Mathematics High School

Find the exact value for cos π 12 applying sum and difference formulas involving π 3 and π 4 .

Answers

Answer 1

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split into π/3−π/4.

cos(π/3−π/4)

Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/3) is 12, so:

(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/4) is √22.

(12)⋅(√22)+sin(π/3)⋅sin(π/4)

The exact value of sin(π/3) is √32.

(12)⋅(√22)+(√32)⋅sin(π/4)

The exact value of sin(π/4) is √22.

(12)⋅(√22)+(√32)⋅(√22)

Simplify each term:

√24+√64

Combine the numerators over the common denominator.

(√2+√6) / 4

Related Questions

Give the slope intercept form of the equation of the line that is perpendicular to 5x-3y=8

Answers

hello : 
let the slope : a    and ; b the slope of the line : 5x - 3y = 8
the line that is perpendicular to 5x-3y=8  so : a×b = - 1 
but : 
5x - 3y = 8...      y = (5/3)x - 8/3  when : b = 5/3
 the slope intercept form of the equation of the line that is perpendicular
 to 5x-3y=8 is : y = (5/3)x +c 

Solve for x
7x-0.15=2x+0.6
Explain

Answers

if you subtract 2x from each side you get 5x-0.15=0.6 because the subtraction of 2x on the right of the equal sign cancels out. Then, if you add 0.15 to both sides you will get 5x=0.75. Finally, if you divide both sides by 5 you get x = 0.15.

Harry's school is selling t-shirts to raise money for the archery team. The school will receive 35% of the total sales which can be modeled by the equation y = 0.35x, where x represents the total number of sales. What is the meaning of the x-intercept in the equation?

Answers

Answer: The x-intercept represents the number of sales when no money has been raised.

Answer:

X-intercept states that the graph crosses the x-axis.

Substitute y = 0 and solve for x.

As per the statement:

Harry's school is selling t-shirts to raise money for the archery team.

The school will receive 35% of the total sales which can be modeled by the equation:

y = 0.35x

where, x represents the total number of sales and y represents the total cost of sale.

By definition of x-intercept:

0 = 0.35x

⇒x = 0

Therefore, the x-intercept in the equation represents:

The number of sales when no money has been raised.

One half of a number is 8 less than the number itself

Answers

The question is a little vague but I believe the answer would be 16. 16 divided in half is 8. And that is 8 less than 16. < Not the answer for this question.

I didn't understand the question until Maria answered, she is completely right! Sorry for the misunderstanding.
1/2 of x is 2/3 of x minus 8

(1/2)x = (2/3)x -8

clear fraction by multiplying by 6

3x = 4x -48

x = 48

If 1 cm = 0.394 inches, how many inches are in 1 kilometer?

Answers

Since 1 km is 100,000 cm there are 39,400 inches in a kilometer

Answer: There are 39400 inches in 1 kilometers.

Step-by-step explanation:

Since we have given that

1 cm = 0.394 inches

As we know that

1 m = 100 cm

1 km = 1000 m

1000 m = 100×1000=100000 cm

1 km = 100000 cm

So, it becomes,

[tex]1\ km=0.394\times 100000\\\\1\ km=39400\ inches[/tex]

Hence, there are 39400 inches in 1 kilometers.

(01.02) kim earns $30 for babysitting on friday nights. she makes an average of $1.25 in tips per hour. write the function of kim's earnings, and solve for how much she would make after 3 hours. (1 point) y = 1.25x + 30; $33.75 y = 30x + 1.25; $43.75 y = 30x + 1.25; $91.25 y = 1.25x + 30; $31.25

Answers

y = 1.25x + 30 <== ur function

for 3 hrs.....x = 3
y = 1.25(3) + 30
y = 3.75 + 30
y = 33.75 <=== for 3 hrs

Janet Fog's uncle, Pete Moore, promised her a gift of $30,000 upon her graduation from law school or $1500 every quarter for the next four years. if the money could be invested at 12% compounded quarterly, which offer should Janet choose?

Answers

First calculate the future value of the annuity
The formula to find the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT quarterly payment 1500
R interest rate 0.12
K compounded quarterly 4
N time 4 years
Fv=1,500×(((1+0.12÷4)^(4×4)
−1)÷(0.12÷4))
=30,235.32

Now compare the amount of the annuity with amount of the gift
30,235.32−30,000=235.32
So as you can see the amount of the annuity is better than the amount of the gift by 235.32

Second offer is better

Hope it helps!

A certain roller coaster can accommodate 1600 riders per hour a digital sign states that there are 345 people in line if you get in line about how many minutes will it take you to get to the front of the line

Answers

Given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

Given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

Therefore, it will take you 12.94 minutes to get to the front of the line.

A student has to earn a total of at least 280 points on four tests in his math class to pass the class, and his total on the first three tests is 197 points. set up an inequality necessary to find the minimum number of points that he must earn on the fourth test to pass the class. then solve the inequality.

