Prove that sin³A + sin³(60° + A) + sinº(240° + A) = -3/4sin3A
Answers
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A}[/tex]
Step 1Rewrite 240° as (180° + 60°):
[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]
Step 2As sin(180° + x) = -sin(x), we can rewrite sin³(180° + 60° + A) as:
[tex]\sin^3(180^{\circ}+60^{\circ}+ A)=-\sin^3(60^{\circ}+ A)[/tex]
Step 3Substitute this into the expression:
[tex]\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]
Step 4As the last two terms cancel each other, we have:
[tex]\sin^3A[/tex]
Hence proving that:
[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A[/tex]
As one calculation:
[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]
[tex]=\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]
[tex]=\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]
[tex]=\sin^3A[/tex]
[tex]\hrulefill[/tex]
[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A}[/tex]
Step 1Use the sine and cos double angle identities to rewrite sin(3x) in terms of sin(x):
[tex]\begin{aligned}\sin(3x)&=\sin(2x+x)\\&=\sin2 (x)\cos (x)+\sin (x)\cos2 (x)\\&=(2\sin (x)\cos (x))\cos (x)+\sin (x)(1-2\sin^2 (x))\\&=2\sin (x)\cos^2 (x)+\sin (x)-2\sin^3 (x)\\&=2\sin (x)(1-\sin^2 (x))+\sin (x)-2\sin^3 (x)\\&=2\sin (x)-2\sin^3 (x)+\sin (x)-2\sin^3 (x)\\&=3\sin (x)-4\sin^3 (x)\end{aligned}[/tex]
Rearrange to isolate sin³x:
[tex]\begin{aligned}\sin(3x)&=3\sin (x)-4\sin^3 (x)\\\\4\sin^3 (x)&=3\sin (x)-\sin (3x)\\\\\sin^3 (x)&=\dfrac{3\sin (x)-\sin (3x)}{4}\end{aligned}[/tex]
Step 2Use this expression to rewrite the terms in sin³A on the left side of the equation:
[tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]
[tex]=\dfrac{3\sin A-\sin3A}{4}+ \dfrac{3\sin (120^{\circ} + A)-\sin (3(120^{\circ} + A))}{4}+\dfrac{3\sin (240^{\circ}+ A)-\sin (3(240^{\circ}+ A))}{4}[/tex]
[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (360^{\circ} + 3A)+3\sin (240^{\circ}+ A)-\sin (720^{\circ}+ 3A)}{4}[/tex]
Step 3As sin(x ± 360°n) = sin(x), we can simplify:
[tex]\sin(360^{\circ}+3A) = \sin (3A)[/tex]
[tex]\sin(720^{\circ}+3A) = \sin (3A)[/tex]
Therefore:
[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (3A)+3\sin (240^{\circ}+ A)-\sin (3A)}{4}[/tex]
[tex]=\dfrac{3\sin A-3\sin3A+3\sin (120^{\circ} + A)+3\sin (240^{\circ}+ A)}{4}[/tex]
Factor out the 3 in the numerator:
[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)+\sin (240^{\circ}+ A)\right)}{4}[/tex]
Step 4Rewrite 240° = 180° + 60°:
[tex]\sin(240^{\circ} + A) = \sin(180^{\circ} + 60^{\circ} + A)[/tex]
As sin(180° + x) = -sin(x), we can rewrite sin(180° + 60° + A) as:
[tex]- \sin(60^{\circ} + A)[/tex]
Therefore:
[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]
Step 5As sin(120° + x) = sin(60° - x) then:
[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (60^{\circ} -A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]
Step 6As sin(60° - x) - sin(60° + x) = -sin(x), then:
[tex]=\dfrac{3\left(\sin A-\sin3A-\sin A\right)}{4}[/tex]
Step 7Simplify:
[tex]=\dfrac{-3\sin3A}{4}[/tex]
[tex]=-\dfrac{3}{4}\sin3A[/tex]
Hence proving that:
[tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A[/tex]
Related Questions
How many quarts are equivalent to 5 pints
Answers
Answer: 3 quarts is equivalent to 5 pints
A car dealership has 10 cars on display. They have 7 cars and 3 trucks. What decimal number shows the number of trucks they have on display?
