Mathematics High School

What is the exact value of cos 30° ?

Answers

Answer 1

Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.

Side AB will be the hypotenuse.

cos 60° = AC / AB -------[ cos 60° = 1/2]

So, AB = 2 AC -------------------------------(1)

Apply Pythagorean Theorem to find BC

AB² = BC² + AC²

4 AC² = BC² + AC²

So, BC = √3 AC ------------------------(2)

Now, we shall find the value of cos 30°

cos 30° = CB / AB

or, = √3 AC / 2 AC -------using equations (1) and (2)

So, cos 30° = √3 / 2

Hence, the exact value of

Since ∠A = 2∠B. So, cos 30° will be √3 / 2

Answer 2

The answer is √3 / 2

Related Questions

40 POINTS!

Find the exact value by using a half-angle identity.

⬇️⬇️⬇️

Answers

[tex]\cos\dfrac{5\pi}{12}=\cos\left(\dfrac{6\pi}{12}-\dfrac{\pi}{12}\right)=\cos\left(\dfrac{\pi}{2}-\dfrac{\pi}{12}\right)=(*)[/tex]

[tex]Use: \cos(\alpha-\beta)=\cos\alpha \cos\beta+\sin\alpha \cos\beta[/tex]

[tex](*)=\cos\dfrac{\pi}{2} \cos\dfrac{\pi}{12}+\sin\dfrac{\pi}{2} \sin\dfrac{\pi}{12}\\\\=0\cdot\cos\dfrac{\pi}{12}+1\cdot\sin\dfrac{\pi}{12}=\sin\dfrac{\pi}{12}[/tex]

[tex]\dfrac{\pi}{12}=\dfrac{\dfrac{\pi}{6}}{2}[/tex]

[tex]The\ half-angle\ identity\ \sin^2\dfrac{\alpha}{2}=\dfrac{1}{2}\left(1-\cos\alpha\right)[/tex]

[tex]Using\ the\ above\ formulas,\ we\ get:\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\cos\dfrac{\pi}{6}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\dfrac{\sqrt3}{2}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}-\dfrac{\sqrt3}{4}[/tex]

[tex]Since\ 0 \ \textless \ \dfrac{\pi}{12} \ \textless \ \pi,\ then\ \sin\dfrac{\pi}{12}\ is\ a\ positive\ number.\\\\ Therefore,\ we\ have:\\\\\sin\dfrac{\pi}{12}=\sqrt{\dfrac{1}{2}-\dfrac{\sqrt3}{4}}=\sqrt{\dfrac{2-\sqrt3}{4}}=\dfrac{\sqrt{2-\sqrt3}}{2}[/tex]

[tex]Answer:\ \boxed{\cos\dfrac{5\pi}{12}=\dfrac{\sqrt{2-\sqrt3}}{2}}[/tex]

I agree with him because it's correct and makes sense!

Jeff drinks 2/3 of a glass of juice. Write
a fraction equivalent to 2/3

Answers

A fraction that means the same as 2/3 is 4/6.

To find this, you can simply multiple both the numerator and denominator (top and bottom) by any number as long as it's the same number for both top and bottom.
In this case, we used 2 as the number, and multipled it to the top and bottom of 2/3, to get 4/6.

I hope this helps!

The length of a rectangle is twice the width. the area is 256 squared. find the length and the width.

Answers

The solution is quite simple.
First, draw a rectangle. Label two opposite sides as "w", representing the width. Label the other two sides as "2w", since the length is twice the width.
Next, write an equation. In this case, the equation would be 256=2w*w.
Simplify the equation to 2w^2=256. Divide both sides by two to get w^2=128. The width would be the square root of 128. The length would be twice that, so it would be the square root of 256. That would be 16, so the length is 16.

Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.

Answers

To solve this problem you must apply the proccedure showb below:

1. You have the following equation:

2x^2+9y^2=18

2. Dividing the equation by 18, you have:

(x^2/9)+(y^2/2)=1

3. The center is:

[(x-0)^2/9]3^2[(y-0)^2/√2]=1

(h,k)=(0,0)

The center is (0,0)

4. The vertices are:

a^2=9
a=3

Vertices: (-3,0) and (3,0)

5. The foci is:

c^2=a^2-b^2
c=√7

The foci is: (-√7,0) and (√7,0)

A restaurant offers 88 appetizers and 99 main courses. in how many ways can a person order a two-course meal

Answers

Number of ways = 88 x 99 = 8712

Answer: 8712

Consider the equation . how many different solutions does this equation have if all the variables must be positive integers? enter the exact numeric answer.

