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2 years ago

Trig: A sector of a circle has area 25 cm2 and centralangle

Mathematics

1 answer:

Alchen [17]2 years ago

3 0

Answer: Radius = 10 cm and Arc length = 5 cm

Step-by-step explanation:

The area of a sector with radius r and central angle $\theta$ (In radian) is given by :-

$A=\dfrac{1}{2}r^2\theta$

Given : A sector of a circle has area $25 cm^2$ and central angle 0.5 radians.

Let r be the radius , then we have

$25=\dfrac{1}{2}r^2(0.5)\\\\\Rightarrow\ r^2=\dfrac{2\times25}{0.5}\\\\\Rightarrow\ r^2=\dfrac{50}{0.5}=100\\\\\Rightarrow\ r=\sqrt{100}=10\ cm$

Thus, radius = 10 cm

The length of arc is given by :-

$l=r\theta=10\times0.5=5\ cm$

Hence, the length of the arc = 5 cm

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The valid probability distributions are the ones in options C and D.

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1 year ago

The ratio of Ds to As in the school was 4 to 72. If there were 1080 As in the school this term, how many Ds were there?

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3 years ago

Read 2 more answers

Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.

nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

$\sin (x+y) = 3\sin (x-y)$

Using the identities

$\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\$

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$\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y$

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

$3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}$

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3 years ago