Answers
Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 1 < 3
Answers
The graph of the function |x| + 1 < 3 is plotted and attached
How to plot the graphThe graph is an absolute value graph merged with inequality. hence the attributes of inequality which involves shading of the graph will be seen in the graph
To create a table of values for the inequality |x| + 1 < 3, we can evaluate the inequality for each value of x within that range.
For x = -2:
|(-2)| + 1 < 3
2 + 1 < 3
3 < 3
This inequality is not true for x = -2.
For x = -1:
|(-1)| + 1 < 3
1 + 1 < 3
2 < 3
This inequality is true for x = -1.
For x = 0
|(0)| + 1 < 3
0 + 1 < 3
1 < 3
This inequality is true for x = 0.
For x = 2:
|(2)| + 1 < 3
2 + 1 < 3
3 < 3
This inequality is not true for x = 2.
Therefore, the values of x that satisfy the inequality |x| + 1 < 3 are: x = -1 and x = 0.
the graph is attached
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Which expression is equivalent to..?
Answers
The equivalent expression is the one in the last option:
[tex]\sqrt[10]{y}[/tex]
Which expression is equivalent to the given one?Here we want to find an expression equivalent to:
[tex](\frac{1}{\sqrt{y} } )^{-1/5}[/tex]
Remember the two rules for exponents that we need to use here:
[tex]x^{-n} = (1/x)^n[/tex]
[tex]x^{1/n} = \sqrt[n]{x}[/tex]
Using the first rule, we can rewrite our expression as:
[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5}[/tex]
Now we can rewrite the root of a root to get:
[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5} = \sqrt[5]{\sqrt{y} } = \sqrt[10]{y}[/tex]
Where in the last step we just multiplied the exponents for the roots, we can see that the correct option is the last one.
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Plot and connect the points A(4, 6), B(4, 0), C(1, -3), and D(1, 3), and find the area of the parallelogram formed.
Answers
Answer:
18 square units
Step-by-step explanation:
The parallelogram has been plotted in the attached figure
The area of a parallelogram is b x h
where b is one side and h is the vertical distance between the two bases
In the figure, we see that base = AB is parallel to the y-axis
This means the y-coordinates of A and B are the same and the distance is obtained by taking the absolute difference between the x-coordinates of A and B
b = |x1 - 2| = |6 - 0| = 6
The height h is a perpendicular line from point D(1, 3) to the base which touches the base at point E
Since this line is horizontal to the x-axis in the figure, the y coordinates of the endpoints of the line are the same i.e y1 =3 and y2 = 3
Therefore h = absolute difference between the x coordinates
= |1-4| = 3
Given b = 6, h = 3
area = 6x 3 = 18 square units
Jen’s soccer team is playing 4 games next week. How many different outcomes are there for the four games
Answers
Answer:
4 outcomes
Step-by-step explanation:
8 1/2 x 4 1/4 = Answer
Answers
Answer:
Answer is 36 1/8
Step-by-step explanation:
8x4 is 36. 1/2 x 1/4 is 1/8
Answer:
36 1/8
Step-by-step explanation:
8 1/2 = 17/2 x 17/4 = 289/8 = 36.125 = 36 1/8
50 POINTS + BRAINLIEST. If you choose to answer this question, make sure its correct, or no brainliest.
The table displays data collected, in meters, from a track meet.
1/3 2 4 1 7
2/3 4/5 5/2
What is the median of the data collected?
