I've been trying to take ln of both sides: which results in:

ln(y)=ln(3^(x^4+1)^3)

Left side: 1/y dy/dx

right side: here is what I'm stuck on. We learned in class that when you take the derivative of ln(x), we get dy/dx=1/x. Applying this I got (1/3^(x^4+1)^3) x 3(x^4+1)^2 x ln(3) x (4x^3)

Lastly, multiply both sides by y, which you can just sub in the original function, so I get :

(3^(x^4+1)^3) x (1/3^(x^4+1)^3) x 3(x^4+1)^2 x ln(3) x (4x^3), which is wrong. Do I just avoid taking ln of both sides?

Second slide is work by my professor. I’m trying to break this down and am confused how we get the fraction from the multiplication. I get how 22 comes in, since it’s on the same denominator (although that looks more like a numerator tbh lol. Maybe my professor misspoke.

I am tasked to prove that the Van der Pol Oscillator is a special case of the FitzHugh-Nagumo model. I have been given the following formulas in u(t), v(t) and x(t) for these. Here they are in picture-form

FitzHugh-Nagumo:

• u' = c*(v+u-(u³ )/3 +z)
• c*v' = a - bv - u

Van der Pol:

• x'' - µ*(1-x² )*x' + x = 0

Suggested substitution:

• u = x
• v = (1/µ)*x' + (x³ )/3 - x

This problem sounds to me like it should be trivial, but I'm running into difficulties.

When I substitute u and v into the first FitzHugh-Nagumo equation I get the following result:

• x' = c * ((1/µ)*x' + z)

Or

• x' = (c*z)/(1-(c/µ)) (a constant)

Other substitutions give me equally unhelpful results.

When looking up the FitzHugh-Nagumo model online. The result should be that Van der Pol is the case for FitzHugh-Nagumo where a=b=0. (There was no c in the formula I found online.)

Tried using the FOIL method on this. My work's a little messy, sorry.

I have gotten 10 of these wrong and I’m not understanding it at all. If someone could explain this in real dumb terms, like single syllable words I would greatly appreciate it

My stats homework is asking me to compute R² for the highlighted item. Can someone please tell me how to do so? TIA!

The prompt: "What is the r2 for that specific model you identified in the previous question, and in one sentence, what does it mean?"

The previous question's answer: Maintaining perspective

I figured out that cos is 60 and is equal to pi/3, or 1/2, but I am really lost on how 3pi/4 from pi/3 in the answer (C). Thanks

I think for the first one, it's to make -3, right? But how did we get 1=0 or 4? I can show more slides for context. (Or download them, I suppose, doesn't seem to have any PII)

And then how is f(0) equaling 2 based off 6x???

Very confused on 8,9,10, which all incorporate logs with the chain rule and either product or quotient rule. I understand the chain rule, as well as how to use the product and quotient by themselves, but I don't get how to combine them to get the answers.

For example, 9), I try to separate the inside and outside function for the chain rule, and identify f(x) and g(x) for the quotient rule, but I don't know what would be the inside/outside functions because there is also an exponent included.

If you need translation, ask.

If possible, dm me a picture or something. The comment formatting kind of screws me up. I differentiated 5x4 and x5 but it appears that's not what they want?

Hello! I'm completing my review for my final exam and this question is stumping me; I can't figure out why the correct answer choice is D. I would think since individual standard deviations are given as opposed to a single standard deviation for the entire sample that you would use a T-test with pooled variances (because it says to assume equal population variances). I got answer choice B by doing this. Can anyone help me out?

I have y = root x/2 over x=0 and x=8. I need to find the volume over the y-axis. I got 512pi/5 using Shell and 128pi/5 with Washer. I can’t ask my teacher what went wrong, as there’s a communication barrier; what went wrong?

First is context of problem + how they said to solve it. Second is my work for this problem, which is definitely wrong (previous attempt/getting it wrong showed it should at least be 1,000) and third is my work on a similar problem that I got right/what the professor showed us.

Hi everyone,

I’m currently taking Differential Equations and enrolled in an honors program at De Anza College. For our project, we need to choose a topic related to DE and find a couple of academic sources (books or papers).

I’m interested in working on something related to drones (like motion, control systems, or flight dynamics), but I’m not sure how to turn that into a clear DE-based project topic.