Answers

What is the equation?

A. 0

B. 1

C. 2

D. 3

Answers

-19 to -15 would be a positive 4 difference

19 to 15 = 4 this would be a -4 difference

3 to 7 is a positive 4 difference

-3 to 7 is a difference of 10

so there is 1 with a -4 difference
answer is B.

The diameter of a circle has endpoints (-3, 2) and (3, -2) which is closest to the length of the diameter of the circle?

Answers

D=√((x2-x1)²+(y2-y1)²)

D=√((x2-x1)²+(y2-y1)²) = √(3-(-3))²+(-2-2)²) = √(6² + 4²)=√(36+16)=√52
D=2√13≈7.21

[tex]\text{Diameter = } \sqrt{(2+ 2)^2+ (-3-3)^2 } = \sqrt{16 + 36} = \sqrt{52} = 7.21 \text{ units}[/tex]

Answer: Diameter = 7.21 units

What is the sun made of (by mass)?
a. 50 percent hydrogen, 25 percent helium, 25 percent other elements
b. 70 percent hydrogen, 28 percent helium, 2 percent other elements
c. 90 percent dark matter, 10 percent ordinary matter
d. 100 percent hydrogen and helium?

Answers

B. 70 percent hydrogen, 28 percent helium, 2 percent other elements

What is the volume of the cone to the nearest tenth?

1,244.1 m^3

829.4 m^3

552.9 m^3

1,520.5 m^3

Answers

The formula for the volume of a cone is
V = (1/3)π*r^2*h
Of course, the radius is half the diameter, so is 11 m. Substituting the given values, you have
V = (1/3)π(11 m)^2*(12 m)
V = 484π m^3
V ≈ 1520.5 m^3

The volume of the cone to the nearest tenth is ...
1520.5 m³

sigma notation 2+ (-8)+32+(-128)+...

Answers

here u go hope this helps

The weight of a mandarin orange is about 6 ounces. A basket that weighs 4 ounces will hold m mandarin oranges, the total weight is 70 ounces. Which equation represents the basket of oranges?1. 4 + 6m = 70 2. 6 + 4m = 70 3. 70 + 4m = 6 4.70 + 6m = 4

Answers

The answer to this is the first option; 4 + 6m=70.

Answer:

A is the answer on Edgen.

Step-by-step explanation:

4 + 6m = 70

6 + 4m = 70

70 + 4m = 6

70 + 6m = 4

Whst is the remainder when f(x)=x^3+3x^2-10x-4 is diveded by x-3

Answers

The polynomial remainder theorem allows us to calculate the remainder when a polynomial is divided by a linear polynomial:
The remainder of f(x) divided by (x-k) equals f(k).

Thus
f(x)=x^3+3x^2-10x-4 divided by x-3
gives a remainder of
f(3)=27+3(9)-10(3)-4=27+27-30-4=20
Therefore the remainder required is 20.

The remainder when the polynomial [tex]f(x)=x^3+3x^2-10x-4[/tex] is divided by x-3 is found using the Remainder Theorem and is 20.

The remainder when a polynomial f(x) is divided by a linear divisor such as x - 3 can be found using the Remainder Theorem, which states that the remainder is simply f(3). To find the remainder for [tex]f(x)=x^3+3x^2-10x-4[/tex], we substitute x = 3 into the polynomial.

Calculate f(3):

[tex]f(3) = (3)^3 + 3*(3)^2 - 10*(3) - 4[/tex]

f(3) = 27 + 27 - 30 - 4

f(3) = 54 - 34

f(3) = 20

Therefore, the remainder when f(x) is divided by x - 3 is 20.

Mary has 7 1/4 yard of fabric. she cuts off 3/4 foot fabric to make the edge even. Mary wants to end up with 3 pieces of fabric that are the same size. how long will each piece be?

Answers

7 1/4 - 3/4 = 6 5/4 - 3/4 = 6 2/4

6 2/4 ÷ 3 = 26/4 ÷ 3 = 26/4 x 1/3 = 2 1/6

Answer: 2 1/6 yd

Final answer:

Mary has 7 1/4 yards of fabric, and after cutting off 3/4 foot (which is 1/4 yard), she is left with 7 yards. When she divides this equally into 3 pieces, each piece will be 2 1/3 yards long.

