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

Answers

Answer 1

Answer:

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\cos A = \frac{1}{2}[/tex]

Required

Determine [tex]\cos(\frac{1}{2}A)[/tex]

To do this, we make use of the following identity

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}[/tex]

Substitute: [tex]\cos A = \frac{1}{2}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}[/tex]

Solve the numerator

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}[/tex]

Rewrite as:

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}[/tex]

[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}[/tex]

Take square roots

[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]


Related Questions

b) Assume that 80 persons die, and 250 babies are born around the world each minute. how many more/fewer humans do you expect there to be on Earth at the end of 2021? Show your work. (population growth rate=birth rate – death rate (assuming zero migration)).

Answers

Answer:

ratio 80:250

Step-by-step explanation:

there will be less people than babies

Solve the system using
the elimination method.
(3x + 4y = 6
<
(2x + 3y = 3

Answers

Answer:

[tex]3x + 4y = 6 - - - (a) \\ 2x + 3y = 3 - - - (b) \\ 2 \times (a) - 3 \times (b) : \\ = > 0x - y = 3 \\ y = - 3 \\ 2x - 9 = 3 \\ 2x = 12 \\ x = 6 \\ { \boxed{x = 6}} \\ { \boxed{y = - 3}}[/tex]

The quadrilateral shown is a rectangle. What is measure zvw

Answers

Answer:

measure of zvm is 119°

Step-by-step explanation:

xvw+zvw=180°{straight angle}zvm=180-61=119°

stay safe healthy and happy.

What is the volume of the cylinder below? 9- 7 - 5 OA. 1757 units3 B. 2257 units3 C. 357 units3 D. 70n units3​

Answers

Answer:

175 pi ^3

Step-by-step explanation:

The volume of the cylinder is 175π cubic units or 175π units³ if the radius of the base r is 5 units and the height of the cylinder h is 7 units option (A) 175π units³ is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

Volume can be defined as a three-dimensional space enclosed by an object or thing.

As we know,

We can find the volume of the cylinder by using the given formula:

[tex]\rm V = \pi r^2 h[/tex]

The radius of the base r = 5 units

The height of the cylinder h = 7 units

[tex]\rm V = \pi (5)^2 (7)[/tex]

V = 25x7π

V = 175π cubic units

Or

V = 175π units³

Thus, the volume of the cylinder is 175π cubic units or 175π units³ if the radius of the base r is 5 units and the height of the cylinder h is 7 units option (A) 175π units³ is correct.

Learn more about the cylinder here:

brainly.com/question/3216899

#SPJ5


14 In a book, 98% of the pages contain text, diagrams on both. If 88% of the pages
contain text and 32% contain diagrams, what percentage contain

a.neither text nor diagrams
b. only diagrams
c.only text
d.both text and diagrams?​

Answers

Answer:

2%

10%

66%

22%

Step-by-step explanation:

For the first one we just need to find the compliment of the union (.98) which is .02

Union formula:

A∪B=A+B-A∩B

We will let T= text and D= diagram

we know that

.98=.88+.32-T∩D

Solve and find that T∩D= .22

Only diagram: .32-.22= .1

Only text: .88-.22= .66

Text and diagrams is the intersection we found earlier or .22

Please help







Thanks I really need help and appreciate it

Answers

Answer:

umm can you tell us the options then I can say what the answer is and I'll edit or put it in the comments

Step-by-step explanation:

have a good rest of your day tho :) ❤

Find the area of the regular nonagon

Answers

Answer:

267.3

Step-by-step explanation:

area of a regular polygon =

(perimeter * apothem)/2

perimeter: 9 * 6.6 = 59.4

area: 59.4 * 9 = 534.6

534.6/2 = 267.3

area = 267.3

Ilus
Translate algebraic words to symbols.
Half of R subtracted from y cubed
A. 1/2R - y3
B. y3 - R/2
C. R/2 - 3y
D. 3/y - R/2

Answers

Answer:

        [tex]\bold{B.\quad \ y^3-\dfrac R2}[/tex]

Step-by-step explanation:

"half of R" it is:   [tex]\dfrac R2[/tex]

"y cubed" it is:   [tex]y^3[/tex]

Therefore, half of R subtracted from y cubed is:  [tex]y^3-\dfrac R2[/tex]

SOMEONE PLEASEEEE HELPPPP

Answers

[tex]adjacnt {}^{2} = opposite {}^{2} + hypotenuse {}^{2} \\ adjacent {}^{2} = 8 {}^{2} + 12 {}^{2} \\ adj {}^{2} = 64 + 144 \\ adj {}^{2} = 208 \\ adjacent = \sqrt{208} \\ adjacent = 4 \sqrt{13} [/tex]

Solve by using substitution.

