User contributions for EmmaHansen
30 April 2024
- 21:4321:43, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 C/December 2023/Question 30 No edit summary
- 21:4321:43, 30 April 2024 diff hist +323 N Science:Math Exam Resources/Courses/MATH100 C/December 2023/Question 30/Statement Created page with "Let <math display="inline">f(x)</math> be a function with <math display="inline">f'(x),f''(x)>0</math> for all <math display="inline">x</math>. What is the maximum number of horizontal asymptotes that such a function <math display="inline">f(x)</math> might have? What is the minimum number? Justify your answers carefully." current
- 21:4321:43, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 C/December 2023/Question 28 No edit summary
- 21:4221:42, 30 April 2024 diff hist +468 N Science:Math Exam Resources/Courses/MATH100 C/December 2023/Question 28/Statement Created page with "Doctor Roberts considers starting up a new factory making umbrellas. The factory would have fixed costs of $5,000 per month and each umbrella would cost $8 to produce. Market research indicates that if <math display="inline">x</math> thousand umbrellas are produced every month, they can be sold at price <math display="inline">p(x) = 30-x</math> dollars. Determine the optimal profit per month and the production level at which it occurs. Give units for your answers." current
- 21:3321:33, 30 April 2024 diff hist +1 Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 29(b) No edit summary current
- 21:3321:33, 30 April 2024 diff hist +1 Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 29(a) No edit summary current
- 21:3221:32, 30 April 2024 diff hist +1 Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 27(a) No edit summary current
- 21:3021:30, 30 April 2024 diff hist +1 Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 17 No edit summary current
- 21:2321:23, 30 April 2024 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 08 No edit summary current
- 21:2021:20, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(f) No edit summary
- 21:2021:20, 30 April 2024 diff hist +8 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(f)/Statement No edit summary Tag: Visual edit
- 21:2021:20, 30 April 2024 diff hist +301 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(f)/Statement Created page with "For this part, let <math display="inline">k_1</math> and, for notational simplicity, rename <math display="inline">k_2 = k</math>. What is the optimal daily drug quantity to administer so as to maximize the fraction of patients surviving? Justify carefully that you have indeed found a global maximum."
- 21:1721:17, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(e) No edit summary
- 21:1021:10, 30 April 2024 diff hist +165 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(e)/Statement Created page with "Part e: Interpret what <math display="inline">k_2</math> represents in medical terms. What do high and low values of <math display="inline">k_2</math> correspond to?"
- 21:1021:10, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(d) No edit summary
- 21:1021:10, 30 April 2024 diff hist +81 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(d)/Statement Created page with "Part d: Find <math display="inline">Q(x) = \lim_{k_2\rightarrow k_1} S(x)</math>."
- 21:0921:09, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(c) No edit summary
- 21:0921:09, 30 April 2024 diff hist +83 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(c)/Statement Created page with "Part c: Find <math display="inline">R(x) = \lim_{k_2\rightarrow\infty} S(x)</math>."
- 21:0921:09, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(b) No edit summary
- 21:0921:09, 30 April 2024 diff hist +125 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(b)/Statement Created page with "Part b: Find <math display="inline">\lim_{x\rightarrow \infty} S(x)</math>. Explain what your finding means in medical terms."
- 21:0821:08, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(a) No edit summary
- 21:0821:08, 30 April 2024 diff hist +1 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(a)/Statement No edit summary
- 21:0821:08, 30 April 2024 diff hist +628 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 30(a)/Statement Created page with "A drug used to treat cancer is effective at low doses with an efficacy (ability to cure) that increases with the quantity of the drug used. However, at sufficiently high doses, the drug becomes toxic (can cause death). The fration of patients surviving cancer with this drug treatment is given by <math display="block">S(x) = \frac{x}{k_1 + x} - \frac{x}{k_2 + x} </math> where <math display="inline">x</math> is the drug quantity in hundreds of milligrams/day given to the..."
- 21:0721:07, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 29(b) No edit summary
- 21:0721:07, 30 April 2024 diff hist +258 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 29(b)/Statement Created page with "Comparing your sketch for the initial condition <math display="inline">y(0) = -1</math> against your calculation in question 21, you should find them to be inconsistent. Explain in what way they are inconsistent and what you might do differently to fix that."
- 21:0721:07, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 29(a) No edit summary
- 21:0721:07, 30 April 2024 diff hist +374 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 29(a)/Statement Created page with "Consider the differential equation from questions 20 and 21: <math display="block">y' = -y(y-2)(y-10).</math> Part a: Sketch the solution to the differential equation for each of the initial conditions <math display="inline">y(0) = -1</math>, <math display="inline">y(0) = 3</math> on the same graph. Any inflection points should be visible, but can be positioned roughly."
- 20:5620:56, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11 No edit summary
- 20:5520:55, 30 April 2024 diff hist +1,148 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11/Solution 1 Created page with "Consider the picture below. The quantity that we are looking for is the rate of change of the distance <math display="inline">\ell</math> between the car and the police officer, when the car is <math display="inline">3</math>m away from the point on the road closest to the officer (labelled <math display="inline">A</math>). We need to come up with an equation for how <math display="inline">\ell</math> changes with respect to the distance, <math display="inline">d</math>..."
