Rectangle ghij inscribed in a circle, gk⊥jh, gk = 6cm, m∠ghj = 15°. find the radius of the circle. pls

6(2 + √3)  

Step-by-step explanation:

Given : Rectangle GHIJ inscribed in a circle. GK⊥JH, GK =  6 cm and m∠GHJ=15°.

To find: Radius(KH) =?

Sol:  As given in figure 1, Since GK⊥JH ∴ m∠GKH = 90° . Let GK = x cm.

Now, In ΔGKH,

        (∵ tan 15° = 2 - √3)

On rationalizing the above expression,

Therefore, radius of the circle (KH) = 6 (2+√3)

This is how to find the value of tan 15°

tan 15° = tan (45° -30°)

Now using,

On rationalizing,

Taking 2 common from numerator,

tan 15° = 2 - √3

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

find the magnitude of the trig term  

csc

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−

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by taking the absolute value of the coefficient.

1

find the lower bound of the range.

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y

=

−

2

find the upper bound of the range.

tap for more

y

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the range is  

y

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or  

y

≥

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(

−

∞

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∪

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{

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step-by-step explanation: