Question:

The Sustainability Club has recently elected new officers, including Sophia, Hana, Wolt, and Joshua, who assumed the roles of president, vice president, secretary, and treasurer. In the context of a provided set of clues, ascertain the appropriate logical reasoning approach to determine the specific positions held by each elected officer. You can use any type of visual representations to solve this problem.

i. Joshua is younger than the president but older than the treasurer.

ii. Sophia and the secretary are both the same age, and they are the youngest members of the group.

iii. Wolt and the secretary are next-door neighbours.

My Answer:

Table of Elimination #1:

Order of age: President(?) > ?(Joshua) > Treasurer(?), Secretary(?) = Sophia(?)

Since Joshua is older than the treasurer but younger than the president, he can't be either of them, nor the secretary as they are the youngest. Hence, Joshua is the vice president.

Wolt can't be the secretary because he's mentioned to be the neighbour of the secretary. Though Sophia and the secretary are the same age, I assume this means that they are different people.

Table of Elimination #2:

Order of age #2: President(?) > VP(Joshua) > Treasurer(?), Secretary(?) = ?(Sophia)

Since Sophia and the secretary are the youngest, there's no way for Sophia to be the president (who is the oldest). Assuming that the secretary and Sophia are different people, then she also can't be the secretary. Hence, Sophia is the treasurer.

Table of Elimination #3:

Order of age #3: President(?) > VP(Joshua) > Treasurer(Sophia), Secretary(?) = Treasurer(Sophia)

Hence, Wolt is the president, and Hana is the secretary.

Order of age #4: President(Wolt) > VP(Joshua) > Treasurer(Sophia), Secretary(Hana)

Can some please help me figure this question out I’ve been stuck on it for sometime and can’t figure out how to solve it

i dont want to have to try both, is there a way just by looking at the question in general how to know which to convert to right off the bat

I know how to solve problems with one Ka value, it's using the Henderson-Hasselbalch equation.

But I don't know how to solve the following problems.

d) 100 ml Na3PO4 (0,20 mol/l) + 100 ml NaH2PO4 (0,10 mol/l)

Answer: 11,9

e) 100 ml Na3PO4 (0,10 mol/l) + 50 ml NaH2PO4 (0,40 mol/l)

Answer: 7,5

Ka,1 = 7,1 x 10^-3

Ka,2 = 6,3 x 10^-8

Ka,3 = 4,4 x 10^-13

How do I get to the answer? What Ka values are used?

ie is there a formula that int f'(x)f(x) = something?

"In a container of stable temperature and variable volume, there's the chemical equilibrium xA(g) + B(s) -> C(g) + 2D(g). At first, the total P=8atm. When we decrease the volume to V/2, the total P becomes P'=16atm. What is the coefficient x"

answers are: x=1, x=2, x=3 or x=4.

I found that C'=2C.

I don't know how to proceed and im getting discouraged because its the 2nd god damn question lol

So we are proving inequalities, i know how to prove them by algorithm but i dont understand what am i doing, in other words i have no idea what it means.

For example, prove that tgx>x for x€(0,pi/2). Then by algorithm we form function f(x)=tgx-x and we want to show that this function is positive on (0,pi/2) Then we find derivative of function f'(x)=1/cos² x - 1 now we look where x belongs that is (0,pi/2) and if this is >0 function is increasing function or <0 decreasing function. 1/cos^2 x - 1 <0 so function is decreasimg and because f(0)=0 we have f(x)<0 on (0,pi/2). And thats the end of proof, i have no idea why are we finding derivative why then is it > or <0, i just know by algorithm.

Or another example. Prove that e^x >=1+x , for x>=0. Algorithm, function f(x)=e^x -1-x, then we want to show that function is positive on [0,+infinity). First derivative e^x -1 >0, so function is increasing , has minimum in x=0, so f(0)=0, we have f(x)>=0 for x€[0,+ininity), e^x >=1+x.

Can you explain why are we forming functions , why showing that is positive, why derivative and is it increasing or decreasing? Im intersted in thinking process, thanks.

there is my attempt at it, at some point i just started writing everything as products of primes to try to see any distinction. the denominator seems easy enough, as its just u to the power of 2n (except for the second and first derivative for some reason) but what’s really troubling is the polynomial on the nominator, any direction for a solution is very appreciated, any idea or anything!!

I am working through a book in mortgages which has the following question:

Determine the forward rates from the following spot curve. Then, determine the par-yield curve from the spot rates and the forward par-yield curve from the forward spot rates.

