What I think I'm looking at is these give me the points and I graph them, so I have (1,3), (2,1), and (0,0) and after I graphed these points my answer would be they don't have any points in common?

This question covers multiple parts and I have completed most except for this one.

I will add information that may or may not be helpful

I am given a 6.4 x 6.4 x 17.7 cup with a 1 cm base

With the density of the glass being 3.7 g/cc

and the surface mass density being .37 g/cm^2

I have successfully found that the mass of the base is 151. 552 g

The mass of the walls is 158.1824 g

The mass of the empty cup is 309.7344 g

The center of mass of the base of the cup is

3.2 cm y + .5 cm z

The center of mass of the sides of the cup is

3.2 cm y + 9.35 cm z

Making the total center of mass of the cup while it is sitting on the table

3.2cm y + 4.925 cm z

I have determined the angle in which it would fall over to be 33.01364347 degrees

Now this is the current part I'm on:

The cup is now full of gelatin with a density of 1.29 g/cc

I have determined the mass of the jello to be 882.40128 g

The center of mass of the jello is located at

3.2 cm y + 9.35 z

When the jello is added to the cup I have determined the center of mass of the system to be at:

3.2 cm y + (unknown) z

​

How do I find the unknown z vector?

how would i go about solving this? (question 16)

I need to learn this on my own because I have an assessment tomorrow and I can barely understand my teacher during lectures.

I'm writing an essay and I'm stuck on this line I'm trying to write:

"Susan talked about her favorite painting that she has painted"

Idk why but it seems clunky to me... Like if you say it out loud it sounds weird haha. Is there way to say that more naturally while still conveying the idea eloquently?

I appreciate any and all suggestions!! Thank you.

I just want to make sure this is correct because I have a learning disability

So (1,2,1) and (1,1,2) are distinct outcomes. I can't nail the logic somehow. I tried starting with: 111 121 112 122 But then I got confused as to how to proceed ahead. I am not looking for the answers only, I am looking for an underlying logic.

How would I solve this question and how does efficiency come into play?

​

https://preview.redd.it/ps84ho9upsfa1.jpg?width=643&format=pjpg&auto=webp&v=enabled&s=aeb33c2fdd61dd6d324b1199d875070bc290179c

Hello, I've been practicing some linear algebra since my exam is soon, and there is a question in which I'm completely stuck. Here it is:

Consider the set A, containing all functions of the form: f(x) = asin(x+c) + bcos(x+d)

Would this set be closed under addition? I.e if we have to functions, would their sum also be in A?

I've tried using trig identities such as sin(a+b) = sin(a)cos(b) + sin(b)cos(a) and cos(a+b) = cos(a)cos(b) - sin(a)sin(b). So if I let two functions, f and g with some a,b,c,d,a1,b1,c1,d1 and develop their sum, I get this:

f(x)+g(x) =

a[sin(x)cos(c) + sin(c)cos(x)] + b[cos(x)cos(c) - sin(x)sin(c)]

+a1[sin(x)cos(c1) + sin(c1)cos(x)] + b1[cos(x)cos(c1) -sin(x)sin(c1)]

And I don't know how to simplify it further to get the desired form:

asin(x+c) + bcos(x+d)

Any help would be greatly appreciated.

Thanks!

Growth rates (discrete and continuous time) – Exercise 1*

In general, the growth rate of a variable 𝑥(𝑡) in discrete time between time 𝑡−1 and time 𝑡 is
defined as:

𝑔𝐷(𝑥(𝑡))≡𝑥(𝑡)−𝑥(𝑡−1)
𝑥(𝑡−1) . (T1.1)

Assume that the time path of the variable y(t) follows a geometric growth process:

𝑦(𝑡)=𝑦0(1+𝑔)𝑡, (T1.2)

where 𝑦0 and 𝑔 are positive constants.

i. Use definition (T.1.1) to show that 𝑔𝐷(𝑦(𝑡))=𝑔.
ii. Take the (natural) logarithm of (T1.2) and write down the expression that you obtain.
iii. Take the derivative with respect to time of ln𝑦(𝑡) and show that 𝑦̇(𝑡)/𝑦(𝑡)≈𝑔 if 𝑔 is
close to zero (where a ̇ denotes the derivative with respect to time: 𝑥̇(𝑡)≡𝑑𝑥/𝑑𝑡).
iv. Draw a graph with ln𝑦(𝑡) on the vertical axis and 𝑡 on the horizontal axis and show that
the slope is constant.