If
[tex] \cos(330°) = \frac{ \sqrt{3} }{2} [/tex]
Then prove that:
[tex] \cos(165°) = - \frac{ \sqrt{3} + 1}{2 \sqrt{2} } [/tex]
Please help me!
Answers
Answer: see proof below
Step-by-step explanation:
Given: cos 330 = [tex]\frac{\sqrt3}{2}[/tex]
Use the Double-Angle Identity: cos 2A = 2 cos² A - 1
[tex]\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}[/tex]
Proof LHS → RHS:
LHS cos 165
Double-Angle: cos (2 · 165) = 2 cos² 165 - 1
⇒ cos 330 = 2 cos² 165 - 1
⇒ 2 cos² 165 = cos 330 + 1
Given: [tex]2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1[/tex]
[tex]\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}[/tex]
Divide by 2: [tex]\cos^2 165 = \dfrac{\sqrt3+2}{4}[/tex]
[tex]\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}[/tex]
[tex]\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}[/tex]
Square root: [tex]\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}[/tex]
Scratchwork: [tex]\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2[/tex]
[tex]\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}[/tex]
Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE
[tex]\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}[/tex]
LHS = RHS [tex]\checkmark[/tex]
![If [tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]Then Prove That:[tex] \cos(165) = - \frac{ \sqrt{3} +](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/rqx8lqLuvlOjKFYIkFL7QIczeMylqnO2.png)
![If [tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]Then Prove That:[tex] \cos(165) = - \frac{ \sqrt{3} +](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/m2q5P95M4DyUANinPX9OuxhKKfqm4Lf1.png)
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Rewrite in simplest terms: 4s-10(-10s-3)
Answers
Answer:
corect answer
Step-by-step explanation:
Chester Boles reviewed his credit card's monthly statement. It shows a $2,376.10 previous balance and this month's new purchases of $875.22, $65.75, $45.22, and $21.23. It also shows a $875.22 credit and a $45.30 finance charge. He also made the minimum payment of 2.5% of the previous balance. What is the new balance?
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The new balance after considering the new purchases, credits, finance charge, and minimum payment is $2,494.20.
Here,
To calculate Chester Boles' new credit card balance, we need to take into account the previous balance, new purchases, credits, and finance charge, as well as the minimum payment.
Add up the new purchases:
$875.22 + $65.75 + $45.22 + $21.23 = $1007.42
Add up the credits:
$875.22 (credit)
Calculate the total balance before the finance charge:
Previous Balance + New Purchases - Credits
$2,376.10 + $1007.42 - $875.22 = $2,508.30
Add the finance charge:
Total Balance + Finance Charge
$2,508.30 + $45.30 = $2,553.60
Calculate the minimum payment:
2.5% of the previous balance:
2.5% * $2,376.10 = $59.40
Subtract the minimum payment from the total balance:
$2,553.60 - $59.40 = $2,494.20
The new balance after considering the new purchases, credits, finance charge, and minimum payment is $2,494.20.
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A number n tripled equals -27
Answers
n = - 9
Step-by-step explanation:Hi there !
3n = - 27
n = - 27/3
n = - 9
Good luck !
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Step-by-step explanation:
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Or no solution
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Pls Help Only if you know the answer Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x)−7 ?
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The graph of g(x) is the graph of f(x) translated 7 units down.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.
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Answer:
The graph of g(x) is the graph of f(x) translated 7 units down
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Because 3/8 plus 1/4 equal 5/8, and then the two 5/8s cancel out.
Three out of seven soccer players wore headbands in a soccer league. A.Write the ratio of soccer players who wore headbands to soccer players who did not. B. If there were 36 players in the league who did not wear headbands, how many players were in the league brainily
Answers
Answer:
A. 3:4
B. 63 soccer players
Step-by-step explanation:
A. If out of 7 players, 3 wore headbands, then it means 4 out of 7 did not wear headbands.
Ratio of players who wire headbands to those who didn't wear headbands would be 3:4
B. Let x represent number of players who wore headbands
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Answers
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Step-by-step explanation:
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Answers
Correct arrangement of the question is;
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Option C) the square root of 5
Step-by-step explanation:
We are given: five to the three fourths power all raised to the two thirds power
Translating that statement means 5 is raised to ¾ raised to ⅔.
In indices, when we have two powers attached to a number, the two powers will multiply each other.
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Now, when a number is raised to the power ½, it is said to be square root of that number.
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Answers
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Step-by-step explanation:
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