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mojhsa [17]
2 years ago
9

If cosa=1/2(a+1/a), verify that. cos2a=1/2(a²+1/a²)​

Mathematics
1 answer:
Alborosie2 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

using the identity

cos2a = 2cos²a - 1 , then

cos2a

= 2[ \frac{1}{2}(a  + \frac{1}{a}) ]² - 1

= 2 [ \frac{1}{4} (a² + \frac{1}{a^2} + 2) ] - 1

= \frac{1}{2} (a² + \frac{1}{a^2} ) + 1 - 1

= \frac{1}{2} (a² + \frac{1}{a^2} ) ← thus verified

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6 to the power of 2 equal ?
EleoNora [17]

Answer:

36

Step-by-step explanation:

Whenever something is to the power of 2, just think of the number multiplied twice :) Hoped this helped.

6 0
3 years ago
Which of the following are solutions to the equation below? Check all that apply. x2 + x - 20 = 0
Mila [183]
Δ = 1 + 4*20 = 81
x' = (-1 + 9)/2 = 4
x'' = (-1 - 9)/2 = -5
4²  + 4 - 20 = 0
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Ok !
7 0
3 years ago
Read 2 more answers
.<br> Evaluate the series 1 + 0.1 + 0.01 + . . .
EastWind [94]

We can employ a simple repeated decimal trick:

x=1.111\ldots

0.1x=0.111\ldots

\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9

###

Alternatively, we can compute the partial sum of the series.

\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}

S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}

0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}

\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}

\implies S_n=\dfrac{10}9-\dfrac9{10^n}

As n\to\infty, the second term vanishes and we're left with \dfrac{10}9. Notice that this is really just a more formal version of the earlier trick.

6 0
3 years ago
Read 2 more answers
What number makes the equation true?<br> + 13 = 47
olga_2 [115]

Answer:

x=34

Step-by-step explanation:

Just take 47-13=34

7 0
3 years ago
Question 13 (1 point)
Ugo [173]

Answer:

A) Fixed Expenses

Step-by-step explanation:

Because you pay every month

6 0
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