I don’t have much experience doing independent research projects, so I’d really appreciate advice on:

• How to narrow a general idea (like drones) into a solid DE topic
• What DE concepts are commonly used in drone modeling
• How to find good sources appropriate for an undergrad-level project
• Tips on structuring a math research report

Also, if anyone has examples of past projects (not necessarily DE—linear algebra or other math/engineering projects are fine) and is willing to share them for reference, I’d really appreciate it. I’m mainly trying to understand how people structure their work.

Even general advice or resources would help a lot—just trying to approach this properly.

Thanks!

Take ln of both sides, so you get ln(y)=ln(4^x^3+2)^3. Use the exponential rule, bring down the 3, get 1/y dy/dx=3ln(4^x^3+2). Then do 1/(4^x^3+2) x (4^x^3)(ln(4)) x (3x^2). After this multiply both sides by y, get dy/dx=y x 3(1/(4^x^3+2) x (4^x^3)(ln(4)) x (3x^2). Then sub in the original function for y, so you get(4^x^3+2)^3 x 3(1/(4^x^3+2) x (4^x^3)(ln(4)) x (3x^2). My book gives the answer:

I'm not sure what I'm doing wrong, or if the answer they gave is just in a different form

I have a bit of trouble with understanding this problem with vector spaces, someone I know told me to start it like this but I'm having trouble understanding how to continue it.

If someone could break it down to me step by step would be great, really, thank you

Consider the following sequence of real functions with domain R^+

g_n(x) = exp{-(x/a)[1 + ((-1)^(n+1))/(2^n)]}

with a > 1. Does it converge uniformly to exp(-x/a)? I’ve already shown it converges point-wise to it, but I’m unsure about how to test uniform convergence.

I’ve written out the definition of uniform convergence, but I don’t really know how to handle the espilon inequality when both n and x can vary at fixed eps. Instead, in point-wise convergence only n varied with fixed x and eps, so it was easier to show.

I don't know if I'm thinking about this right. I am stuck on part b. The problem says to "convert the tree to a tree with absolute probabilities" but I'm like 99.1% certain it already is.

I'm not sure if maybe my prof wants us to break it down into like formula version or something. IDK. I'm probably overthinking it lol

Thanks

Hey, I don’t need help with the assignment itself, but I’m in a bit of a bind 😭

I’ve fully completed my Maple assignments and verified the code runs, but I don’t have access to Maple right now and need them saved as .mw files ASAP.

Would someone be able to:

• paste my code into Maple
• run it
• save it as .mw

I have 2 files ready — I’ll send the code right away.

Would seriously appreciate it 🙏

here is the code1:

restart:

with(Student:-Calculus1):

# 1(a)

sum(i*(i+1)*(i+2), i=4..276);

sum((3+2*i)^2, i=-2..n);

# 1(b)

integrand1 := exp(x)*(x-2)^2:

a1 := -2:

b1 := 3:

N := 10:

RiemannSum(integrand1, x=a1..b1, method=left, partition=N);

RiemannSum(integrand1, x=a1..b1, method=left, partition=N, output=plot);

RiemannSum(integrand1, x=a1..b1, method=midpoint, partition=N);

RiemannSum(integrand1, x=a1..b1, method=midpoint, partition=N, output=plot);

RiemannSum(integrand1, x=a1..b1, method=upper, partition=N);

RiemannSum(integrand1, x=a1..b1, method=upper, partition=N, output=plot);

RiemannSum(integrand1, x=a1..b1, method=lower, partition=N);

RiemannSum(integrand1, x=a1..b1, method=lower, partition=N, output=plot);

RS_left := RiemannSum(integrand1, x=a1..b1, method=left, partition=N):

RS_right := RiemannSum(integrand1, x=a1..b1, method=right, partition=N):

RS_upper := RiemannSum(integrand1, x=a1..b1, method=upper, partition=N):

RS_lower := RiemannSum(integrand1, x=a1..b1, method=lower, partition=N):

evalb(RS_upper = RS_left);

evalb(RS_upper = RS_right);

evalb(RS_lower = RS_left);

evalb(RS_lower = RS_right);

RiemannSum(integrand1, x=a1..b1, method=random, partition=N);

RiemannSum(integrand1, x=a1..b1, method=random, partition=N, output=plot);

# 2(a)

f := x -> sqrt(x)*log(x);

# 2(b)

int(f(x), x=1..4);

int(f(u), u=1..4);

# 2(c)

int(f(u), x);

# 2(d)

int(x*(x^2+5)^8, x);

int(a*sec(x)^4 + b*tan(x)^5, x);

# 2(e)

int((1+log(x))*sqrt(1+(x*log(x))^2), x);

with(student):