- 20:5420:54, 30 April 2024 diff hist +247 N File:Q11 MATH100B solution.jpg Uploaded own work with UploadWizard current Tag: Upload Wizard
- 19:4919:49, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11 No edit summary
- 19:4919:49, 30 April 2024 diff hist +49 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11/Hint 1 No edit summary current
- 19:4919:49, 30 April 2024 diff hist +432 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11/Statement No edit summary
- 19:3919:39, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 20 No edit summary
- 19:3819:38, 30 April 2024 diff hist +301 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 20/Statement Created page with "Sketch the phase line for the differential equation <math display="block"> y' = -y(y-2)(y-10). </math> Clearly indicate the steady states (also called equilibrium points), and indicate with arrows where <math display="inline">y</math> is increasing or decreasing on either side of each steady state." current
- 19:3819:38, 30 April 2024 diff hist −1 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 20/Hint 1 No edit summary current
- 19:3819:38, 30 April 2024 diff hist +258 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 20/Hint 1 Created page with " Recall: if <math display="inline">y</math> is at an equilibrium point, then the function <math display="inline">y</math> is not changing with time. Given that the derivative is the rate of change, what is happening to the derivative at an equilibrium point?"
- 19:3819:38, 30 April 2024 diff hist +1,507 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 20/Solution 1 Created page with "We know that if the function <math display="inline">y</math> is at an equilibrium point, then it is not changing, which means the derivative of the function is zero. Since we are given the differential equation in factored form, we can read off the zeros easily: <math display="inline">y'=0</math> when <math display="inline">y = 0, 2, 10</math>; these are the equilibrium points. To determine if the function is increasing or decreasing on either side of the equilibrium poi..." current
- 19:3719:37, 30 April 2024 diff hist +261 N File:Math100 B 2023 Q20 solution.png Uploaded a work by MATH100B 2023 instructors from MATH100B 2023 final exam with UploadWizard current Tag: Upload Wizard
- 19:2519:25, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 25 No edit summary
- 19:2519:25, 30 April 2024 diff hist +794 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 25/Solution 1 Created page with "The two residual values we have for the model <math display="inline">y(x) = ax</math> are <math display="inline">y(2) - 2</math> and <math display="inline">y(3) - 2</math>. The sum of squared residuals is <math display="block">R = (y(2) - 2)^2 + (y(3) - 2)^2 = (2a - 2)^2 + (3a - 2)^2 .</math> which is quadratic in <math display="inline">a</math> and concave up, so we know that the zero of the derivative of <math display="inline">R</math> with respect to <math display="..." current
- 19:2519:25, 30 April 2024 diff hist +189 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 25/Hint 1 Created page with "Recall that a residual is the difference between an estimate of a function (a model), and its true value. Since we are given two data points for the model, we will have two residual values." current
- 19:2519:25, 30 April 2024 diff hist +242 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 25/Statement Created page with "Find the value of <math display="inline">a</math> that minimises the sum of squared residuals for the model <math display="inline">y = ax</math> fitting the data points <math display="inline">(2,2)</math>, <math display="inline">(3,2)</math>." current
- 19:2419:24, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 24 No edit summary
- 19:2419:24, 30 April 2024 diff hist +691 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 24/Solution 1 Created page with "We know the absolute maximum is found on the boundary of the domain. We can also see from the function <math display="inline">f</math> and its domain that <math display="inline">x</math> has a positive coefficient, <math display="inline">y</math> has a negative coefficient, and the intervals where <math display="inline">x</math> and <math display="inline">y</math> can exist are both positive. From this we can deduct that <math display="inline">f(x,y)</math> will be maxim..." current
- 19:2419:24, 30 April 2024 diff hist +114 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 24/Hint 1 Created page with "Recall that on a closed domain, the absolute maximum (or absolute minimum) is found on the boundary of the domain." current
- 19:2419:24, 30 April 2024 diff hist +208 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 24/Statement Created page with "Find the absolute maximum of the function <math display="block"> f(x,y) = 2x-3y </math> on the rectangular domain <math display="inline">0\leq x\leq 2</math> and <math display="inline">0\leq y\leq 1</math>." current
- 19:2319:23, 30 April 2024 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 21 No edit summary
- 19:2319:23, 30 April 2024 diff hist +586 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 21/Solution 1 Created page with "Recall that the Taylor series for a function <math display="inline">y(t)</math> is <math display="block">y(t) = y(t_0) + y'(t_0)(t-t_0) + ... .</math> We are given <math display="inline">t_0 = 0</math>, <math display="inline">t-t_0 = 1/10 = \Delta t</math>, and we have an equation for <math display="inline">y'(t)</math>. Substituting this all in gives <math display="block">\begin{aligned} y &= y(0) + y'(0)(\Delta t) \\ &= -1 + (-(-1)(-1-2)(-1-11))(\frac{1}{10}) \\ &=..." current
- 19:2319:23, 30 April 2024 diff hist +51 N Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 21/Hint 1 Created page with "Taylor series are often used to estimate functions." current