Rewrite 2 cos 75 degrees sin 75 degrees a double angle identity
Answers
It follows from the double angle identity for sine,
sin(2x) = 2 sin(x) cos(x),
that
2 cos(75º) sin(75º) = sin(2•75º) = sin(150º)
Alternatively, recall that
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
Adding these together gives
sin(x + y) + sin(x - y) = 2 sin(x) cos(y)
Set x = y = 75º; then
2 sin(75º) cos(75º) = sin(75º + 75º) + sin(75º - 75º)
2 sin(75º) cos(75º) = sin(150º)
2 cos 75° . Sin 75° = Sin 150°
Notice:
Sin 150 º = Sin 30°
See that Sin 75° = Cos 15°
Cos 75° = Sin 15°
So :
2Cos 75° . Sin 75° = 2 Sin 15°Cos°15 = Sin 30°
Related Questions
First right answer gets brilliant. Can someone please help? It is due today!
Answers
Answer:
Step-by-step explanation:
A, x=31
E, b=11
N, m=61
Y, b=15
I, a=80
G, k=-78
U, x=-13
R, u=88
O, y=13
A, w=104
H, d=-7
V, n=1/36
Sorry, don't want to give away all the answers!
Hope this helps!!!
what is 0.8 x 0.8? im very confused on this, and im not very good with decimals. could someone help me?
Answers
To test her math skills, Isabella’s father told her he would give her 6/8 of
a dollar if she could tell him how much money it is, as well as the
money amount in decimal form. What should Isabella tell her father?
Show your calculations.
Answers
Answer:
0.75 cents is the correct answer.
Step-by-step explanation:
When finding a fraction of an amount, the key rule to remember is to divide the amount by the denominator and multiply your answer by the numerator. If asked to increase or decrease an amount by a fraction make sure you add or subtract from the original amount at the end of the question! :)
To calculate the amount of money Isabella's father would give her, we need to multiply the number of dollars Isabella would receive by the amount of each dollar. In this case, Isabella's father promised her 6 /8 of a dollar.
The term "by" often represents multiplication in math problems. Therefore, we can interpret "6/8" as 6 multiplied by 8. Multiplying 6/8 gives us the amount of money in non-decimal form. Calculating 6 multiplied by 8, we get: \(6 x 8 = 48\) So, Isabella's father would give her 48 dollars. To convert this amount to decimal format, we divide the number of dollars by 100.
Since there are 100 cents in a dollar, Isabella would receive: \(48 / 100 = 0.48\) dollars Therefore, Isabella would receive 48 dollars and 0.48 dollars in decimal form. To provide her answer to her father, Isabella should tell him that he would give her 48 dollars and 48 cents (or 0.48 dollars) in decimal form. It's important to note that in this problem, "by" is used to represent multiplication. In other contexts, it might have a different meaning, so it's important to consider the context and use proper mathematical operations when solving math problems.
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can someone help? im not sure about this questons and its getting me so stressed out :( pls help :(
Answers
Answer:
Lets start:
Picture 1:-
1. Length of EH= 12cm
2. Angle G= 55 degrees
Picture 2:-
1. Scale factor= 1/4 (I'm not sure about this but this is what I think it is ;-;)
2. Value of y= 28 cm
Picture 3:- [Picture 3 is cropped so I'm guessing its the last one so imma answer those questions :D]
1. Scale factor= 5 (Again I'm not sure but its my best guess)
2. Value of z= 5
Picture 4:-
1. Scale factor= 4 (I'm pretty sure you know that my scale factor answers are guesses so yea ;-;)
2. Value of b= 12
Step-by-step explanation:
Since i can't add links in answers you can watch:
Similar figures
-By The Organic Chemistry Tutor
It'll help you understand how we solve these questions
Well anyways i hope this clears your concepts :D
Answer:
Step-by-step explanation:
EH is 12cm as the shape has been enlarged by scale factor two (all sides have been multiplied by 2).
Angle G remains the same at 55 degrees.
PART A
Scale factor for the triangle = 1/4
Value of y = 28cm
3) z = 5, scale factor = 5
SIMILAR RECTANGLES:
Scale factor = 4
Side b = 12cm
Hope these answers work out for you
Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise.
