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svetoff [14.1K]
3 years ago
13

Given f(x)=cos c and g(x)=cot x, what are the domain and range of f(g(x))?

Mathematics
1 answer:
ololo11 [35]3 years ago
8 0

Answer:

Alternative C is the correct answer

Step-by-step explanation:

The first step is to determine the composite function;

f[g(x)]

f[g(x)]=cos[cot(x)]

We then employ a graphing utility to determine the range and the domain of the new function.

The range is the set of y-values for which the function is defined. In this case it is;

[-1,1]

On the other hand, the domain refers to the set of the x-values for which the function is real and defined. In this case; it is the set of real numbers x except x does not equal npi for all integers n.

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2x=5x1800+1500(56-7)
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Elena has one and a half times as much money as ramon. together they have $225. how much money does each have? choices for ramon
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E= 1.5R
E+R=225
1.5R+R=225
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3 years ago
In a casino on a Saturday, 90% of the visitors lost $100 each, 9% of the visitors lost $1,000 each, and the rest won $10,000 eac
liq [111]

x = total amount of visitors


so we have 90% that lost $100, 9% that lost $1000, now 90+9 = 99%, what's left is just 1% then, so 1% won $10,000.

Profit is Revenue - Cost.

so the profit for the casino, is not who wins, because from the wins the casino needs to pay that to the winner, so they're losing that much, so for the casino, profits is when a player loses, so their profit will come from the 99% that lost money then.

keeping in mind that

\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em} \begin{array}{llll} \stackrel{\textit{90\% of x}}{\left( \cfrac{90}{100} \right)x}\implies 0.9x\qquad \stackrel{\textit{9\% of x}}{\left( \cfrac{9}{100} \right)x}\implies 0.09x \\\\\\ \stackrel{\textit{1\% of x}}{\left( \cfrac{1}{100} \right)x}\implies 0.01x \end{array}


since we know that 90% lost $100, that means 0.9x(100) is the total amount lost by all of them, since we also know that 9% lost $1000, then 0.09x(1000) is the total amount lost by them, and the wins are of course just 0.01x(100000).


\bf \stackrel{\textit{90\% at \$100}}{0.9x(100)}~~+~~\stackrel{\textit{9\% at \$1000}}{0.09x(1000)}~~-~~\stackrel{\textit{1\% at \$10000}}{0.01x(10000)}~~=~~\stackrel{\textit{casino's profit}}{80000} \\\\\\ 90x+90x-100x=80000\implies 80x=80000\\\\\\ x=\cfrac{80000}{80}\implies x=1000

4 0
4 years ago
Does this system of equations have one solution, no solutions, or an infinite number of solutions? 
In-s [12.5K]
This system of equations has an infinite number of solutions. 
6 0
3 years ago
Read 2 more answers
What is the equation in slope-intercept form of the line that passes through the points (4, 5) and (8,3)?
larisa86 [58]

Answer:

y = -1/2x+7

Step-by-step explanation:

First find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = (3-5)/( 8-4)

   = -2/4

  = -1/2

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = -1/2x+b

Substitute a point into the equation

3 = -1/2(8) +b

3 = -4+b

Add 4 to each side

3+4 = -4+b+4

7 = b

y = -1/2x+7

3 0
3 years ago
Read 2 more answers
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