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Andrew [12]
3 years ago
13

Solve the following equation on the interval [0,2 \pi) Cot(3x)=\sqrt{3}

Mathematics
1 answer:
Orlov [11]3 years ago
4 0
Cot(3x)=3^(1/2)

cot(x)= cos(x)/sin(x)

cot(3x)= cos(3x)/sin(3x)

look at a unit circle chart

find a value for cos that has sqrt(3) in it

which one will reduce so that the cos/sin will equal sqrt(3)?

pi/6 radians

now cot(3x) implies that x is one third this value

pi/18 is the answer
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last summer, at camp okey-fun-okey, the ratio of the number of boy campers to girl campers was 8:7. If there were a total of 195
Evgen [1.6K]

The ration of boy campers to total campers is 8:15, and the ratio of girl campers to total campers is 7:15.  Using this information, we can answer this question by setting up proportions.

<u>For boys:</u>

\frac{8}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1560

<em>*Divide both sides by 15*</em>

x=104

There are 169 boy campers.


<u>For girls:</u>

\frac{7}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1365

91=x

There are 91 girl campers.


Hope this helps!!

7 0
3 years ago
Read 2 more answers
Theresa is comparing the graphs of y=2x and y=5x. Which statement is true?
abruzzese [7]

Answer:

Both graphs have a “y-intercept” at (0,0), so i believe the answer would be they don’t have y intercepts

Step-by-step explanation:

7 0
3 years ago
Solve the equation <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B10%7D%20%2B8%3D17" id="TexFormula1" title="\frac{n}{10} +8
jonny [76]
Its 90 because 90 divided by 10 simplifies down to 9, and 9+8=17
3 0
3 years ago
Complete the inequality. 9% ___ 0.4
Alex73 [517]
9% is less than 0.4. 0.4 is really 4/10 which is 40% 40 is greater than 9 therefore 9% is less than 0.4! So your answer is 9%<0.4! I hope this helped!
3 0
3 years ago
Parking spaces at a business school are arranged by a random monthly lottery. there are 3 spaces for every 10 students who want
Alexus [3.1K]

27.034%  
Let's define the function P(x) for the probability of getting a parking space exactly x times over a 9 month period. it would be: 
P(x) = (0.3^x)(0.7^(9-x))*9!/(x!(9-x)!)  
Let me explain the above. The raising of (0.3^x)(0.7^(9-x)) is the probability of getting exactly x successes and 9-x failures. Then we shuffle them in the 9! possible arrangements. But since we can't tell the differences between successes, we divide by the x! different ways of arranging the successes. And since we can't distinguish between the different failures, we divide by the (9-x)! different ways of arranging those failures as well. So P(4) = 0.171532242 meaning that there's a 17.153% chance of getting a parking space exactly 4 times. 
Now all we need to do is calculate the sum of P(x) for x ranging from 4 to 9.

So
 P(4) = 0.171532242
 P(5) = 0.073513818
 P(6) = 0.021003948
 P(7) = 0.003857868
 P(8) = 0.000413343
 P(9) = 0.000019683
  And
 0.171532242 + 0.073513818 + 0.021003948 + 0.003857868 + 0.000413343
+ 0.000019683 = 0.270340902 
 So the probability of getting a parking space at least four out of the nine months is 27.034%
5 0
3 years ago
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