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Inessa05 [86]
3 years ago
7

Find sin 2a and cot 2a:

Mathematics
1 answer:
geniusboy [140]3 years ago
8 0

Answer:

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

Step-by-step explanation:

\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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we know that 1 gallon = 4 quarts so...

17 gallons of root beer + 12 gallons of punch = 29 gallons in total

29 gallons ÷ 4 = 7.25 quarts

so she needs 7 bottles of quarts for her 29 total gallons.

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3 years ago
Beth is putting liquid fertilizer on the plants in 4 flowerpots. her measuring spoon holds 1/8 teaspoon the directions say to pu
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Read 2 more answers
How can we solve this?
Delvig [45]
Both angles will equal 180, as there is a line bisecting line AB to create the two angles.

Set up the following equation to have both angles equal 180:

(x + 35) + (x - 23) = 180

x + 35 + x - 23 = 180

Combine like terms:

x + x = 2x
35 - 23 = 12

2x + 12 = 180

Subtract 12 from both sides:

2x = 168

Divide both sides by 2:

x = 84

We now know the value of x, so plug it into the equation we set up:

(84 + 35) + (84 - 23) = 180

119 + 61 = 180

An obtuse angle will have a measure above 90 degrees. The number on the left side that is above 90 degrees is 119. This would be the measure for the obtuse angle.

The obtuse angle is 119 degrees wide.
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3 years ago
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cestrela7 [59]

Answer:

- 7 {x}^{2}  + 7 {x}^{3}

Step-by-step explanation:

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disa [49]

Step-by-step explanation:

well, the first solution that comes to my mind is :

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the reason : the only numerator I can "cut" into integer pieces is 8.

5 and 7 are prime numbers.

so, it tried to keep 5 and 7 whole, and then add a part of 8 to make this equation true. and that worked right away.

7 0
2 years ago
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