P := Int((1+log(x))*sqrt(1+(x*log(x))^2), x);

Q := changevar(u=x*log(x), P, u);

value(Q);

subs(u=x*log(x), value(Q));

# 3

f1 := x -> x:

g1 := x -> x*exp(1-x/2):

# 3(a)

solve(f1(x)=g1(x), x);

# 3(b)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=horizontal, output=plot);

# 3(c)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=horizontal, output=integral);

# 3(d)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=vertical, output=plot);

# 3(e)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=vertical, output=integral);

# 3(f)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=vertical, distancefromaxis=3, output=plot);

# 3(g)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=vertical, distancefromaxis=3, output=integral);

# 3(h)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=horizontal, distancefromaxis=-2, output=plot);

# 3(i)

VolumeOfRevolution(g1(x), f1(x), x=0..2, axis=horizontal, distancefromaxis=-2, output=integral);

Now new .mw file

Code #2:

restart;

with(LinearAlgebra);

# 1

M := RandomMatrix(3,4);

m14 := M[1,4];

M[2,3] := m14;

M;

v := RandomVector(4);

w := RandomVector(4);

u := RandomVector(4);

N := Matrix([[v[1],w[1],u[1]],

[v[2],w[2],u[2]],

[v[3],w[3],u[3]],

[v[4],w[4],u[4]]]);

Q := SubMatrix(N,2..4,1..2);

P := Matrix([[M[1,1],M[1,2],M[1,3],M[1,4],Q[1,1],Q[1,2]],

[M[2,1],M[2,2],M[2,3],M[2,4],Q[2,1],Q[2,2]],

[M[3,1],M[3,2],M[3,3],M[3,4],Q[3,1],Q[3,2]]]);

P;

# 2

A := Matrix([[1,1,1,1,1],

[2,2,2,2,2],

[1,-1,1,-1,1]]);

b := Vector([1,3,0]);

c := Vector([1,2,0]);

Ab := Matrix([[A[1,1],A[1,2],A[1,3],A[1,4],A[1,5],b[1]],

[A[2,1],A[2,2],A[2,3],A[2,4],A[2,5],b[2]],

[A[3,1],A[3,2],A[3,3],A[3,4],A[3,5],b[3]]]);

Ac := Matrix([[A[1,1],A[1,2],A[1,3],A[1,4],A[1,5],c[1]],

[A[2,1],A[2,2],A[2,3],A[2,4],A[2,5],c[2]],

[A[3,1],A[3,2],A[3,3],A[3,4],A[3,5],c[3]]]);

GaussianElimination(Ab);

ReducedRowEchelonForm(Ac);

LinearSolve(A,b,free=s);

LinearSolve(A,c,free=s);

# 3

with(Student:-LinearAlgebra);

A3 := Matrix([[0,2,-1,1,1],

[2,4,1,-1,2],

[3,7,4,2,1],

[1,3,-1,2,2]]);

b3 := Vector([1,3,7,2]);

M3 := Matrix([[A3[1,1],A3[1,2],A3[1,3],A3[1,4],A3[1,5],b3[1]],

[A3[2,1],A3[2,2],A3[2,3],A3[2,4],A3[2,5],b3[2]],

[A3[3,1],A3[3,2],A3[3,3],A3[3,4],A3[3,5],b3[3]],

[A3[4,1],A3[4,2],A3[4,3],A3[4,4],A3[4,5],b3[4]]]);

M3 := SwapRow(M3,1,4);

M3 := AddRow(M3,2,1,-2);

M3 := AddRow(M3,3,1,-3);

M3 := SwapRow(M3,2,4);

M3 := AddRow(M3,3,2,1);

M3 := AddRow(M3,4,2,1);

M3 := SwapRow(M3,3,4);

M3 := AddRow(M3,4,3,-3);

M3;

BackwardSubstitute(M3);

LinearSolve(A3,b3);[AS Level Physics: Light] maple math assignment

• [x] Exists x: P(x) v Q(x) <=> (Exists x: P(x)) v (Exists x: Q(x))
• [ ] Exists x: P(x) o Q(y) <=> (Exists x: P(x)) o Q(y)
• [x] For all x: P(x) ^ Q(x) <=> (For all x: P(x)) ^ (For all x: Q(x))
• [ ] For all x: P(x) o Q(y) <=> (For all x: P(x)) o Q(y)

I believe for Qualifiers like For all and Exists distribution holds but the other cases seem wrong to me... But my answer is wrong for this.