Questions
A child swinging on a swingset with chains of length l wants to swing and jump...

A child swinging on a swingset with chains of length l wants to swing and jump off the swing to get as far as possible. At what angle θ_jump should the child let go of the swing to maximize the landing distance? What is the distance jumped as a function of θ_jump?

Results should be functions of θ_jump and variables/parameters which should be introduced as required.

Model swinging using simple pendulum and jumping using projectile motion. Note, the child is not being pushed.

In: Advanced Math

At 1:43pm, a can of soda is placed in a fridge where the temperature is 34◦F....

At 1:43pm, a can of soda is placed in a fridge where the temperature is 34◦F.
At 1:46pm, the temperature of the can had dropped 15◦F. At 1:49pm, the temperature
of the can had dropped another 6◦F. What was the temperature of the can when it was
put in the fridge?

In: Advanced Math

For a tetrahedron -describe the type of groups of a rectangle -describe the orders of the...

For a tetrahedron

-describe the type of groups of a rectangle

-describe the orders of the groups

-describe the structure of the groups

-describe the elements of the groups (make sure to name all the elements and describe them as a group of permutations on the vertices)

- describe each group as subgroups of permutation groups

-describe all possible orders, types and generators for each subgroup of the group

-are any of these groups cyclic and or abelian?

-are any of these subgroups cyclic and or abelian?

-are there subgroups of every possible order?

-which subgroups are isomorphic and how do you know?

In: Advanced Math

Suppose we have a rod of material of conductivity K = 1 and situated on the...

Suppose we have a rod of material of conductivity K = 1
and situated on the x-axis, for 0 ≤ x ≤ 1. Suppose further that the rod is
laterally insulated, but has a known internal heat source f(x). The left and
right ends of the rod are held at 0 ◦C (degrees Celsius). With n = 5
Solve the linear system in Jupyter using Gauss-Jordan Elimination. See the notes on
the first problem of this set for hints on how to use and report the results from Gauss-Jordan Elimination.
This equation can be
understood as balancing the flow of heat from a node to its neighbors:
−yi−1 + 2yi − yi+1 = h2/k f(xi)

In: Advanced Math

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is...

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is a subspace. If U is a subspace, then find a basis which span U.

In: Advanced Math

Lesson 8 Explain why the word "average" should not be used to describe measures of center....

Lesson 8

  • Explain why the word "average" should not be used to describe measures of center.
  • Explain the advantages and disadvantages of the mean.
  • Explain the procedure for finding the standard deviation.
  • Explain why the range is not usually the best measure of variation.

In: Advanced Math

Solve the following linear programming problem. You must use the dual. First write down the dual...

Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem.

(a) Minimize w = 4y1 + 5y2 + 7y3

Subject to: y1 + y2 + y3 ≥ 18

2y1 + y2 + 2y3 ≥ 20

y1 + 2y2 + 3y3 ≥ 25

y1, y2, y3 ≥ 0

(b) Making use of shadow costs, if the 2nd original constraint changed to

2y1 + y2 + 2y3 ≥ 24, now what will the minimum of w be? Explain clearly.

(c) Making use of shadow costs, if the 1st original constraint changed to

y1 + y2 + y3 ≥ 21, now what will the minimum of w be? Explain clearly.

In: Advanced Math

How do I graph this step function? f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1) Please show step by...

How do I graph this step function?

f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1)

Please show step by step.

How is it the same graph as

f(t) = H(t-1)-3H(t-2)+H(t-1)*2(t-1)-H(t-2)*6(t-2)?

Please show why as well.

In: Advanced Math

Explain effectiveness of Cost Model Data Set in your examples.

Explain effectiveness of Cost Model Data Set in your examples.

In: Advanced Math

Design a randomized comparative experiments to test whether fluoxetine is effective at reducing depression. the participants...

Design a randomized comparative experiments to test whether fluoxetine is effective at reducing depression. the participants are 100 people suffering from depression and the response variable is the change on a standard questionnaire measuring level of depression.
Describe how randomization will be used in the design
Describe how the placebo will be used
Describe how to make the experiment double blind

In: Advanced Math

Determine a differential equation that has x = 0 as a regular singular point and that...

Determine a differential equation that has x = 0 as a regular singular point and that the roots of the index equation are i and i. Find a solution around x = 0.

In: Advanced Math

a. What are the maximal and minimal elements, if any, of the set (N+,|)? Is there...


a. What are the maximal and minimal elements, if any, of the set (N+,|)? Is there a minimum or maximum element? (N+={1,2,3,4,...}).
b. There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. We can have three scoops. How many variations will there be?

In: Advanced Math

Describe the stereographic projection on the Riemann sphere of the set {z : Re z =...

Describe the stereographic projection on the Riemann sphere of the set {z : Re z = 1} by an equation in (x, y, z)

In: Advanced Math

Let f : [a, b] → R be a monotone function. Show that the discontinuity set...

Let f : [a, b] → R be a monotone function.

Show that the discontinuity set Disc(f) is countable.

In: Advanced Math

What is the meaning of calculating the "flux" when solving integrals? - Also; What is the...

What is the meaning of calculating the "flux" when solving integrals? -

Also; What is the difference between these integrals?
-Line integral
-Double integral
-Triple integral
-Surface integral
-Flux, flux integral

In: Advanced Math