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erma4kov [3.2K]
3 years ago
8

Twenty students bought tickets for a school party. All of the money received for these 20 tickets was used to purchase beverages

. Then, an additional 10 students bought tickets. Rather than use this additional money to buy more refreshments, all 30 students received a $3.00 refund. How many dollars were used to buy beverages?​
Mathematics
2 answers:
Charra [1.4K]3 years ago
3 0

Answer:

87

Step-by-step explanation:

joja [24]3 years ago
3 0

Answer:

$87 were used on beverages

Step-by-step explanation:

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\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\

sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}

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