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3 cot(x)+ #sqrt(3)#=0

Answer 1

James Adkins

See below

#3 cot(x)+ sqrt3=0# #3 cot(x)=-sqrt3# #cot(x)=-sqrt3/3#

Looking at the unit circle, when is #cotx= -sqrt3/3#

Remember #cot# and #tan# are only negative in quadrant 2 and 4:

Also using the #cos# which is the x-value and the #sin# which is the y-value, create a quotient: #cosx/sinx= cotx#

You will find that the coordinate points at #(2pi)/3# and #(5pi)/3# work: At #(2pi)/3# : #x= -1/2# #y=sqrt3/2#

#Cot((2pi)/3)= x/y# #Cot((2pi)/3)= -1/2*2/sqrt3= -1/sqrt3*sqrt3/sqrt3= -sqrt3/3#

Now to write a general solution, since #tan and cot# have a period of #pi#, we can say that: #x= (2pi)/3+pin, "where n" ∈ Z#

N is an element of all integers, as the value for #cot# will repeat every #pi# radians

Here's a graph: graph{3cotx+sqrt3 [-6.36, 13.64, -5.655, 4.345]}

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Answer 2

Victoria Adebayo

The answer to the question "What is the percentage composition by mass of nitrogen in calcium nitrate?" is obtained by calculating the molar mass of calcium nitrate (Ca(NO3)2), determining the mass of nitrogen in one mole of calcium nitrate, and then using the formula:

Percentage composition of nitrogen = (mass of nitrogen in calcium nitrate / molar mass of calcium nitrate) * 100%.

The molar mass of calcium nitrate is calculated by adding the molar masses of calcium, nitrogen, and oxygen atoms present in one molecule of calcium nitrate. The mass of nitrogen in one mole of calcium nitrate is determined by multiplying the number of nitrogen atoms in the formula by the molar mass of nitrogen.

Once these values are determined, the percentage composition of nitrogen can be calculated using the provided formula.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.