The pier in Santa Monica, CA, is a popular destination for both tourists and locals. Visitors ride the Ferris wheel (F), eat ice cream (C), or just walk around on the pier (W). Write a dynamical model for the numbers of people engaged in these activities given the following assumptions. (Hint: Start by drawing a diagram of this system and labeling the stocks and flows. People entering the pier always start by just walking around. E people enter the pier each minute. Visitors leave at a constant per capita rate d. They can leave only when they are walking around. Due to fear of nausea, people do not go directly from eating ice cream to riding the Ferris wheel. Visitors prefer to go on the Ferris wheel with friends. Thus, the probability that any one individual will go on the Ferris wheel is proportional to the number of people walking around, with proportionality constant b. Riders leave the Ferris wheel at per capita rate n. When visitors leave the Ferris wheel, a fraction z of them go directly to eating ice cream. The others walk around. Visitors who are walking around prefer to avoid long lines for ice cream. Thus, the per capita rate at which they get ice cream is proportional to the inverse of the number of people already doing so, with proportionality constant m. People who are eating ice cream stop doing so at a constant per capita rate k.

Let V be a vector space, and suppose that U and W are both subspaces of V. Show that U ∩W := {v | v ∈ U and v ∈ W} is a subspace of V.

please answer with coding from The second edition C programming language textbook

/* Changes all occurrences of t in s to u, result stored in v

*

* Example:

*

* char v[100];

* replace("hello", "el", "abc", v) => v becomes "habclo"

* replace("", "el", "abc", v) => v becomes "" (no change)

* replace("hello", "abc", "def", v) => v becomes "hello" (no change)

* replace("utilities", "ti", "def", v) => v becomes "udeflidefes"

*

*/

void replace(char *s, char *t, char *u, char *v)

{

}

Write about what college success means to you. How will you define success,and what strategies will you use to achieve success? Please write 300 words. Please cite in text research paper author and year.

Effective process control distinguishes between attribute and variable data.  

• Describe some attribute data and variable data, as defined by the author, and label which category includes quantitative vs qualitative variation and how this applies to control charts?

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

If V = U ⊕ U^⟂ and V = W ⊕ W^⟂, and if S₁: U → W and S₂: U^⟂ → W^⟂ are isometries, then the linear operator defined for u₁ ∈ U and u₂ ∈ U^⟂ by the formula S(u₁ + u₂) = S₁u₁ + S₂u₂ is a well-defined linear isometry. Prove this.

Prove that if U, V and W are vector spaces such that U and V are isomorphic and V and W are isomorphic, then U and W are isomorphic.

If G = (V, E) is a graph and x ∈ V , let G \ x be the graph whose vertex set is V \ {x} and whose edges are those edges of G that don’t contain x.

Show that every connected finite graph G = (V, E) with at least two vertices has at least two vertices x1, x2 ∈ V such that G \ xi is connected.