Here’s the directions , I just need to know number 1thank you

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

6 0

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What is the domain of the function y=tan (x/8)<br> Please Help<br> 15 Points

7nadin3 [17]

1. You have the function $y=tan(\frac{x}{8} )$

2. You know that $y=\frac{sinx}{cosx}$ with $cosx\neq 0$ , because the division by zero is not defined. So , $cosx=0$ for $\frac{(2n+1)\pi}{2}$ where $n$ is a integer number.

3. Then, to find the domain of the function given in the problem, you must make $\frac{x}{8} \neq \frac{k\pi}{2} \\ x\neq 4k\pi$

Where $k$ is odd number.

4. Therefore:

$x\neq 4\pi (2n+1)$

5. Finally, the domain is: $4\pi (2n+1)$

The answer is: $4\pi (2n+1)$

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3 years ago

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Population Growth Using 20th-century U.S. census data,

asambeis [7]

The population of Ohio will be 10 million in the year 1970

The population growth of Ohio is represented by the function:

$P(t)=\frac{12.79}{1+2.402e^{-}0.0309t}$

P is the population in millions

t is the number of years since 1900

To find the year that the population of Ohio will be 10 million, substitute P = 10 into the function P(t) and solve for t

$10=\frac{12.79}{1+2.402e^{-}0.0309t}\\\\10(1+2.402e^{-}0.0309t)=12.79\\\\1+2.402e^{-}0.0309t=\frac{12.79}{10} \\\\1+2.402e^{-}0.0309t=1.279\\\\2.402e^{-}0.0309t=1.279-1\\\\2.402e^{-}0.0309t = 0.279\\\\e^{-}0.0309t =\frac{0.279}{2.402} \\\\e^{-}0.0309t =0.116\\\\-0.0309t=ln0.116\\\\-0.0309t=-2.154\\\\t=\frac{-2.154}{-0.0309} \\\\t=69.7$