Explanation:

Mary has 7 1/4 yards of fabric. To convert the fabric she cuts off, which is 3/4 foot, to yards, we use the fact that 1 yard = 3 feet. Thus, 3/4 foot is 1/4 yard. After cutting off 1/4 yard from her fabric, she is left with 7 yards (7 1/4 yards - 1/4 yard). Mary wants to divide this into 3 equal pieces. To find the length of each piece, we divide 7 yards by 3, which is 2 1/3 yards for each piece.

A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?

Answers

45 rpm=2π rad*45/60=1.5π rad/sec
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft

A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

Answers

Trip upstream took 90v−390v−3 hours and trip downstream took 90v+390v+3 hours. Also given that the difference in times was 1212 hours --> 90v−3−90v+3=1290v−3−90v+3=12;

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

24 MIN LEFT anyone know the answer?

Answers

Because the two shapes are congruent to one another, we can assume all angles of ABEF to be the same as CBED. Create a formula that adds up to 360 degrees using the values given and equate it to 360 degrees. Then, solve algebraically.

A+B+E+F=360
A+152+82+98=360
Angle A=28 degrees

At the zoo on Monday, 65 percent of the people in attendance were children. If 520 children were in attendance, how many people in total were visiting the zoo on Monday?

Answers

800 people because when you try to find the number of people, x, you do cross multiply. So it will be 520/x = 65/100, next you multiply 520 by 100, then divide that by 65 to get 800 people

Answer:

800+

Step-by-step explanation:

Find the quotient of -36x^3-6x^2+12x/-6x

Answers

Answer:
6x² + x - 2

Explanation:
To find the quotient of a polynomial expression divided by a monomial, divide each term by the monomial.

[tex]\frac{-36x^3-6x^2 + 12x}{-6x}[/tex] becomes [tex]\frac{-36x^3}{-6x} + \frac{(-6x^2)}{(-6x)} + \frac{12x}{(-6x)}[/tex]

-36x³ / (-6x) = 6x²

(-6x²) / (-6x) = 1x = x

12x / -6x = -2

Place each of these terms together into an polynomial expression once more and the quotient is: 6x² + x - 2

A bage contains 5 blue marbles, 3 red marbles, and 2 yellow marbles. You select a marble at radom. What is p(yellow)

Answers

Total marbles = 5 + 3 + 2 = 10
Total yellow marbles = 2
P(yellow) = 2/10 = 1/5

Answer: 1/5

The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work.

Answers

we know that
circumference=2*pi*r-------> r=circumference/(2*pi)
circumference=30 in
r=circumference/(2*pi)------> 30/(2*pi)-----> 4.7746 in
the radius of a standard basketball is 4.77 in

the distance between the ball and the rim is equal to
radius of a basketball rim minus radius of a a standard basketball
radius of a basketball rim =18/2------> 9 in
radius of a a standard basketball=4.77 in

the distance between the ball and the rim=[9-4.77]------> 4.23 in

the answer is
4.23 in

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above:

- The diameter of a basketball rim is 18 inches.
- A standard basketball has a circumference of 30 inches.

2. Therefore, the diameter of the standard basketball is:

D=30 inches/π
D=9.54 inches

3. Therefore you have:

(18 inches-9.54 inches)=8.45 inches on both sides

4. Then, the distance the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim, is:

d=8.45 inches/2
d=4.22 inches

The answer is: 4.22 inches

sam had four test last month his scores were 81 94 83 and 91 what is the median of his scores

Answers

put them in order of least to greatest and then cross out them till you get the middle number. 81,83,91,94. answer is 91.

Final answer:

The median of Sam's test scores (81, 83, 91, 94) is 87, calculated by averaging the two middle numbers after arranging the scores in ascending order.

Explanation:

To find the median of Sam's test scores, we first list the scores in numerical order: 81, 83, 91, 94. Since there are an even number of scores, the median will be the average of the two middle numbers, which are 83 and 91. To find the median, you add those two middle scores and divide by 2: (83 + 91) / 2 = 174 / 2 = 87. Therefore, the median of Sam's scores is 87.