=3−8

=−4

Answers

Answer:

I'm going to assume that you meant y=3x-8 and y=-4

This means that you would substitute -4 into the spot of y which gives you -4=3x-8. Once solved you would receive x=4/3.

Hope I helped have a nice day :)

PLS HELP !!!!!!!
i rlly need this T__T

Answers

Answer:

(3,4) -> (8,3)

(-2,4) -> (3,3)

(-2,5) -> (3,4)

The triangle is translated 5 units to the right and 1 unit down.

Step-by-step explanation:

Add 5 to each x on the (x,y) coordinate and subtract 1 from each y.

The perimeter of a rectangle is 48cm. its length is 4 cm. what is its width?

Answers

Answer:

P = 48

4 + 4(two given lengths) = 8

48(perimeter) - 8(length of two given lengths) = 40(length of two unknown sides)

40(length of two unknown lengths) divided by 2(two missing sides) = 20 cm

math question 30 points if you answer

Answers

Answer:

Step-by-step explanation:

h(t) = - 16t² + 22t + 6

h = 13.5625 ft

slove the system of substitution


y=x-8

y=2x-4

Answers

Answer:

x + y = 4 ,  x − y = 2

x + 2 y = 4 ,  x − y = − 3

x 2 − y = 2 ,  2 x − y = − 1

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

x-8=2x-4

+8        +8

---------------

x=2x+4

-2   -2

-----------

-x=4

-1    -1

----------

x=-4

for the bud to see... and one person to get poi.nts XD
so addison got banned yesterday but got her account back today and then drake got banned today

Answers

Answer:

WHAT!? THEY BOTH GOT BANNED?! HOW

I need this answered quick alot of points on the line here 2 pictures down below

Answers

Answer:

1.x=10 and x=−2.

2. the answer is x=7,-1

3.=3, =1

Step-by-step explanation:

1.Since it is a quadratic equation, then it has, at the most, two solutions because the square root of the variable has a positive and negative value. Thus, the solutions to the given equation are x=10 and x=−2.

2.Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula. the you would simplify the equation.and the last thing that is to separate the equation.

3.-(-4)+/-sqrt(-4)^2-4^1^3/2*1,x=4+/-sqrt(-4)^2-4*1*3,x=4+/3sqrt16-4*1*3,x=4+/-sqrt16-12,/2*1,x=4+/-sqrt4/2*1,x=4+/-2/2*1,x=4+/2/2,x=4+2/2,x=4-2/2

Find the solution of the system of equations.

-2x-6y=8
-6x-6y=0

Answers

x=-7
y=7

First solve for x in -2x-6y=8, and you will get -7. Then plug -7 into x for -6x-6y=0 and you will get 7.

Obtuse can have right angles.
True or False

Answers

False. Obtuse is always greater than 90°.

Answer:

False

Obtuse triangles can't have right angles

Find the distance between the points (-4,9) and (5, -3).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units
Submit

Answers

Answer:

15 units

Step-by-step explanation:

The formula of a distance between two points:

[tex]A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}}[/tex]

We have:

[tex]A(-4;\ 9);\ B(5;\ -3)\\\\|AB|=\sqrt{(5-(-4))^2+(-3-9)^2}=\sqrt{9^2+(-12)^2}=\sqrt{81+144}\\\\=\sqrt{225}=15[/tex]

solve for x. enter you answer below as a fraction ​

Answers

Answer:

x=9/80

Step-by-step explanation:

Answer:

9/80

Step-by-step explanation:

[tex]1)\ x + \frac{9}{20} = \frac{9}{16}[/tex]

[tex]2)\ x = \frac{9}{16} - \frac{9}{20}[/tex]

[tex]3)\ x = \frac{9}{16} - \frac{9}{20}[/tex]

[tex]4)\ x = \frac{45}{80} - \frac{36}{80}[/tex]

[tex]5)\ x = \frac{9}{80}[/tex]

The scale shown is not balanced.