1
1.5
2
2.5
Answers
Answer:
2
Step-by-step explanation:
First, we need to arrange the data in order. We can convert the mixed numbers to improper fractions for ease of comparison:
1/3, 2/1, 4/1, 1/1, 7/3, 4/5, 5/2
Now, let's arrange them in ascending order:
1/3, 4/5, 1, 7/3, 2, 5/2, 4
The median is the middle value in the data set. Since we have an odd number of values, the median is the middle value when the data is arranged in order. Therefore, the median is:
median = 2
Therefore, the correct option is C
Answer:
1.5
Step-by-step explanation:
1/3 2 4 1 7 2/3 4/5 5/2
Write the numbers in ascending order.
1/3 2/3 4/5 1 2 5/2 4 7
The median is the middle value if there is an odd number of numbers.
If there is an even number of numbers, the median is the mean of the middle two numbers.
Here, there are 8 values, so we do the mean of the middle 2 values.
median = (1 + 2)/2
median = 1.5
According to the NCAA, 12.8% of high school men's lacrosse players will end up playing at the collegiate level. If 20 male high school lacrosse payers are selected at random, find the probability that exactly four of them will play at the college lacrosse. Express your answer as a probability between C and 1 and round to three decimal places.
Answers
This question involves using the binomial distribution.
Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).
The probability of exactly 4 players playing at the college level is given by the formula:
P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)
Using a calculator, we can evaluate this expression to find:
P(X=4) = 0.155
Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).
Note that we rounded to three decimal places as requested .
What are the coordinates of S? the image is below
Answers
The coordinates of point S are (4, 3.5)
How to find the coordinates of point S?Remember that the coordinates of a point are written in the notation (x, y), such that the first value is the value in the horizontal axis, and the second value is the value in the vertical axis.
Each one of the squares is one unit, then the x-value of the point S is:
x = 4
And for the y-value we can see that the point is halfway between the third and the fourt lines, then:
y = 3.5
Thus, the coordinates of point S are (4, 3.5)
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A company studied how much they pay employees. They found the mean and median annual salaries. These values are given in the table.
Annual Salary Data
Mean Annual Salary $62,000
Median Annual Salary $35,000
Which measure of center is best to describe salaries at the company? Select the statement that BEST explains your choice.
a. the mean, because people who earn too little make the median too small
b. the mean, because most workers earn a salary that is near this value
c. the median, because it is the measure of center with the lower value
d. The median, because people who earn a lot make the mean too large
Answers
The best measure of center to describe salaries at the company is the median. The Option D is correct.
Why is median best measure to describe salaries?The reason is that the median is less affected by extreme values or outliers which can greatly affect the mean. In this case, the mean annual salary is $62,000 while the median is only $35,000.
This large difference suggests that there are some very high earners at the company that are pulling up the mean. The median indicates that half of the employees earn less than $35,000 and half earn more which gives a more accurate picture of the typical salary at the company.
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Please help me guys
Answers
Answer:
True
False
True
solve the inequality-2+4x<14
Answers
Answer: x<4
Step-by-step explanation:
If we break this down as
-2+4x<14 and we add 2 to both sides
4x+<16 and divide by 4
and you get x<4
The graph of which equation passes through the point
(4, - 3) and has a slope 4
A.5x+4y=8
B.5x - 4y = 8
C.4x + 5y = 8
D.4x - 5y = 8
Answers
The equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.
To determine which equation passes through the point (4, -3) and has a slope of 4, we can substitute the values of x and y into each equation and check if the resulting equation is true.
Let's substitute x = 4 and y = -3 into each equation:
A. 5x + 4y = 8
Substituting x = 4 and y = -3:
5(4) + 4(-3) = 20 - 12 = 8
The equation is true for points (4, -3).
B. 5x - 4y = 8
Substituting x = 4 and y = -3:
5(4) - 4(-3) = 20 + 12 = 32
The equation is not true for points (4, -3).
C. 4x + 5y = 8
Substituting x = 4 and y = -3:
4(4) + 5(-3) = 16 - 15 = 1
The equation is not true for points (4, -3).
