# change

1. ### rates of change

A spherical snowball is melting at a rate proportional to its surface area. That is, the rate at which its volume is decreasing at any instant is proportional to its surface area at that instant. If the snowball loses half of its volume in an hour, how long more will it take for it to melt...
2. ### Need Help With Change of Variables from Cartesian to Spherical Coordinates

Hello there! Cutting straight to the chase, I need help with the derivation best described in this video here @ 7:48: https://youtu.be/AjDSLq-Pzcs?t=7m48s By this point in the video, Adam Beatty has already established: x=r*cos(Φ)*sin(θ) , y=r*sin(Φ)*sin(θ) , z=r*cos(θ) It also makes sense to...
3. ### Change of Basis?

After looking through my book and watching countless khan academy videos I still have no idea how to set up this problem, Find the matrix with respect to the basis B = {(1,1,1),(1,2,-1),(2,3,1)} of the linear transformation T:R3->R3 with T(x,y,z) = (3x+y+2z, 3x+y+2z, 3x+y+2z) Can anyone help?
4. ### Change of Variable Formula

Let R be the solid torus in R3 obtained by revolving the circle (y-a)2+z2<=b2 in the yz-plane about the z-axis. Note that the mapping T defined by x=(a+wcosv)cosu, y=(a+wcosv)sinu, z=wsinv maps the interval Q={(u,v,w) : u, v are [0,2pi] and w is [0,b]} onto this torus. Apply the change of...
5. ### Integration and rates of change, clarifying needed

The entire first question in this set has me slamming my head against my desk. I don't understand how the rate of addition of the wolves relates to the population already in place, and therefore, I don't know what W(t) even is. I'd thought it was something like: 20 + mt(12-t) or 20 +...
6. ### Finding the average rate of change.

How would one go about finding the average rate of change from 0 to pi/2 for a function. the function is f(x) = sin x. at x = 0 the y = 0, and at x = pi/2 the y = 1. So is the rate of change just 1 or am I doing this wrong? Thanks in advance.
7. ### Aquarium water change - how much waste? Formula design

Hi, I'm looking to design a formula which will take the following inputs and provide the following solution. The intent of the formula is to determine how much waste there will be (in litres) if I do a water change in my aquarium while simultaneously draining the tank to make room for the new...
8. ### Simple derivative to find rate of change

I'm having a problem with a practice problem. So if you want to find the rate of change of x (on a right triangle) and only know that Y is a constant 20ft, the radians of the angle between x and the hyp is .15 radians and also that the radian measure is going up by .1 every minute (0.1rad/min)...
9. ### Does changing our expected results change what our sample size should be?

I had this question from a school assignment, and my thinking is no that what we expect does not change what our sample size would be. I know a larger sample size is best, but , For example 1. If we have a Fair 3 sided dice and expect 1, 2, or 3 to have equal probability of coming out, and we...
10. ### Index change

I do not understand why the indices of S, i.e. kl, change to pl, upon differentiation: d/dcp* (c†Sc) = d/dcp* ("sum from k to N" "sum from l to N" ck*Sklcl) = "Sum from k to l" Splcl Here, * indicates complex conjugation. Differentiating should leave Sc as this part is constant. I assume...
11. ### Rate of Change in sinusoidal function

I'm having trouble finding the intervals in which the function A(t) = 0.25sin((Pi/730)t) + 0.55 is descreasing. The restriction on t is 0 <= t <= 2920 - Thanks
12. ### rate of change of height

15 feet ladder is resting agianst the wall. the bottom is initially 10 feet away from the wall and is being pushed 0.25ft/s towards the wall. how fast is the top of ladder moving up the wall 12 seconds after start pushing . 15 ^2 = (b^2 + c^2 ) d 15 ^2 / dt = d (b^2 + c^2 ) / dt 2b/(db/dt)...
13. ### Can i change the order of quantifiers in this case?

In this sentence: "No hero is cowardly and some soldiers are cowards." Assuming h(x) = x is a hero s(x) = x is a soldier c(x) = x is a coward. So the sentence is like this i think: (∀x (h(x)->¬C(x))∧(∃y (s(y)∧C(y)) In this case, are prenex formulas bellow the same thing? ∀x ∃y...
14. ### Vertical & Horizontal Rate of Change

See picture on the left.
15. ### Rate of Change

Find the rate of change of the distance between the origin and a moving point on the graph of y = x^2 + 1 if dx/dt = 2 cm per second. I must find dy/dt. d/dt [y] = d/dt [x^2 + 1] dy/dt = (dx/dt)*2x + d/dt (1) dy/dt = 2*2(0) + 0 dy/dt = 0 cm/second Book' Answer: [2(2x^3...
16. ### Calculus Homework Help (Limits and Instantaneous rate of change)

Hey guys, I'm new to this forum and I need some serious help with calc please. I feel like I'm doing my assignment wrong (Headbang) and I was just hoping that someone with more experience (and confidence) would just look over my answers. I kinda suck at math (Thinking) and I would really...
17. ### Angular Rate of Change

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object. The position function is given to be h(t) = -16t^2 + 256. The object is released at time t = 0. It takes the object 4 seconds to...
18. ### related rates of change

is there anyone who can help me to solve this?
19. ### Question about percentage change involving negative and positive numbers

It's not possible to quantify a percentage change if one of the values is negative, correct? \frac{x_{2}-x_{1}}{x_{1}} Where x_1 is the beginning value, and x_2 is the ending value. As an example, my bank account started the month with 100, and ended the month with -15, or vice versa. There...
20. ### Change in value question

This question is bugging the cr*p out of me. I asked my teacher for clarification and then forgot how he described it and went to go solve it on my own weeks later and I'm stuck again. Here is the question, the answer is -2.4kw*h. Some solar energy systems are used to supplement the utility...