Drag base ten blocks to the box to show the amount that x needs to be to balance the scale.

HELP PLEASEEEEE

Answers

Answer:

1 (100block)

5 (10block)

3 (1block)

Step-by-step explanation:

221-68=153

1x100=100

5x10=50

3x1=3

The amount that x = 53 needs to be to balance the scale.

What is an equation?

The term "equation" refers to a pair of algebraic expressions with the same value and the sign "=" in between.

We have an equation,

221 = x + 68

x = 221 - 68

x = 153

In 153,

1 is in place of hundred 100, 5 is in the place of 10 so, 50.

Therefore, x = 53 is the amount that needs to be to balance the scale.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ2

Giving brainlist to whoever answers

Answers

Answer:

c

Step-by-step explanation:

Answer:

your answer is option number C 9mm

which of the following are solutions to the equation below ​

Answers

Answer:

B & F

Step-by-step explanation:

(±√14 - 4)/3 =>

(√14 - 4)/3 or (-√14-4)/3

A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.

Answers

Answer:

look at the picture i sent......

Jordan scored 19 points during a basketball game. She made a total of 9 baskets.

If Jordan made only one-point free throws and three-point baskets, how many of each did she make?

A
1 one-point basket; 6 three-point baskets
B
4 one-point baskets; 5 three-point baskets
C
5 one-point baskets; 4 three-point baskets
D
6 one-point baskets; 3 three-point baskets

Answers

Answer:

B) 4 one-point baskets: 5 three-point baskets

Step-by-step explanation:

(4 x 1) + (5 x 3) = 19

Answer:

B

Step-by-step explanation:

5x3=15

4x1=4

15+4=19

PLUS a total of 9 baskets.

Therefore, your answer is B

A trader made a profit of 24% by selling an article for #372 how much should he have sold it to make a profit of 48%

Answers

Answer: #444

Step-by-step explanation:

First find the original selling price of the article.

When sold for #372 the profit was 24%. Assume the original price is x.

372 = x + 24% * x

372 = 1.24x

x = 372 / 1.24

= #300

If he wanted to make a profit of 48% he should have sold for:

= Original price + (original price * 48%)

= 300 + (300 * 48%)

= #444

Can someone help me with this

Answers

Answer:

C

Step-by-step explanation:

1. Absolute values are in the shape of a V, so the answer is automatically C.

2. If you did not know that, you can see that the graph is a function because it passes the vertical line test. This rules out option A. By looking at the graph, you can see it passes the x-axis twice, meaning that it has 2 x-intercepts. This rules out option B. X-intercepts always have a y-coordinate of 0, so we can rule out option D. The only option left after this is C.

The answer is going to be C :)

Help meeeeeeeeeeeeee

Answers

Answer:

36.87( round if needed(

Step-by-step explanation:

we know a side adjacent to the angle and opposite of the angle so we apply tangent function

[tex] \tan(x) = \frac{3}{4} [/tex]

[tex] \tan {}^{ - 1} ( \frac{3}{4} ) = 36.87[/tex]

Round if neededd

beau completed 2/5 of his science project on Friday and 1/3of the project on Saturday what fractional part of his project did she complete during these two days​

Answers

Answer:

beau completed 2/5 of his science project on Friday

beau completed 1/3 of his science project on Friday

Now

he completed during these two days=1/3+2/5=11/15 part of his project

The product of (7x+2) and 20-3x/4

Please help me on this problem

Answers

Answer:

1. (7x+2)

