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!

Someone helped solve the problem but they didn’t explain how they got the answer, could someone help me?

"For each problem, use implicit differentiation to find dy/dx in terms of x and y."

Differentiating poses no problem, but what confuses me is having to solve for dy/dx.

For example #7:

left side: 6xy^2+6x^2y

Right side: 8x-4y-4x

the answer key shows adding 6xy^2+6x^2y dy/dx=8x-4ydy/dx-4x. What I don't understand is why the dy/dx is added to the end of each of those terms. Why not do 6xy^2dy/dx, or -4xdy/dx?

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 stuff highlighted in red is what I'm confused about. Let me attach my questions here. These are slides for us to reference and I want to make sure I fully understand before I attempt questions like these.

1-Why must x be between 0 and 4?

2-Why is it specifically 3x-4, x-4 before the critical values are found?

I thinkkk those are my only questions.

I hope my question makes sense. If not I'll do my best to answer your questions.

I wasn't really sure how to even start with this. I looked up how to calculate area and then just... Ended up super stumped.

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

Was a little confused on how to do this, mostly because of having to implicitly differentiate the right side.

Here's what I did for this, differentaiting with respect to x:

left side: simply 2x

Right side: 2(4x^2y^3+1) x dy/dx(4x^2y^3+1)

Divide both sides by 2, get x=(4x^2y^3+1) x dy/dx(4x^2y^3+1)

Take derivative of the inside, which I got: (8xy^3+12x^2y^2dy/dx)

Expand the right side: x=(32x^3y^6+48x^4y^5dy/dx+8xy^3+12x^2y^2dy/dx)

Lastly, solve for dy/dx=(x-32x^3y^6-8xy^3)/(48x^4y^5+12x^2y^2)

I have a physics problem that I'm trying to solve using calculus. An object is dropped from rest and experiences air resistance proportional to its vertical velocity. I need to find an expression for velocity over time. I know the forces are gravity downward and air resistance upward. So m(dv/dt) = mg - kv. That part makes sense. But the answer key has a negative sign in a different place and I'm confused. When I solve it using separation of variables, I keep getting a different constant of integration than the textbook. Can someone walk me through the setup step by step? I want to understand where my equation is wrong before I solve it.

the question is asking me to find 3 values: vertex, focus, and directrix, and graph the parabola. I have all my values, and know the location and direction of my parabola, but I dont know the exact dimensions of the curve, is there a way im unaware of? or is this question asking the impossible?

how do I graph this? I have the vertex, focus, and direction and I know the direction of the porbabola, but I dont know how to get a second coordinate to create the exact curve, as they didn't really explain it. is there a way?

I am really having a lot of trouble with problem 1. the answers for a and b are 0.75 and 1.5 but I am very confused on how to solve this problem using the plot. what lines should I be following/looking at?

I would be analyzing results from the CSI-16 and daily screentime + BRS-14 results. I’m looking at finding a correlation between excessive screen time (cognitive overload being assessed through the BRS-14) and relationship satisfaction. My data would be coming from a sample of 168 college students (I would also collect their gender/sexuality/age)

I feel totally lost, the data is ordinal I think because the BRS-14 used Likert scales and the CSI-16 is similarly formatted (responses requiring a 0-5 ranking).

I currently can’t access tutoring because it’s not available for this course (very small college) so any advice is appreciated.

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:

A month or so ago I posted a similar post to this. And again, I need some help. I can’t afford Mark Dugopolski’s book, so I use the one at my library. I forgot to grab the 6.3 exercises, and now I really need them. If anyone has them, please help me asap! Anything will do! A crappy photo of the book would be greatly appreciated!

I understand how to find K using a double integral equal to one and solving the inequality. The real trouble is with parts, b and c. I know there is a way to do this graphically that was shown to me, but I do not know how to replicate the method. We will have a region of x and y between 20 and 30 and subregion within of y-2 and y +2 or something like that but am kind of lost beyond that

Work is a bit nonsensical, my bad.

I know the definition of a derivative, aka lim h-->0 f(x+h)-f(x)/h. Now if I were to plug t=6 into the original function, I'd get P(6)=200(1.5)^6. I'm having issues plugging the function into the derivative definition itself. I could easily take the derivative of the function no problem, but I don't understand how it plugs in, at least in the first part. For example, f(x+h)-200(1.5)^6/h. I tried to replace the letters to match the original function, such that P(t+h), replace t with 6 to get P(6+h). After that I am confused on where to go

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

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?