Calculating the median of a set of values involves organizing them in ascending order, as done with Sam's test scores. In cases where there is an even number of values, the median is determined by averaging the two middle numbers. This method ensures a representative central value for the dataset, providing insight into the typical test performance. In Sam's case, with test scores 81, 83, 91, and 94, the median is computed as 87, offering a balanced perspective on his overall performance.

in a certain area of Brazil, deforestation is currently the most critical Socio economic problem. The area of a certain rain forest is currently 1156.25 square miles. after every year, the area of this rain force decreases by 2% which of the following statements is correct
A- deforestation problem is an example of exponential growth
B- The growth or decay rate for the area of the rainforest is 0.2
C- The function of equals 1156.25(1 -0.02 )^t
D- in less than a century the rain forest will be completely wiped out
E- in about 35 years the area of the rain forest will be cut by more than half
F-The domain of the function that model the deforestation problem above is 0<_t<_100 (less than or equal to <_)

Answers

i need help with this answer!!!!!

A is INCORRECT because here we have degrowth and growth

B is INCORRECT because the decay factor is 2% or 0.02 , not 0.2

C is CORRECT, the function is which is used to calculated the area of rainforest at time t is given by 1156.25(1 -0.02 )^t

D is INCORRECT, if we plug in t=100 in the above equation , we get = 1156*(1-0.02)^100 = 153 square miles of forest. So it will not be wiped out

E is CORRECT, if we plug in t =35, we get = 1156*(1-0.02)^35 = 570 square miles. So more than half will be cut in 35 years

F is INCORRECT becuase domain goes beyond 100 years as shown by option D

So, correct options are C and E

How to solve x in a trapezoid

Answers

For Volume is V=(base1 + base2)h and then divide by two

How many ways could the students Amy, Ben, and Lorenzo, come in 1st, 2nd, and 3rd place?

Answers

A1, B2, L3
A1, L2, B3
L1, B2, A3
L1, A2, B3
B1, A2, L3
B1, L2, A3

[tex] 3!=6 [/tex]

..........

a catering company needs to know how much roast beef to slice for sandwiches for an event.They are making 30 club sandwich, which requires 1/8lb of roast beef each. They are also making 20 french dip sandwiches, which require 1/5lb each. How many pounds of roast beef should they slice in total?

Answers

1/8(30)+1/5(20)= 31/4 = 7.75
You should slice 7 and 3/4 lbs of roast beef

The would need 7 3/4 pounds (8 if you round up) of roast beef.

To find this you'd multiply 30/1 (30 as a fraction) by 1/8. To do so, you multiply straight across which gives you 30/8 or 3 3/4 when simplified. You repeat this process for the next two numbers too (20/1*1/5 = 20/5. Simplified it equals 4). Finally you add 4 and 3 3/4 together to get your answer of 7 3/4. Round up to 8 if needed.

I hope this helps!

One circle has a circumference half as large as that of a second circle what ratio compares the diameter of the first circle

Answers

The diameter of the first circle is 1/2 the diameter of the second circle.

These are linear measurements. This means that the ratio of the circumference, distance around, of two circles is the same as the ratio of their diameters, or distance across.

The diameter of first circle is half of the second one.

What is a circle?

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre. The centre of the circle does not lie on it. The tangents drawn from the same point outside a circle are equal in length.

The given problem can be solved as follows,

The circumference of a circle is given as C = πd where d is the diameter of the circle.

Suppose, the circumference and diameters for both the circles are C₁, d₁ and C₂,d₂ respectively.

Now, the expression for circumference can be written as,

C₁ = πd₁

And, C₂ = πd₂

As per the question C₁ = 1/2C₂, then the following equations can be written as,

πd₁ = 1/2πd₂

⇒ d₁ = 1/2d₂

Hence, the diameters of the two circles are also in the same ratio.

To know more about circle click on,

brainly.com/question/11833983

#SPJ5

A right triangle has legs that measure 7cm and 3cm. What is the length of the Hypotenuse?

Answers

7² + 3² = c²
49 + 9 = c²
58 = c²
c = √58

Answer:

square root of 58

Step-by-step explanation:

If its wrong e2020 says its right

Tabby Soft believes that it will need new equipment in 5 years. The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000? a. $22,558.87 c. $22,390.94 b. $23,948.47 d. $19,346.44

Answers

The following compounding formula applies:
A = P (1+R/2)^2t

Where, A = Amount after 5 years = $26,000; P = Amount invested now; R = Annual rate of earning = 6% = 0.06; t = time = 5 years.

Substituting;
26000 = P(1+0.06/2)^2*5 = P(1.3439)

Therefore, P = 26000/1.3439 = $19,346.44

The correct answer is d.