2. 2 - 3x/4

Other Questions
What is an example of a regular polygon? What impact did the influence of the Church have on the Renaissance? Will give brainliestAnd please, no linksIs what I highlighted correct? Why might you want to annotate your notes as you record information from sources?A. to provide additional information about the process you used to find sources.B. to begin forming your own ideas about the topic, based on what information you find.C. to teach yourself some new and interesting words used in some of your sources.D. to provide mostly accurate citation information for sources used in your project. Consider the system consisting of the box and the spring, but not Earth. How does the energy of the system when the spring is fully compressed compare to the energy of the system at the moment immediately before the box hits the ground? Justify your answer. How to find the central angle The more variation there is within genes, the better that organism's chances are for survival. This is because gene variations can cause an organism to develop new or different traits. Such variations come about either by sexual reproduction (and the mixing of two parents' genes) or by mutation.Mutations, remember, are rare and random changes in one of an organism's genes. Normally, there may be only one mutation in a thousand, or even a million, cell divisions. But with millions of cells in a complex organism or millions of similar one-celled organisms in a particular environment, such accidental changes are always possible. Since mutations are completely random, most mutated cells simply die. But sometimes a mutated cell survives and even benefits the organism. And if a mutation occurs in a sex cell, it can be passed on to the organism's offspring.An organism with a mutated cellAmost likely wont pass its mutation down to offspring.Bis more likely to survive than an organism without that mutation.Cdecreases the amount of genetic variation.Dlikely developed in order to help a species survive and grow. Simplify. 24 7/12 - 4 3/820 4/420 5/2420 4/965/24 this is year 2050 and you have been asked to write about the coronavirus pandemic for a meseum.What story would it be WHAT WILL BE A GOOD TITLE FOR IT In "Ellis Island" the author mentions medical inspections. Which central idea does this detail best support? find the axis of symmetry of the parabola Help, please!Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.Online Content: Site 1How was China reunited under the Sui dynasty? (Site 1) I need help ill give brainliest NO LINKS Our highways, espressways, and streets become increasingly congested every day as our population increases and more new drivers enter the road. Distracted driving isn't justa problem for teenagers; it's also a problem for adults. However, today's problems are not the same as they once were. We now have laws prohibiting texting while driving, as well as statistics on the number of people who die as a result of texting while driving. Because of texting and driving, the number of people killed in car accidents has risen. People are nowengrossed in their modern gadgets such as phones, iPods, and other similar devices, rather than wasting time trying to locate a station on the radio. Texting while driving continues to be one of today's most serious distractions for drivers.Florida has enacted legislationprohibiting it, but the penalty is just $30. Although it was formerly a secondary offense and is now a $30 fine, I believe it should be increased. A teens's license can indeed be strippedaway if they are found testing and driving.If an adult is caught, I believe their driver'slicense should be revoked. If all you have to do is pay a thirty-dollar fee then that won't get anyone to stop distracted drivers. We need to do something to grab their attention more than their phones do In the year 2013, the state of Florida enacted legislation prohibiting texting while driving. Even though the legislation was passed, it stipulates that in order to be prosecuted for this crime and fined the $30, you must commit two crimes, which has sparked concerns among citizens about the law's effectiveness.Some residents were concerned that otherresidents (mostly teens and other young and reckless drivers) would be resistant to the new legislation. Furthermore, some residents may live in fear of someone violating the law, resulting in an accident, and innocent people dying as a result of a simple text message thatshould have been delayed. The issue is that some residents want to establish a more updated and stricter regulation, which is understandable, but Florida is currently doing the best itcan to help discourage texting and driving Forty-two states, which include Florida, have declared texting while driving illegal. These states, have taken steps to improve the way they are by making the amount of injuries less than they were in the state. As a result, this bright sunshine state will be able to provide highways with drivers who will not damage their surroundings. It's believed that people want a much better rule, but Florida is still working to make this wish a reality for residents. The feelings of the citizens about making this rule, or even a more powerful law, are reciprocal or much stronger.Can someone write at lest a 5 sentence conclusion for the writing above?? Needed ASAP for FLVS. Multiply the binomials:(3x + 4)(5x-2)A. 15x^2 + 20x-8B. 15x^2 + 14x + 8C. 15x^2- 14x-8D. 15x^2+ 14X-8 Which of the following are alternate exterior angles? Simplify -4(2x - 3) + 7 x 1. An element in a similar period to carbon would beA chlorineB. hydrogenC. fluorineD. magnesium What are two step equations that equal 17? PRATIQUONS- POSSESSION DE/D1) Alexandre's father___________Le pre d'Alexandre.2) Alexandre's sister_____3) Alexandre's aunt______4) Alexandre's grandmother_______5) Alexandre's girl cousin______6) Alexandre's uncle______7) Alexandre's brother______8) Alexandre's dog______9) Alexandre's cat______10) Alexandre's fish______