chemical equation for the reaction is:
NaHCO (s)+HCI (aq)- NaCI (aq)+CO2 (g)+ H2O (I)
Given: A = 100m, 30°NofE; B⃑ = 80m, 30°WofNandC = 40m, 55°SofW
a. Plot the given vectors in the coordinate plane.
b. Calculate the components of vectors A, B and C.
c. Write each vector in terms of the unit vectors.
d. Determine the resultant vector.
- now we look at the role taxes play in determining equilibrium income. Suppose we have an economy described by the following functions:
C = 500 + 0.8YD
I = 700
G = 300
TR = 100
TA = 400
NX = -100
a. Calculate the equilibrium level of income and the multiplier in this model.
b. Calculate also the budget surplus, BS.
c. Suppose that TA increases to 500. What is the new equilibrium income?
Ram is given a positive integer N. He wishes to convert this integer into a single numeral . He does so by repeatedly adding the numerals of the number until there is only a single numeral . Help Ram by providing the single - numeral number finally obtained .
Input
The input is a single line containing a positive integer N.
Output
The output should be a single line containing a single-numeral number.
Explanation
In the example, the given number is 545.
As the number is more than a single numeral, repeatedly add the numerals like
5 + 4 + 5 => 14
1 + 4 => 5
So, the output should be 5.
Sample Input 1
545
Sample output 1
5
Sample Input 2
111
Sample output 2
3
Calculate the mole fraction of the solute in the following solutions.
a) 100g C2H6O in 100g H2O
b) 30% HCI solution by mass
Calculate the mole fraction of the solute in 30% HCL solution by mass
Question:- Like everything in Minecraft game, an Astronomer started thinking what will happen if our Sun would have been a square of similar luminosity.
a. If the Sun was a cube, what would be its surface temperature?
b. In what interval, does its magnitude lie as seen from the Earth?
Hint: The volume for Cube Sun remains the same as usual.
Question:- Like everything in Minecraft game, an Astronomer started thinking what will happen if our Sun would have been a square of similar luminosity.
a. If the Sun was a cube, what would be its surface temperature?
b. In what interval, does its magnitude lie as seen from the Earth?
Hint: The volume for Cube Sun remains the same as usual.