U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(4, 0), W′(1, −4)
U′(−1, 1), V′(4, 0), W′(1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)
Answers
The correct answer is U′(1, −1), V′(4, 0), W′(1, 4). When a point is rotated 90° counterclockwise about the origin, the x-coordinate and y-coordinate change places, and the sign of the new x-coordinate is the opposite of the original y-coordinate. So for example, point U(−1, 1) becomes U′(1, −1).
Please help me this is due today
Answers
a) The predicted heating cost for a month with temperature of 25 ºF is given as follows: $65.70.
b) The predicted heating cost for a month with temperature of 0 ºF is given as follows: $96.20
c) For an increase of one degree Fahrenheit, the predicted decrease in the cost is of $1.22.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The slope and the intercept for the function in this problem are given as follows:
Slope of -1.22, meaning that for an increase of one degree Fahrenheit, the predicted decrease in the cost is of $1.22.Intercept of 96.2, meaning that the predicted heating cost for a month with temperature of 0 ºF is of $96.20.Hence, the predicted cost for a month with temperature of 25ºF is given as follows:
y = -1.22(25) + 96.20 = $65.70.
More can be learned about linear functions at https://brainly.com/question/24808124
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Help Please
find the solution to this system of equations
Answers
Answer:
-8x + 4y = 24 ----> 2x - y = -6
-7x + 7y = 28 ----> -x + y = 4
-------------
x = -2, y = 2
A pilot is flying an airplane at an average altitude of 32,000 feet above the ground. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth.
The quotient that best represents the rate of change in the plane’s altitude is___feet/minute.
Answers
Answer:
The plane altitude is 65 feet.
Find out more about Planes here
Look at the desert image.
How far did I travel to reach my destination on each day of my three-day Trip?
a. On Day 1, after traveling 5/8 of the way to the first day's destination, I still had 15 miles left to go before reaching my first destination.
b. On Day 2, after traveling 18 miles, I still had 2/5 of that day's distance left to go before reaching my second destination.
c. On Day 3, after traveling 5/11 of that day's distance, I still had 6 more miles to travel than what I had already traveled that day, before reaching my third destination.
Answers
Answer:
81 miles
Step-by-step explanation:
Day 1
3/8---15 miles
1/8---5 miles
8/8---40 miles
Day 2
3/5---18 miles
1/5---6 miles
5/5---30 miles
Day 3
6/11---6 miles
1/11---1 mile
11/11---11 miles
Total: Day 1 + Day 2 + Day 3
40+30+11=81
the ratio of the number of oranges to apples to bananas is 8:5:2. if there are 120 fruits in total, how many bananas are there
Answers
Answer:
Step-by-step explanation:
To find the number of bananas, we need to determine the proportion of bananas in the total number of fruits based on the given ratio.
Let's assume that the ratio of oranges, apples, and bananas can be represented by 8x, 5x, and 2x, respectively, where x is a common multiplier.
The sum of the parts in the ratio is 8x + 5x + 2x = 15x.
We know that the total number of fruits is 120. Therefore, we can set up the following equation:
15x = 120
To solve for x, we divide both sides of the equation by 15:
x = 120 / 15
x = 8
Now that we know the value of x, we can find the number of bananas by multiplying it by the corresponding part of the ratio:
Number of bananas = 2x = 2 * 8 = 16
So, there are 16 bananas in total.
We can add all the parts to the ratio and get 15. Out of 15 parts, 2 are bananas. Now we can calculate how many fruits are in one part. One fifteenth of 120 is 8, so there are 8 fruits in one part. 2 parts are bananas, so multiplying 8 with 2 gives us our answer, 16.
Question 1 (1 point)
Probability is the likelihood that an event occurs. Probability is expressed using numbers between 0 and 1.
Question 1 options:
True
False
Question 2 (1 point)
Independent Events are events that depend on each other, where one event has an effect on the other.
Question 2 options:
True
False
Question 3 (1 point)
Is the following event Independent or Dependent?
Flipping a coin twice and rolling a dice twice.