Finding the forward rates from the given spot rates is straightforward. Essentially, investing in a 2 year bond now earns 9% compounded. So, the one year rate one year from now (x) can be found so that 1.09 * 1.09 = 1.1 * (1+x)

The current par-yield curve is also easily determined. For e.g., if the current par yield curve for year 2 is 8 % it means that discounting 8 by 1.1 (from the spot yield curve above for year 1) and discounting 108 by 1.09 * 1.09 (from the spot yield curve above for year 2) should yield 100/par.

So far, so good. I am completely unclear about what the "forward par-yield curve" even is. The answers provided are as follows at the back of the book. I have been able to obtain the forward zero rates, but the "forward par rates" are completely unclear how to obtain. Any help is appreciated.

Forward zero rates:

Forward par rates (?? how is the table below obtained??):

For things like this how did they determine the radius and centre? For c I sort of get it cause it's an easier example but for e.g d how do they determine this?

How do you do these questions? Every method I try gives me a different result...

In this question is it correct that you do f(x)-r(x)? When I do that I get c=-4 and d=-12, is that correct?

I need to prove that: x - y  ≤ | x^2 \* ln(x) - y^2 * ln(y) |  ≤ 3 * e * | x - y | and x,y ∈ [1,e]

Let f ( t ) = t^2 * ln(t). Using Lagrange theorem.

This function is defined and continuous on [0,+∞) and thus on the interval [1,e]. This function is differentiable on [1,e] .

From the Lagrange theorem it follows that there is a point c ∈ (1,e) such that f'(c) * ( y -x) = f ( y ) - f ( x ), this means that the derivative at that point is 2 * c * ln(c) + c.

This means that it is
2 * c * ln(c) + c = ( y^2 * ln(y) - x^2 * ln(x) ) / ( y - x )

We want to have 2 * c * ln(c) + c bounded.
Since c ∈ (1,e) , then 1 < c< e, so then we have c ≥ 1 and ln(c) ≥ 0 , this means that
2 * c * ln(c) + c ≥ 2 * 1 * 0 + 1 = 1

Then c ≤ e and ln(c) ≤ 1 , that is 2 * c * ln(c) + c ≤ 2 * e * 1 + e = 3 * e.

Now we have 1 ≤ 2 * c * ln(c) + c ≤ 3 * e that is
( y - x ) ≤ y^2 * ln(y) - x^2 * ln(x) ≤ 3 * e ( y - x ).

When we take the absolute value we can replace that is
| x - y | ≤ | x^2 * ln(x) - y^2 * ln(y) | ≤ 3 * e * | x - y | , but i need to get

x - y ≤ | x^2 * ln(x) - y^2 * ln(y) |.

Could it be mistake in exercise setup that my professor forgot about absolute value?

Thank you

The answer to part ii is this. How do they know that point D is on the y-axis?

third derivative and still dont know where its going

I can’t seem to figure out how to do this. I need to be able to identify which color is which molecule/atom but I have no idea where to start. This crystalroster is Mg3Si4O10(OH)2 (I know OH is supposed to count as one ball) any help is much appreciated!

Hi! So for the last month of my first term in uni, our physics professor handed out 31 questions to help study for next exam until the end of next month and I'm hard-stuck on the last one and would love some help (I emailed him but since its Christmas break he hasn't answered and both of my friends from uni gave up on the last question after many failed attempts), the question is originally in Swedish but ill do my best to translate it as accurately as possible. The question is in the field of nuclear physics but as of now we have not gone into molar masses and avogadros constant so this should be doable without it.

Question:

In a body of water there is 6500 the amount of hydrogen-atoms as deuterium-atoms. Assume you can utilize all the deuterium atoms in the 1m3 body of water to produce energy according to this reaction equation:

How much energy can you extract/obtain?

Now in my book I have the masses for neutrons, deuterium and helium nucleus, the water I need to calculate by myself and I get it to 18,01u per molecule but not sure how correct it is or if its even needed but I did it anyways. After that I went into getting the mass defect and I got it to 0,00349u, using the massdefect I could calculate how much energy I get per reaction (I got a hint from a friend to do so but I still don't really understand it?) but after getting the energy for the mass defect I'm kind of lost, I tried using the mass of one water molecule to get the number of molecules in water and the total number of particles of deterium knowing it has a ratio of 1/6500 but I still go wildly wrong answers form 0,02 GJ to 5 TJ to 20TJ

I checked what the answer is in a answer sheet the professor posted but it did not include a method only that the final answer is 3 TJ.

So yeah I would love to get some help here :)

TYVM

Edit: Forgot picture

Edit: Ok nvm I finally solved it, I think.. Got it to 2,6 TJ which I assume rounded up to 3 TJ from the significant figure of "1" in "1 cubic meter of water"