Give an example of a Pythagorean triple that is not a multiple of 3, 4, 5.

Find the general solution of the separable differential equation given. Note that this problem, maybe the general solution will be a relationship between x and y, rather than y = f(x).

$$x y \frac{d y}{d x}=\frac{\ln x}{\sqrt{1-y^{2}}}$$

Compare the attitude toward the beloved in Petrarch's "Sonnet 292” with that in Shakespeare's “Sonnet 130.” How does each speaker view his beloved?

Determine whether each set is a Pythagorean triple. 3, 4, 5

Según la información de la etiqueta, ¿cuántas calorías tiene una ración de arroz con frijoles negros? ¿Cuántos gramos de proteínas tiene una ración?

A Pythagorean triple is a group of three whole numbers that can represent the lengths of the sides of a right triangle. The smallest Pythagorean triple is 3, 4, 5. Which of the following are Pythagorean triples?

a) $7,24,25$

b) $3,6,8$

c) $9,21,23$

d) $31,35,38$

The hypotenuse of a $30^{\circ}$ $-60^{\circ}$ $-90^{\circ}$ triangle has a length of 2r. What are the lengths of the other two legs?

What can you say about the determinant of an $n \times n$ matrix with the following form?

$$\left[\begin{array}{ccccc}{0} & {0} & {\cdots} & {0} & {1} \\ {0} & {0} & {\cdots} & {1} & {0} \\ {\vdots} & {\vdots} & {} & {\vdots} & {\vdots} \\ {0} & {1} & {\cdots} & {0} & {0} \\ {1} & {0} & {\cdots} & {0} & {0}\end{array}\right]$$

The maximum production of a soft-drink bottling company is 5000 cartons per day. The company produces two kinds of soft drinks, regular and diet. It costs $1.00 to produce each carton of regular and$1.20 to produce each carton of diet. The daily operating budget is $5400. The profit is$0.15 per carton on regular and $0.17 per carton on diet drinks. How much of each type of drink is produced to obtain the maximum profit?

Triples of whole numbers such as the earlier 3-4-5 and 5-12-13 are called Pythagorean triples because they are positive integers that fit an x squared + y squared = z squared relationship. Which of the following are Pythagorean triples?

a. 5, 6, and 7

b. 6, 8, and 10

c. 9, 12, and 15

d. 12, 16, and 20

e. If x, y, and z give a Pythagorean triple, will kx, ky, and kz also be a Pythagorean triple?

f. Use the idea in part (e) to generate 12 more Pythagorean triples.

What is object performance?

A manufacturer produces custom steel products from recycled steel in which each ton of the product must contain 4 pounds of chromium, 8 pounds of tungsten, and 7 pounds of carbon. The manufacturer has three sources of recycled steel: Source l: Each ton contains 2 pounds of chromium, 8 pounds of tungsten, and 6 pounds of carbon. Source 2: Each ton contains 3 pounds of chromium, 9 pounds of tungsten, and 6 pounds of carbon. Source 3: Each ton contains 12 pounds of chromium, 6 pounds of tungsten, and 12 pounds of carbon. Let x, y, and z denote the percentages of the first, second, and third recycled steel sources that will be melted down for one ton of the product. Find (but do not solve) a linear system in x, y, and z whose solution tells the percentage of each source that must be used to meet the requirements for the finished product.

When would it be beneficial to use exclusive distribution rather than intensive distribution?

For each x in [0, 1], let $f(x) = x$ if x is rational, and let $f(x) = 1- x$ if x is irrational. Prove that: (a) $f(f(x))=x$ for all x in [0, 1]. (b) $f(x)+f(1-x)=1$ for all x in [0, 1]. (c) f is continuous only at the point $x=\frac{1}{2}$. (d) f assumes every value between 0 and 1. (e) $f(x+y)-f(x)-f(y)$ is rational for all x and y in [0, 1].