note: w - means you are required to show work. nc - means you are not allowed to use a calculator so you must show work
day problem i problem ii problem iii
mon 2. using the “real number chart” given out in class: classify the number (you must use all the labels that apply) $pi$
3. write the following number in scientific notation. 26,496
1. by tradition, horse races are measured in furlongs. a furlong is $\frac{1}{8}$ of a mile. how long is a 5 - furlong race in miles?
tues simplify 3. $5r^{3}cdot2r^{7}$
simplify 1. $\frac{3x^{8}}{18x^{3}}$
1. a commercial jet flies from st. louis, missouri, to buenos aires, argentina, a distance of 4,707 nautical miles. if the plane flies at 210 knots, how long will the trip take? (a knot is 1 nautical mile per hour.)

Question

Accepted Answer

### Mon - Problem I
# Explanation:
## Step1: Recall number - type definitions
A real number is any number on the number line. A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. $\pi = 3.14159\cdots$ is non - repeating and non - terminating.
Since $\pi$ is a non - repeating, non - terminating decimal, it is a real number but not a rational number. It is an irrational number.
# Answer: Real, Irrational

### Mon - Problem II
# Explanation:
## Step1: Recall scientific notation form
Scientific notation is $a	imes10^{n}$, where $1\leq|a|\lt10$ and $n$ is an integer.
## Step2: Rewrite the number
For $26496$, move the decimal point 4 places to the left to get $a = 2.6496$ and $n=4$. So, $26496=2.6496	imes 10^{4}$
# Answer: $2.6496	imes 10^{4}$

### Mon - Problem III
# Explanation:
## Step1: Set up the proportion
If 1 furlong is $\frac{1}{8}$ of a mile, and we want to find out how many miles is a 5 - furlong race. Let $x$ be the number of miles in a 5 - furlong race. Then the proportion is $\frac{1}{8}=\frac{x}{5}$.
## Step2: Solve for $x$
Cross - multiply: $x=\frac{5}{8}=0.625$ miles
# Answer: $0.625$ miles

### Tues - Problem I
# Explanation:
## Step1: Use the product rule of exponents
The product rule states that $a^{m}\cdot a^{n}=a^{m + n}$. For $5r^{3}\cdot2r^{5}$, first multiply the coefficients: $5	imes2 = 10$, then add the exponents of $r$: $r^{3}\cdot r^{5}=r^{3 + 5}=r^{8}$
# Answer: $10r^{8}$

### Tues - Problem II
# Explanation:
## Step1: Use the quotient rule of exponents
The quotient rule states that $\frac{a^{m}}{a^{n}}=a^{m - n}$ for $a
eq0$. For $\frac{3x^{8}}{18x^{3}}$, first simplify the coefficient: $\frac{3}{18}=\frac{1}{6}$, then subtract the exponents of $x$: $x^{8-3}=x^{5}$
# Answer: $\frac{1}{6}x^{5}$

### Tues - Problem III
# Explanation:
## Step1: Recall the time - distance formula
The formula is $t=\frac{d}{v}$, where $t$ is time, $d$ is distance, and $v$ is velocity. Here, $d = 4707$ nautical miles and $v=210$ knots (since 1 knot = 1 nautical mile per hour).
## Step2: Calculate the time
$t=\frac{4707}{210}=22.41$ hours
# Answer: $22.41$ hours

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QUESTION IMAGE

Question

Explanation:

Mon - Problem I

Step1: Recall number - type definitions

Step1: Recall scientific notation form

Step2: Rewrite the number

Step1: Set up the proportion

Step2: Solve for $x$

Answer:

Mon - Problem II