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motikmotik
3 years ago
8

If cos A = 1/3 , then what is the positive value of sin 1/2​A, in simplest radical form with a rational denominator?

Mathematics
1 answer:
wolverine [178]3 years ago
5 0

Answer:

Step-by-step explanation:

You should remember from theory (one is the formula of the cosine of the double angle, and the other is the classic sum of squares being 1). cos A = cos^2 \frac A2 - sin^2 \frac A2 = 1- 2sin^2 \frac A2

At this point let's grab the first and last step of the chain, replacing values:

\frac 13 = 1-2sin^2\frac A2 \rightarrow 2sin^2 \frac A2 =\frac23\\sin^2 \frac A2 = \frac13 \rightarrow sin \frac A2 = \frac{1}{\sqrt3} = \frac{\sqrt3}{3}

Last passage you multiply top and bottom by the square root of 3 to rationalize.

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Krutika and Natasha win some money and share it in the ratio 3:4. Krutika gets £39. How much did Natasha get?
grin007 [14]

Answer:

22.28 Pounds

Step-by-step explanation:

Add 3+4=7

39 ÷ 7=5.57

Because Natasha has the ratio of 4 she would get

5.57 × 4=22.28

Answer=22.28

4 0
3 years ago
Complete the square to form a perfect square trinomial x^2-14x+
fiasKO [112]
Answer: x^2 - 14x + 49

Explanation:

1) Divide the coefficient of x by 2:

14 / 2 = 7

2) so you have to add 7^2 = 49

x^2 - 14x + 49

3) that trinomial is equivalent to:

=> (x - 7)^2

4) prove that using the formula (a - b)^2 = a^2 - 2ab + b^2

(x - 7)^2  = x^2 - 14x + 49

Then you have to add 49 to complete the square. and form a perfect square trinomial.
7 0
3 years ago
Simplify (5x−2+3x^2)+(4x+3)
Art [367]

Answer:

3x^2 + 9x + 1

Or

3x ( x + 3 ) + 1

Step-by-step explanation:

(5x - 2 +3x^2 ) + (4x + 3 )

To make this a little bit more easier to read, you can remove the parentheses:

5x - 2 + 3x^2 + 4x + 3

Now, write in a way so that the like terms are next to each other:

3x^2 + 5x + 4x - 2 + 3

Now simplify the 'x' terms to get:

3x^2 + 9x - 2 + 3

Now, simplify the integers (the ones with now variables with them) to get:

3x^2 + 9x + 1

If you want, you can factor out the 3x for two of the terms to get :

3x ( x + 3 ) + 1

Therefore, your simplest form can either be 3x^2 + 9x + 1 OR 3x (x + 3 ) + 1

5 0
3 years ago
Find the midpoint from (-2,-2) to (6,6)
timama [110]
(2,2)


(x1+x2)/2, (y1-y2)/2
(-2+6)/2=(2)
(-2+6)/2=2
4 0
3 years ago
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How do you find The area of a composite shape
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Answer:

Step-by-step explanatiArea of Composite Shapes. Composite shapes are shapes that have a combination of 2-D shapes. To find the area of composite shapes you just need to break down the shape into individual pieces and calculate their separate pieces then add them back together again to find a total areaon:

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3 years ago
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