Answers

try this equation 280 - 197 = x

The difference of the squares of two positive consecutive even integers is 20 . find the integers. use the fact​ that, if x represents an even​ integer, then xplus 2 represents the next consecutive even integer.

Answers

If x is the first number, x+2 is the next consecutive even integer. The difference (subtraction) of their squares equals 20. Therefore:
(x+2)²-x²=20...expand this:
x²+4x+4-x²=20 
x²+4x+4-x²=20
4x+4=20
4x=16
x=4. Therefore the next consecutive even integer is x+2=6.
To check: 6²-4² must equal 20
36-16=20 check!

The positive even numbers are 4 and 6.

Equation

State of quality between two expressions consisting of variable and/or number.

Given

The difference of the squares of two positive consecutive even integers is 20.

To find

The number will be

How do find the numbers?

The difference of the squares of two positive consecutive even integers is 20.

Let x be the even number and positive consecutive even is (x+2)

Then according to the condition

[tex]\begin{aligned} (x+2)^{2} -x^{2} &=20\\x^{2} +4x+4-x^{2} &= 20\\4x &= 20-4\\4x &= 16\\x &= \dfrac{16}{4}\\x &= 4\end{aligned}[/tex]

Then the positive even numbers are 4 and 6.

More about the equation link is given below.

https://brainly.com/question/2263981

round 38562.7 to 1 significant figure

Answers

= 488000
(real number)

= 4.88 × 105
(scientific notation)

= 4.88e5 


maybe this will help ?
to round it to 1 significant figure there needs to be only 1 figure that is above 1 the rest must be zero so the answer is 40000

A 150° angle is an obtuse angle. What do you Notice about the statement below? What do you Wonder about the statement?

Answers

The statement is just a fact.

Solve each equation. Then check your solution. 3-a/7=-2

Answers

3-a/7=-2 (problem)
3-a=-14 ( multiply by 7 on both sides)
-a=-14 (subtract 3 from both sides)
a=14 (divide both sides by negative 1)
Answer: a=14

I need help with equation number 6

Answers

Combine like terms
-2x-4=-2x-4

Since the equations are the same, the answer is infinitely many solutions.

Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the _______________ formula.

Answers

That would be known as the midpoint formula
m = (x1 + x2)/2 , (y1 + y2)/2

How do I solve 28.8=18x

Answers

28.8 = 18x....divide both sides by 18, eliminating the 18 on the right side
28.8 / 18 = x
1.6 = x <==

Erin is 8 years younger than twice Paula’s age. The sum of their ages is 40. How old is Erin

Answers

You do the sum(40) subtracted by 8, the answer from that divided by 2 since Erin's two times younger.
40-8=32
32÷2=16
Then if you want to check it you do the opposite and get the same sum(40) so 16×2=32 and 32+8=40
Final answer:

To solve this problem, we set up two linear equations based on the given information and solved them simultaneously. We found that Erin's age is 24 years.

Explanation:

This problem is a classic example of a linear equation. We can set up two equations based on the information given:

Erin is 8 years younger than twice Paula’s age. This can be written as E = 2P - 8.The sum of their ages is 40. This can be written as E + P = 40.

Upon substituting the value of E (Erin's age) from the first equation into the second, we get: 2P - 8 + P = 40. Simplifying this gives P = 16. Substituting P = 16 into the first equation, we find E = 24. Therefore, Erin is 24 years old.

Learn more about Linear Equations here:

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How would I solve 1/5=125^x

Answers

Hi there,

This question is a bit weird lol, but anyway here is how to do it and the answer:

1/5 = 123² x
1/5 = 15625x
15625x = 1/5

Hence, X = 1/5

Hope this helps :)
This is a log equation. To solve

125^x = 1/5
x log 125 = log 1/5
x = log (1/5) /  log 125
[tex]x = -\frac{1}{3} [/tex]

To show that we are correct. Input -1/3 for x [tex]125^{-1/3}[/tex] with a calculator and it will = 1/5, meaning it is correct.

[tex]125^{-1/3} = \frac{1}{5}[/tex]

Is the relation a function? (3, 6) (10, 13) (11, 1) (13, 6)

Answers

Answer: yes this is a function

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

The reason why is because we don't have any repeated x values. Each input (x) leads to exactly one output (y). If you plotted all the points, then you would not be able to pass a single vertical line through more than one point. So this graph passes the vertical line test.

Yes, Given relation is a function.

Here,

Points are given as,

(3, 6) (10, 13) (11, 1) (13, 6)

What is a function?

A function is defined as a relation between a set of inputs having one output each.

Now,

The given relation is a function because we don't have any repeated x values. Each input (x) leads to exactly one output (y). if we plotted all the points, then we would not be able to pass a single vertical line through more than one point. Hence, this graph complies vertical line test.

So, Given relation is a function.

Learn more about the function visit:

https://brainly.in/question/48224689

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help me please geometry

Answers

If we translate the top figure (ABC) 2 units to the left and reflect over the x axis, then we end up with the bottom figure (A'B'C'). This proves the figures to be congruent. 