D. 4x - 5y = 8
Substituting x = 4 and y = -3:
4(4) - 5(-3) = 16 + 15 = 31
The equation is not true for points (4, -3).
Therefore, the equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.
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Finance and Financial Planning companies are not really looking for employees who are innovators or think outside the box.
True
False
Answers
Finance and Financial Planning companies are not really looking for employees who are innovators or think outside the box: False.
What are financial planning skills?Financial planning skills can be defined as the ability of an individual such as an employee, to determine the most appropriate (best) financing and investing activities for himself or herself, or a business firm after analyzing and evaluating all available financial options.
In this context, we can reasonably infer and logically deduce that financial planning skills ultimately enables an individual such as an employee, to prepare and plan for the future.
In conclusion, most finance and financial planning companies require employees who are innovators and can think outside the box.
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You roll a dice. Find the following probabilities. Round to the nearest hundredth if necessary.
Event
Work
17. The the probability of rolling a 3 or a
number less than 4.
18. The probability of rolling a number less
than five or an odd number.
19. The probability of rolling a four or an
odd number
Answer
Answers
Answer:
18. The probability of rolling a number less than five or an odd number
Hope this helps! :)
Please Brainiest
A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
Blue
Green
Yellow
Purple
17
12
4
12
4
will land
F4330
Answers
Based on the given data, the probabilities of the spinner landing on each color are approximately:
Red: 0.3469
Blue: 0.2449
Green: 0.0816
Yellow: 0.2449
Purple: 0.0816
To calculate the probability of the spinner landing on a specific color, we need to divide the frequency of that color by the total number of spins.
Given the spinner results:
Color Frequency
Red 17
Blue 12
Green 4
Yellow 12
Purple 4
To find the probability of landing on a specific color, we divide the frequency of that color by the total number of spins:
Probability (Red) = Frequency (Red) / Total Spins
= 17 / (17 + 12 + 4 + 12 + 4)
= 17 / 49
= 0.3469 (rounded to four decimal places)
Probability (Blue) = Frequency (Blue) / Total Spins
= 12 / 49
= 0.2449 (rounded to four decimal places)
Probability (Green) = Frequency (Green) / Total Spins
= 4 / 49
= 0.0816 (rounded to four decimal places)
Probability (Yellow) = Frequency (Yellow) / Total Spins
= 12 / 49
= 0.2449 (rounded to four decimal places)
Probability (Purple) = Frequency (Purple) / Total Spins
= 4 / 49
= 0.0816 (rounded to four decimal places)
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At a high school, the probability that a student takes a science class and a history class is 0.48. The probability that a student takes a science class is 0.82, and the probability that the student takes a history class is 0.64. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?
Answers
The probability that a student takes a history class given that the student is taking a science class is 0.59 to the nearest hundredth.
What is the probability?The probability that a student takes a history class given that the student is taking a science class is a conditional probability.
Assuming;
P(H) = Probability of taking a history class
P(S) = Probability of taking a science class
P(H ∩ S) = Probability of taking both a history class and a science class
Given data:
P(H ∩ S) = 0.48
P(S) = 0.82
Solving for P(H | S) using the formula for conditional probability:
P(H | S) = P(H ∩ S) / P(S)
P(H | S) = 0.48 / 0.82
P(H | S) ≈ 0.59
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Jim began a 150-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 6 hours. Of Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour, find the amount of time he spent on the bicycle.
Answers
Answer:
Step-by-step explanation:
150 mile length. We can make an inequality for this with him riding on his bike for r and walking for w.
40r + 4w = 150
r + w = 6
Then we get
r = 7/2
w = 5/2
caculate the circumference of a circle whose diameter is 28cm.
Answers
Answer: about 87.96459430051421
Step-by-step explanation: 28 x 3.14 = the answer
A car left Town A at 9:30 a.m. and reached Town B at 11:30 a.m. Its average speed was 60 km/h. Find the distance between Town A and Town B.
