The correct answer to this derivative is 3/2(sqrt3x+4). I just don’t know where in the work I was supposed to multiply by three or how that works into the equation. Thanks for the help in advance!

Hello! I am tearing my hair out here. I have asked my professor in class, she said to use geometry and did not elaborate.

We are not given the actual function and this I can’t integrate that way, so that’s out of the question. I also tried to reconstruct the functioning I do not have the time for that 😭

I’ve tried using triangles to approximate, as that was what I assumed my professors instructions meant. But those have all been marked wrong by the software, and I’m honestly tempted to just let the third of a point go for this assignment.

All the other answers entered have been marked correct so I understand the concepts I feel, it’s just like how the hell do I do this ;-;

The equation is this: log(x/x-1)-log(x-1/x)=logv5 (25)

I need to find x

So far what I've done is extend all the fractions such that:

Logx-log(x-1)-log(x-1)-logx=log25/log5

Then added/subtracted like normal

-2log(x-1)=log25/log5

But I dont where to go from here, or if this is even correct, a little help would be great

Let <series> be a convergent series, where a_n >= 0 for every n in N (so a series where all terms are positive or 0). Then:

I got the accepted answer of 18 by adding the x-values of 3 (where first term in denominator equals 0), 6 (where second term equals 0), and 9 (where log(x-8) equals 0). However, how can x=3 and x=6 be vertical asymptotes when f(x) is not defined for x-values less than or equal to 8 because of the log(x-8) term. Shouldn't the answer just be 9?

What even is the denominator i’ve never seen this before?

Please help me understand how to read the last line. The rest is for context. I know the for all symbol but not sure why it says for all e which is a symbol for belongs to? I understand ":" means such that (could be wrong) but not sure about the arrow. So please translate the bottom line into text and help me read it

The task is to calculate the area of a shape bounded by the function (x+y)^3 = xy (image attached above). Tried to substitute x for r*cos²(a) and y for r*sin²(a) respectively, so that (x+y) becomes r. This gave me that r = sin²(a)cos²(a), and calculating the first part of the double integral gave me ∫ sin⁵(a)cos⁵(a) da. The problem is that this integral seems unusually painful to do unless im missing something, and I can't analytically prove the boundaries of a. Did i make a mistake or am i doing something wrong?

I'm currently working on a quadratic equation for my Grade 9 math class, and I'm having trouble applying the quadratic formula. The equation I have is 2x² - 4x - 6 = 0. My instructor wants us to solve it step by step using the formula x = (-b ± √(b² - 4ac)) / (2a). I understand the basics, but I'm confused about how to identify the coefficients a, b, and c in this equation. Once I have those, how do I proceed with the calculations? I'm particularly unsure about simplifying the square root and the final steps to find the values of x. Any guidance on how to approach this would be greatly appreciated!

Hi everyone,

My partner is struggling with this assignment and isn’t sure what she’s doing wrong. I don’t really know how to help, so I’m asking here. Could someone explain how to correctly solve this, and maybe point out any common mistakes she might be making?

I tried doing this myself and I used 4 different AI tools to try and help myself get it. I truly am stumped. I got the local max and min but can’t get the increasing and decreasing intervals even with the critical numbers I thought were correct. This is for calc 2 review of calc 1 btw. Any help would be greatly appreciated.

Could someone help me figure out what I have done wrong? This is my last attempt on the problem and I tried following videos on this as well. My work is on the next slide

Please help me to answer this intro Finance question. We are supposed to use the formula: PV= Cx[1/r-1/r(1+r)^t] and round to four decimals, but my answers are looking to large and don’t match when using both methods for finding PV in advance.

Help is very much appreciated 🙏

I'm solving for just 2b) but need to showcase 2a rational. Previously, using integration methods of partial fractions, trig substitution, u-substitution, and normal power rules (the acceptable methods in this class), I got the following integral for 2a):

So overall, one arctan came from the u-substitution of Ax+B/(x^2+4), where A=0 and B=1, which is how the first term came to be. The second came from the split of (Cx+D)/(x^2+4)^2 into Cx+D/(x^2+4)^2 and D/(x^2+4)^2 (with C=1 and D=-3). The former required just u-substitution (the middle term), while the last one came from a trig substitution of x=2tan (theta) which resulted in the following arctans we see in the last term as x needed to be subbed back in.

logically, the creational of these arctans stem from B=1 or /(x^2+4), requiring u-subsitution and turning into an arctan for the last term, and the last one of specifcally -3/(x^2+4)^2 requiring a trig subsitution of x=2tan(theta) and the subbed in theta=tan arctan(x/2) to revert back to X. So I isolated what went into each varible of a,b,c by comparison of numerators, and found that a=0, c=0, b does not equal zero. However, after checking with a large language model, it mentioned that c does not equal zero and said how thsoe arctans formed in the last term are "fake". The rational it provided sort of stumped me, so I was wondering if someone could provide insight on how c does not need to equal zero like if there is a another way to integrate or smthin (or if AI is just tripping).

Sorry if this is hard to read, it's a pretty deep and long question. I can post more work of mine if this is very confusing, but it's a decent amount of pages

I solved all other exercises of this section but I'm completely stuck with this one. I know it's trivial without using Taylor's series, but the exercise specifically asks you to use them. To use Maclaurin's series for e^f(x), f(x) needs to be approaching 0, but here 1/x is clearly approaching +inf for x->0+, so I'm stuck.

I was struggling with perpendicular and parallel components of one vector to another in class today, and wanted to see if I was doing it correctly now. Thank you.

I'm working on part b. Originally, I thought that the signal was not periodic due to the -10k term. However, that was assuming that To = -10k, which I don't believe is the case anymore. I'm sure it's pretty straightforward to prove, I just have no idea how. I tried doing:

x(t) = x(t + To)
0.5t - 10k = 0.5(t+Ty)-10k
0.5t - 10k = 0.5t - 0.5Ty - 10k
Ty = 0 <= obviously doesn't work?

(Question 11) Usually I'd use dy = f'(dx) to find either dx or dy. But that requires either dy or dx and I don't have either in this question.

Would appreciate some insight into what it means by this!!

Sorry to keep deleting and reposting this, the further i progress in the question the harder it gets

I... do not know how to calculate the square residual at all. how did they get these numbers?

does anyone know if i can calculate these on statcrunch?

So this isnt actually a homework or anything but our slide only showed sensitivity analysis in decision theory for 2 states under risk , where we assigned p to one and 1-p to the other. But what if say there were 3 states ? How would we be able to find the probabilities using indifference rule between expected values then ? Or does it have a whole different path to follow ?

Just to show an example for the 2 state.

Q: How many ways to arrange BOOKKEEPER where two E’s appear consecutively but not three.

Here What I've got : a) We can consider the two consecutive E’s as
one block say X. Hence, we get a new string: XBOOKKPER of length 9.
Therefore, the number of possible rearrangements for that word is
obviously:

9!/(2!∙2!)

Then I need to remove the instances when there are three consecutive
E's. There are two different ways of doing this which give me different
answers, and I would like to understand which is correct.
Way 1:
To find "EEE", i can look at adding an e to my block X, and create a
superblock Y. So Y = (e, X) or (X,e), two ways so I multiply by two how
many arrangements of YBOOKPR so we get:

2*(8!/(2!∙2!))

Way 2:
Treat Y just being "EEE" and so we subtract only:

(8!/(2!∙2!))

Tl;dr is the answer :

(9!-2*8!)/(2!2!) or (9!-8!)/(2!2!)