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Orlov [11]
3 years ago
15

If cos(x)cos(π/7)+sin(x)sin(π/7)= - (√2)/2, then x can equal:

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\

\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}

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The distance between itahari and Damak is
Ludmilka [50]

Answer:

8 km by motorbike.

Step-by-step explanation:

The distance between itahari and Damak is  42 km.

Mr. Dhamala travelled 18.325 km by a  bus / 15.675 km by a taxi and the remaining distance by a motorbike.

Let he covered x distance by motorbike. So,

Remaining distance = Total distance -(distance covered by bus + distance by taxi)

= 42 -(18.325 +15.675 )

= 42-34

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So, he travelled 8 km by motorbike.

8 0
2 years ago
How do I solve this problem
velikii [3]

Answer:

Y= -7x + 1397

Step-by-step explanation:

1047- 872 / 125- 150

175 / -25 reduce to lowest form

7/ -1

M= -7

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697= -7(100) +b

697= -700 + b

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b= 1397

hope this helps

8 0
3 years ago
The average of five distinct scores has the same value as the median of the five scores. The sum of the five scores is 420. What
givi [52]

Answer:

The sum of five scores that is not the median is, 336

Step-by-step explanation:

Average defined as the  the sum of the observation to the total number of the observation.

Given: The sum of the five scores is 420

Then, by definition of average;

Average of five distinct score = \frac{420}{5} = 84

It is also, given that the average of five distinct scores has the same value as the median of the five scores.

⇒Median of five scores = 84

Since, scores are distinct, therefore

Sum of all scores that is not the median = Sum of five scores - median = 420-84 = 336

therefore, the sum of five scores that is not the median is, 336

3 0
3 years ago
Two or more expressions joined by an inequality sign is called
marta [7]

Answer:

inequality

Step-by-step explanation:

Inequality are two or more expressions joined by an inequality sign is called

6 0
2 years ago
Aida makes $9.25 per hour. Aida works 14 hours in one week. At the end of the week, Aida deposits 1/5 of her total income into a
Lina20 [59]

Answer:

$103.6 left

Step-by-step explanation:

First, multiply the amount she earns an hour times how many hours she worked:

9.25 x 14 = 129.5

Then divide the total by 1/5:

129.5 / 5 = 25.9

Then subtract that value from the total:

129.5 - 25.9 = 103.6

$103.6 is your answer

Hope this helps!

4 0
2 years ago
Read 2 more answers
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