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forsale [732]
3 years ago
11

I need help with this question

Mathematics
1 answer:
Novay_Z [31]3 years ago
3 0

Answer:

$ \frac{\sqrt{3} - 1}{2\sqrt{2}} $

$ \frac{-(\sqrt{3} + 1)}{2\sqrt{2}} $

$ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $

Step-by-step explanation:

Given $ \frac{11 \pi}{12} = \frac{3 \pi}{4} + \frac{\pi}{6} $

(A) $ sin(\frac{11\pi}{12}) = sin (\frac{3 \pi}{4}  + \frac{\pi}{6}) $

We know that Sin(A + B) = SinA cosB + cosAsinB

Substituting in the above formula we get:

$ sin (\frac{3\pi}{4} + \frac{\pi}{6}) = \frac{1}{\sqrt{2}} . \frac{\sqrt{3}}{2} + \frac{-1}{\sqrt{2}}. \frac{1}{2} $

$ \implies \frac{1}{\sqrt{2}} (\frac{\sqrt{3} - 1}{2}) = \frac{\sqrt{3} - 1}{2\sqrt{2}}

(B) Cos(A + B) = CosAcosB - SinASinB

$ cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}}) $

$ \implies \frac{-1}{\sqrt{2}}. \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} . \frac{1}{2} $

$ \implies cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}) $

$ = \frac{-(\sqrt{3} + 1)}{2\sqrt{2}}

(C) Tan(A + B) = $ \frac{Sin(A +B)}{Cos(A + B)} $

From the above obtained values this can be calculated and the value is $ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $.

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What is the common ratio of 2, 10/3, 50/9
mojhsa [17]

The common ratio of 2, 10/3, 50/9 is \frac{10}{6}

<u>Solution:</u>

Given, series of elements are 2, \frac{10}{3}, \frac{50}{9}

We have to find the common ratio of the above given series.

We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.

So, now take \frac{10}{3} and 2

\text { Then, common ratio }=\frac{\frac{10}{3}}{2}

\begin{array}{l}{\text { Common ratio }=\frac{10}{3} \times \frac{1}{2}} \\\\ {\text { Common ratio }=\frac{10}{3 \times 2}=\frac{10}{6}}\end{array}

Hence, the common ratio of the given series is \frac{10}{6}

6 0
3 years ago
Peter left city a at 9:00 am towards city b at an average speed of 50 mph. Thirty minutes later Emily also leaves city a towards
Archy [21]

Answer:

62.5 mph

Step-by-step explanation:

Given that :

Peter :

Speed = 50mph

Start Time = 9 a. M

Emily :

Start time = 9:30

Speed = x

In other to catch up at 11:30 :

Peter (11:30 - 9:00) = 2hours 30 minutes = 2.5 hrs

Total distance moved by Peter :

Speed * time = 50 * 2.5 = 125miles

For Emily to cover 125 miles in (11:30 - 9:30) = 2 hours

Speed = distance / time

Speed = 125 miles / 2 hours

Speed = 62.5 miles per hour

7 0
2 years ago
Which factor did the railroad contribute to by encouraging population growth in West Texas from 1870 to 1890?
wariber [46]

Answer:

A

Step-by-step explanation:i took the test

7 0
2 years ago
Need help with this question
Sliva [168]

Answer:

EF= 24

Step-by-step explanation:

\sqrt{26^{2} - 10^{2} = 24

7 0
3 years ago
What is the slope of the line that passes through the points (1, 2) and (3, 12)?
Molodets [167]

Answer:

Slope is 5

Step-by-step explanation:

(1, 2) and (3, 12)

m= (y2-y1)/(x2-x1)

m= (12-2)/(3-1)

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3 0
2 years ago
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