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2 years ago

If sin theta =1/4, theta in quadrant II, find the exact value of cos[theta +pi/6]

1 answer:

6 0

Using cos addition formula:
use x for theta
cos(x+π/6)=cosx*cos(π/6)-sinx*sin(π/6)
sinx=1/4
cosx=√15/4
cos(π/6)=√3/2
sin(π/6)=1/2
cos(x+π/6)=(√15/4*√3/2)-(1/4*1/2)
cos(x+π/6)=(√45/8)-(1/8 )
cos(x+π/6)=(√45-1)/8)

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Identify the three similar right triangles in the given diagram.

irga5000 [103]

Answer:

B. ΔABD, ΔADC, ΔDBC

Step-by-step explanation

Step -1 In ΔABD and ΔADC (from figure).

∠DAB=∠CAD (common in both triangles) ,

∠DBA=∠CDA =90 degree, and

∠BDA=∠DCA (rest angle of the two triangles).

therefore ΔABD similar to ΔADC (by AAA similarity theorem).

Step -2 In ΔDBC and ΔADC (from figure).

∠DCB=∠ACD (common in both triangles) ,

∠DBC=∠ADC =90 degree, and

∠CDB=∠CAD (rest angle of the two triangles).

therefore ΔDBC similar to ΔADC (by AAA similarity theorem).

Step -3 In ΔABD and ΔDBC (from figure).

∠BDA=∠BCD (because , ∠ACD=ADB from stap-1 and ∠ACD=∠BCD from figure) ,

∠DBA=∠CBD =90 degree, and

∠BAC=∠BDC (rest angle of the two triangles).

therefore ΔABD similar to ΔDBC (by AAA similarity theorem).

In the above step- ΔABD similar to ΔADC, ΔDBC similar to ΔADC and ΔABD similar to ΔDBC.

Hence ΔABD, ΔADC, ΔDBC similar to each other in the given figure.

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2 years ago

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Darya [45]

Answer: 6/5

Step-by-step explanation:

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2 years ago

What mathematical process is the following formula performing: C2*D3?

tiny-mole [99]

Answer is D because C^2 ×D^2 the * mean ×

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3 years ago

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in 2011, an Action Comics no. 1, featuring first appearance of superman, was sold at auction for $2,161,000. The comic book was

Salsk061 [2.6K]

Price of book in 1938 = $ 0.10

Price of book in 2011 = $ 2,161,000

Number of years over 1938-2011 = 2011 - 1938 = 73

Annual increase in the price = $((\frac{\text{Price of book in 2011}}{\text{Price of book in 1938}}) ^ \frac{1}{\text{Number of years}} - 1 ) * 100$

⇒ Annual increase in the price = $((\frac{2,161,000}{0.1}) ^ \frac{1}{73} - 1 ) * 100$

⇒ Annual increase in the price = (1.260302283 - 1 ) × 100

⇒ Annual increase in the price = 0.260302283 × 100

⇒ Annual increase in the price = 26.0302283 %

⇒ Annual increase in the price = 26%

Hence, the comic book price increased by 26% annually

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2 years ago

Anybody solve this i made it its easy<br> 3(55x2) + 9 + 44 +88 x 9 = your number + 163593

olga55 [171]

Answer:

165*6+53+792= 990+845 = 1,835

Step-by-step explanation:

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2 years ago