Answers
Answer:
120 km
Step-by-step explanation:
its average speed was 60 km an hour and it took 2 hours from town a to town b so 60km + 60km = 120
[tex]{\large {\orange{\underline {\underline {\mathcal {♡AnSwER♡⤵}}}}}}[/tex]
Left Town A at 9:30 am
Reached town B at 11:30 a.m
Therefore, Time taken by the car is =( 11:30 - 9:30) hrs =2 hrs
The speed of the car =60 km/h
So, the distance between Town A and B is = (Speed × Time) =( 60 × 2 )km =120 km.
The distance between Town A and B is 120 km. (Ans)
Hope it helps you
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank ~you~:)}[/tex]
Muya had a 6 2/3hectares piece of land. .He donated 7/8hectares to a school, and 1 1/2 to a children's home. The rest of the land was shared equally between his son and daughter .Find the size of the land
Answers
The size of the land that Muya's son and daughter received is [tex]1\frac{11}{12}[/tex] hectares.
We can see that, Muya started with a [tex]6\frac{2}{3}[/tex] hectares piece of land, which we can write as an improper fraction i.e.:
[tex]6\frac{2}{3}[/tex] = (6 × 3 + 2) / 3 = [tex]\frac{20}{3}[/tex] hectares
The Muya donated [tex]\frac{7}{8}[/tex] hectares to a school and [tex]1 \frac{1}{2}[/tex] hectares to a children's home. The total amount of land he donated is:
[tex]= \frac{7}{8}+ \frac{11}{2} \\\\= \frac{7}{8} + \frac{3}{2} \\\\= \frac{14}{8} + \frac{12}{8} \\\\= \frac{26}{8} \\\\= \frac{13}{4} hectares[/tex]
The size of the land left is:
[tex]\frac{20}{3} - \frac{13}{4} = (\frac{80}{12}) - (\frac{39}{12}) = \frac{41}{12} hectares[/tex]
Muya's son and daughter share this remaining land equally, so each of them gets:
[tex](\frac{41}{12}) / 2 = \frac{20.5}{12} = 1 \frac{11}{12} hectares[/tex]
Therefore, the size of the land that Muya's son and daughter received is 1 11/12 hectares.
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Question
Which of the following is equivalent to 12x + 8?
○ 4(3x + 2)
O4(3x + 8)
O4(3x + 2x)
O 20x
Answers
Answer:
the first one
Step-by-step explanation:
reason - 4 times 3 is 12 and 4 times 2 is 8 so 12x+8
The area of a rectangle painting is 3339cm^2. If the length of the painting is 63 centimeters, what is its width?
Answers
Answer:
Step-by-step explanation:
Width = Area / Length
Width = 3339 cm^2 / 63 cm
Width = (1113/21) cm
Width = (371/7) cm
Width = 52 cm
The senior class at Legion Academy wants to buy jerseys to wear to the basketball games. The cost of
the jerseys can be modeled by the equation C=0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x
jerseys. How many jerseys can they purchase for $430?
Answers
The number of jerseys that the senior class at Legion Academy can purchase for $430, using quadratic equation, is 190.
What is quadratic equation?Quadratic equation is an algebraic equation of the second degree in x, represented in the form of ax²+bx+c=0.
In the quadratic equation, a, b, and c are known values but a ≠ 0 and x is unknown.
Quadratic Equation Formula:x = [-b ± √b² - 4ac]/2a
when ax^2 + bx + c = 0
Equation Model:C = 0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x jerseys.
Simplifying the equation, we get:
x = 0.2 − 2.4 ± 40.4
The two possible values of x are:
1) x = 0.2 − 2.4 + 40.4 = 190
or
2) x = 0.2 − 2.4 − 40.4 = −214
The value of x cannot be negative, therefore, the class bought 190 jerseys for $430.