Answer:

Step-by-step explanation just put D

Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth. 27,16,8,5,19,14,22,31,13,5,23,16,8 Mean: Median: Interquartile range:

Answers

mean: 15.92
Median: 26
interquartile range: 14-16

The mean of the data set is 15.9, the median is 16, and the interquartile range is 14.5 after rounding to the nearest tenth.

To find the mean, median, and interquartile range for the data set 27, 16, 8, 5, 19, 14, 22, 31, 13, 5, 23, 16, 8, we need to follow these steps:

Organize the data in ascending order: 5, 5, 8, 8, 13, 14, 16, 16, 19, 22, 23, 27, 31.

Calculate the mean by adding all numbers and divide by the total count. Mean: (5+5+8+8+13+14+16+16+19+22+23+27+31)/13 = 207/13 ≈ 15.9.

Find the median which is the middle number. Since there are 13 values, the median is the 7th number: Median: 16.

For the first quartile (Q1) and third quartile (Q3), divide the list into two halves. The Q1 is the median of the first half, and Q3 is the median of the second half. Q1: Median of 5, 5, 8, 8, 13, 14 ≈ 8.5; Q3: Median of 19, 22, 23, 27, 31 ≈ 23.

Calculate the interquartile range (IQR) by subtracting Q1 from Q3. Interquartile range: IQR = Q3 - Q1 = 23 - 8.5 = 14.5.

The mean is approximately 15.9, the median is 16, and the interquartile range is 14.5.

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What is the name of the poetic division used in "The Divine Comedy"?A. LibrasB. CantosC. ChaptersD. Pages Which state looks like it has an area shaped like the heel of a boot? PLEASE help!!! what is 4y + 12x= 24 in y intercept form???? What is one of the most effective ways to stop invasive animal species from entering the Great Lakes ecosystem? Q9 Q9.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Ccording to freud, if a child's needs are not met or are overindulged at one particular psychosexual stage, the child may become _____.a. psychoticb. fixatedc. regressedd. immoral A wave has a wavelength of 12 mm and a frequency of 6 hertz. What is its speed? PLEASE CHECK it...Write an invitation to your Christmas party you are having at your house. Use vocabulary studied in this module; explain what is going to happen at the party. You may copy and paste the accented characters from this list if needed: CAN YOU PLEASE CHECK THIS AND MAKE SURE IT'S FEMININE. PLEASEBonjour! Je vous invite la soire que j'organise chez moi le 25 decembre pour mange. Nous allons manger de la nourriture dlicieuse. Nous jouerons des jeux entre amis et en famille. J'espre te voir l-bas. PLEASE HELP !!2.A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft. (a)Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.(b)Would the density of the water change if the aquarium was only half full? Explain. What is the cold war? what factors caused the us and the ussr to become antagonists? (e.g. think about what happens at the end of world war ii, what differing views do they have?) give at least 3 examples. how did kennan explain soviet behavior? how did truman respond to kennan's explanation? define containment and its significance to the cold war. what was the marshall plan? what do you believe were the 2 most defining "events" or moments of the cold war? explain what each event was, and then your justification for why it is a defining moment of the cold war? An interesting result of bigelow's (1977) study examining friendships is that children rarely mentioned _______________ as an important characteristic in best friends. A car moved a total distance of 120 km in 90 minutes. What was the speed of the car? The majority of democracies in the western hemisphere do not recognize the death penalty. the united states, however, still does. in fact, _____ states have the death penalty. How does the atmospheric pressure at altitudes below sea level compare What was Theodore Roosevelt's famous saying Speak softly and carry a big stick a reference to? A.American domestic policy B.American foreign policy C.American labor relations D.American journalism Convert to standard 1.312x10^2 In response to the thirteenth, fourteenth, and fifteenth amendments, southern states quickly passed _____ to limit the civil rights of african americans and developed labor regulations that resembled slavery. Which of the following statements regarding nonspecific immune responses is correct? A. A nonspecific immune response is the body's first line of defense against invaders. B. The influenza vaccine provides immunity by triggering nonspecific immune responses. C. Nonspecific immune responses involve the use of B and T lymphocytes. D. all of these A business letter's tone should be A.casual. B.impersonal. D.indifferent. Anciently the one performing the sacrifice would place the animal on the altar with its head to his right. he would then declare his authority by raising his right arm to the square