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Sergeeva-Olga [200]
2 years ago
13

Suppose that the functions s and t are defined for all real numbers x as follows.

Mathematics
1 answer:
jeka942 years ago
8 0

Answer:

(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39

Step-by-step explanation:

Given functions are:

s(x)= x+6\\t(x)= 4x^2

We have to find:

(s.t)(x) => this means we have to multiply the two functions to get the result.

So,

(s.t)(x) = s(x)*t(x)\\= (x+6)(4x^2)\\=4x^2.x+4x^2.6\\=4x^3+24x^2

Also we have to find

(s-t)(x) => we have to subtract function t from function s

(s-t)(x) = s(x) - t(x)\\= (x+6) - (4x^2)\\=x+6-4x^2

Also we have to find,

(s+t)(-3) => first we have to find sum of both functions and then put -3 in place of x

(s+t)(x) = s(x)+t(x)\\= x+6+4x^2

Putting x = -3

= -3+6+4(-3)^2\\=-3+6+4(9)\\=3+36\\=39

Hence,

(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39

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Answer:

\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

<u>Given</u><u> </u><u>:</u><u>-</u>

• \sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}

<u>To</u><u> </u><u>Prove</u><u> </u><u>:</u><u>-</u><u> </u>

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Therefore , here substituting the value of sinA , we have ,

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Multiply it by 2 ,

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Take out 2 common from the numerator ,

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Simplify ,

\sf\implies cos2A =  1 -\dfrac{ 2-\sqrt3}{2}

Subtract the numbers ,

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Simplify,

\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }

Hence Proved !

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