This is something to do with trial and error really. See attached.

You randomly select one card from a​ 52-card deck. find the probability of selecting a blackblack twotwo or a blackblack eighteight

Answers

Since there are 26 black cards (1/2 of 52) and 2 black twos (one for each suite, and there are 2 black/red suites), we can use the same logic to get that there are 2 black eights. 2+2=4, and since there are 52 cards, you have a 4/52 or 1/13 (we get this because 4 goes into 52 13 times) chance of getting a black 8 or 2.

If you live in Dallas, then you live in Texas, what is the contrpositive of this?

Answers

Thanks for your question!

If you live in Texas, you can live in Dallas.

Hope this helps!

Write the solution to the given inequality in interval notation

Answers

0<x<=6 

X is greater than 0 but less that or equal to 6.

(0,6]
The answer is (0, 6].

This means 0 is not included but 6 is included in the shaded region.

Toni can carry up to 23 lb in her backpack. Her lunch weighs 1 lb, her gym clothes weigh 2 lb, and her books (
b. weigh 4 lb each. How many books can she carry in her backpack? The inequality is . Toni can carry up to books in her backpack.

Answers

1 + 2 + 4b < = 23
3 + 4b < = 23
4b < = 23 - 3
4b < = 20
b < = 20/4
b < = 5....so she can carry, at the most, 5 books <===

help please! Note: Use ELIMINATION!!!

Answers

the answers are 24 and -2

Multiplying the second equation by 4/3 and adding it to the first, we get 36=9x and by dividing both sides by 9, we get x=4. Next, we can plug that into the second equation (it doesn't matter which equation) to get 3*4-3y=18=12-3y. Subtracting 12 from both sides, we get 6=-3y and by dividing both sides by -3 we get y=-2

Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all t-shirts are $10 each.He has $100 to spend and would like to purchase at least 2 pairs of shorts.
a) Write a system of linear inequalities to represent
this situation, then graph.
b)Using your graph, give two possible combinations
of shorts and Brandon can buy.

Answers

Let
x = the number of shorts bought
y =  the number of t-shirts bought

A pair of shorts costs $16 and a t-shirt costs $10. Brandom has $100 to spend.
Therefore
16x + 10y ≤ 100
This may be written as
y ≤ - 1.6x + 10                 (1)

Brandon wants at least 2 pairs of shorts. Therefore
x ≥ 2                               (2)

Graph the equations y = -1.6x + 10 and  x = 2.
The shaded region satisfies both inequalities.

Answer:
Two possible solutions are
(a) 3 pairs of shorts and 4 t-shirts,
(b) 4 pairs of shorts and 2 t-shirts.

Two possible solutions are (a) [tex]3[/tex] pairs of shorts and [tex]5[/tex] t-shirts

                                             (b) [tex]4[/tex] pairs of shorts and [tex]3[/tex] t-shirts.

[tex]x=the\; number\; of shorts\\y=the\; number\; of\ t-shirt\; bought[/tex]

So equation formed is

[tex]16x+10y\leq 100[/tex]

[tex]10y\leq 100-16x\\y\leq 10-1.6x[/tex]---Eq [tex]1[/tex]

Bradon wants at least [tex]2[/tex]  pair of shorts.Therefore

[tex]x\geq 2[/tex]--Eq [tex]2[/tex]

Now put,

[tex]x=3 \\y=10-1.6(3)\\y=10-4.8\\y=5\\[/tex]

Hence [tex]3[/tex] shorts and [tex]5[/tex] t-shirts

Now put,

[tex]x=4 \\y=10-1.6(4)\\y=10-6.4\\y=3\\[/tex]

Now graph the equation,

Learn more about inequalities here:

https://brainly.com/question/15137133?referrer=searchResults

How much is 8% of 1249? round the answer to the nearest hundredth

Answers

First of all you make the multiplier:
8/100 = 0.08

Then you multiply the number by the multiplier:
1249*0.08 = 99.92

Hope this helps! :)
It is 99.92. I'm sure that thats the answer.

A regular hexagon rotates counterclockwise around its center. It turns through angles greater than 0° and less or equal to 360°. At how many different angles of a hexagon map onto itself?

Answers

there are 6 sides to a hexagon

360/6 = 60 degrees

 so it will map onto itself at 60, 120, 180, 240, 300 & 360

 there are 6 different angles



Alexandra is two years older than brad. cecilia is three years younger than alexandra. all three ages added together gives a total of 37 years. how old is each student?

Answers

Let us say that:

x = age of brad

x + 2 = age of Alexandra

(x + 2) – 3 = age of Cecilia = x – 1

 

We are also given that:

x + x + 2 + x – 1 = 37


solving for x:

3x + 1 = 37

3x = 36

x = 12 = age of brad

x + 2 = 14 = age of Alexandra

x – 1 = 11 = age of cecilia

2,226 divided by 53 how do you solve this??

Answers

The answer is 42 becuase you are making 53 groups of 2226 you can also simply solve it by useing long division
2226 divided by 53 is equal to42

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