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joja [24]
3 years ago
10

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

Mathematics
1 answer:
stepan [7]3 years ago
3 0

Answer:

\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}

Step-by-step explanation:

Given

\cos A = \frac{1}{2}

Required

Determine \cos(\frac{1}{2}A)

To do this, we make use of the following identity

\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}

Substitute: \cos A = \frac{1}{2}

\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}

Solve the numerator

\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}

\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}

Rewrite as:

\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}

\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}

Take square roots

\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}

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−1/2 (x+2) + 112x = 3<br><br> x=?
AysviL [449]

Given equation :−1/2 (x+2) + 112x = 3

We have -1/2 in front of parenthesis on left side .

It's better to remove fraction in an equation, in order make it easier to solve.

In order to remove 2 from denominator of 2, we need to multiply each and every term by 2.

Multiplying each term in the equation by 2, we get

2* −1/2(x+2) +2* 112x = 2*3.

On simplifying this step, we get

-1(x+2) +224x = 6.

Distributing -1 over (x+2), we get

-x -2 +224x = 6

Combining like terms on left side, -x+224x=223x

223x -2 = 6

Adding 2 on both sides, we get

223x -2+2 = 6+2

223x = 8

Dividing both sides by 223, we get

223x/223 = 8/223.

x= 8/223.

6 0
3 years ago
Write a quadratic equation with roots of 3/4 and -4
Vaselesa [24]

A quadratic equation given roots is solved by using the relation

{x}^{2}  - (sum \: of \: roots)x + product \: of \: roots

from the question,

sum of the root will be

\frac{3}{4}  + ( - 4) =  \frac{3}{4}  - 4

=   \frac{3 - 16}{4}

=  \frac{ - 13}{4}

and also, product of the roots will

be

\frac{3}{4}  \times ( - 4) =  - 3

now substituting the sum of roots and product of roots into the equation

{x}^{2}  - ( -  \frac{13}{4} )x - 3

=  {x}^{2}  +  \frac{13}{4} x - 3

as the quadratic equation for the root 3/4 and -4

4 0
3 years ago
What are the steps to divide 336/7
Kitty [74]
48
And get a A bc that's the answer
5 0
3 years ago
Mr. Gephart is traveling from his house to the history museum. How many meters will he travel to the museum? The distance from h
snow_lady [41]

Answer: 6700 meters

Step-by-step explanation:

From the question given, we are informed that Gephart is traveling from his house to the history museum and that the distance from home to the history museum is six and seven-tenths kilometers.

In order to know the distance in meters

that he will travel to the museum, we have to multiply the convert the distance given in kilometers to meters. This will be:

1000 meters = 1 kilometer

Therefore, 6 7/10km = (6 7/10 × 1000m)

= 6 7/10 × 1000

= 67/10 × 1000

= 67 × 100

= 6700 meters

He'll travel 6700 meters to the museum.

7 0
3 years ago
How many times would m^1/4 need to be expressed as a repeated factor in order to obtain m^2?
Marianna [84]
B.4
1/4 divided by 2 
do the reciprocal
1/4 times 1/2=2/8
divide 8by 2

3 0
3 years ago
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