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help please very important it would help me
Answers
Answer
Hi!, if you need help right away, chat with a tutor!
Step-by-step explanation:
Answer:
(a) width = 71 ft; (b) length = 77 ft
Step-by-step explanation:
(a) The formula for area of a rectangle is
A = lw, where
A is the area in units squaredl is the lengthw is the widthBecause we're already given the area and length, we can find the width by plugging everything into the formula and solve for width, w:
6319 = 89w
71 ft = w
(b) The formula for perimeter of a rectangle is
P = 2l + 2w, where
P is the perimeterl is the lengthw is the widthSince we're given the perimeter and width this time, we can plug everything into the formula and solve for l:
272 = 2l + 2(59)
272 = 2l + 118
154 = 2l
77 ft = l
We can check our answers for (a) and (b) by plugging in the length and width for (a) into the area formula and seeing whether we get 6319 and plugging in the length and width for (b) into the perimeter formula and seeing whether we get 272
Checking answers for (a):
6319 = 89 * 71
6319 = 272
Checking answers for (b):
272 = 2(77) + 2(59)
272 = 154 + 118
272 = 272
Construct a stem-leaf Plot (Final arrangement): 18, 17, 23, 28, 13, 14, 15, 27, 21, 18, 12, 15, 41, 22, 14, 19, 18, 22, 33, 16
Answers
Stem-leaf plot for the given data:
1 | 2 3 4 5
2 | 1 2 2
3 | 3 3
4 | 1
The stem represents the tens digit and the leaf represents the ones digit of the data points. For example, the number 18 is represented as 1|8 in the plot.
A stem-and-leaf plot for the given data:
1 | 2 3 4
---+-------
1 | 2 2
2 | 2 2 3 8
3 | 3 3
4 | 1
5 |
6 | 6
7 | 7
8 |
In this plot, the tens digit is used as the stem, and the ones digit is used as the leaf. For example, the first two numbers in the data set are 18 and 17, which have stems of 1 and leaves of 8 and 7, respectively. These are shown in the first row of the plot as "1 | 8 7". Similarly, the number 23 has a stem of 2 and a leaf of 3, so it is shown in the second row as "2 | 3". The remaining numbers are arranged in the same way.
The numbers are arranged in ascending order within each row, and there are blank spaces for stems that do not appear in the data.
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Angle A and B are complementary angles and angle B and C are supplementary angles. If angle A equals 20 what is the measure of angle C?
Answers
Answer:
Angle B measures 70°, so angle C measures 110°.
20° + B = 90°, so B = 70°.
70° + C = 180°, so C = 110°.
Which is equivalent to (4 + 44)?
Answers
Answer:
48
Step-by-step explanation:
just add the numbers. 48 is equal to (4+44)
have a great day and thx for your inquiry :)
the ratio of 2/3 to 8 as a fraction in simplest form
Answers
To write the ratio of 2/3 to 8 as a fraction in simplest form, we need to divide the numerator and denominator by their greatest common factor (GCF).The GCF of 2 and 8 is 2.So, we divide both the numerator and denominator by 2:2/3 ÷ 8/1 = (2/3) ÷ (8/1) = 2/3 x 1/8 = (2 x 1) / (3 x 8) = 2/24Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor again.The GCF of 2 and 24 is 2.So, we divide both the numerator and denominator by 2:2/24 ÷ 2/2 = (2/24) ÷ (2/2) = 2/24 x 1/2 = (2 x 1) / (24 x 2) = 1/12Therefore, the ratio of 2/3 to 8 as a fraction in simplest form is 1/12.
Answer:
How to find Ratio?
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10
In order to find the ratio of a certain number to another number or the relation of each other, we also need to know the concept of fraction and percentage.
1/12 or 1 to 12
The ratio is 2/3*8=23⋅8=2/24=1/12
So it is 1 to 12
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