Question 3 options:
Independent: one event does not effect the outcome of the other
Independent: one event effects the outcome of the other
Dependent: one event does not effect the outcome of the other
Dependent: one event effects the outcome of the other
Question 4 (1 point)
A surveyor wants to know how many shoppers at a mall like to read books. He surveys 100 people coming out of a bookstore at the mall.
Why is the sample biased?
Question 4 options:
There are not enough people in the sample.
People who shop in bookstores are likely to read more books than those who do not.
It is unlikely that people who shop in bookstores are interested in surveys.
The surveyor did not sample the entire population at the mall.
Answers
Step-by-step explanation:
Question 1: True
Question 2: False
Question 3: Independent: one event does not affect the outcome of the other
Question 4: People who shop in bookstores are likely to read more books than those who do not. (The sample is biased because it only includes people coming out of a bookstore, who are more likely to be interested in books than the general population at the mall.)
Question 1: True
Question 2: False.
Question 3: Independent.
Question 4: People who shop in bookstores are likely to read more books than those who do not.
What is a biased estimator?An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.
Question 1: True
Question 2: False. Independent Events are events that do not depend on each other.
Question 3: Independent: one event does not affect the outcome of the other.
Question 4: People who shop in bookstores are likely to read more books than those who do not.
The sample is biased because it only includes people who are coming out of a bookstore, and this group is more likely to be interested in reading books than the general population at the mall.
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PLS HELP!!!! I DON'T GET ANY OF THIS,I WILL GIVE BRAINLEST TO THE FIRST ANSWER
Answers
Answer:
theoretical- what is expected to happen, 1/2
experimental- what actually happened, 1/10
Step-by-step explanation:
theoretical does not always mean that it will happen, such as flipping a coin.
it will say there is a 1/2 chance to get heads or tail.
experimental is what actually happens when you test it out. say you flip a coin 10 times and only get heads 3 times. if it was the theoretical possibility then it would say 5 heads and 5 tails.
Help me Guess just help please
Answers
35
Step-by-step explanation:
√441 + 784 =
Add 441 and 784
√1225
Simplify
35
Explanation:
Sqrt(441 + 784)
= sqrt(1225)
= sqrt(5^3 x 7^2)
= 5 x 7 x sqrt(5)
= 35sqrt(5)
07.01)
Which of the following sets shows all the numbers from the set {3, 4, 5, 6} that are part of the solution to the equation 5x + 4 < 29? (4 points)
a. {4, 5, 6}
b. {3, 4, 5}
c. {3, 4}
d. {3}
Answers
help me this one plssssssssssss
Answers
Answer:
The integer that describes the translation from B to B' is (-2,1)
Use the Midpoint Rule with \(n=5\) to estimate the volume obtained by rotating about the y-axis the region under the curve \(y=\sqrt{1+x^3}\), \(0\leq x\leq 1\).
Answers
To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).
Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)
where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.
First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:
\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)
Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:
\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)
Now, we can calculate the approximate volume using the Midpoint Rule:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)
Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Find the missing side length of the right triangle
Answers
Answer:
x=16
Step-by-step explanation:
This is an unidentified triangle or a scaleneThe equation: 14^2+x^2=q^2 This equation is for the pathagoern theorem. (If you have not learned it put a thanks and ask the question about it) This equation 14^2+x^2=q^2 = 14^2=x^2-q^ = x^2= 32 = x = 16I hope this helps!At the carnival, the ratio of people who won the ring toss game to lost it was 9 : 4. If 81 people won, how many people would have lost?
Answers
Answer:
36 people
Step-by-step explanation:
9x9=81
4x9=36
Answer: 36 people lost.
Step-by-step explanation: you take the 81 divided by 9 and you get 9. so you multiply the 4 times 9 and you get 36.
Explain how to find the volume of a cube that has edge length 1/4 yd. Then, find the volume of the cube.
Answer in complete sentences, include all relevant formulas and calculations, and be sure to include appropriate units.
Answers
Answer:
1/64 cubic yards or 0.015625 cubic yards
Step-by-step explanation:
A cube has equal edge lengths.
To find the volume of a cube using edge length, simplify raise the value of the edge length to the 3rd power or cube it.
⇒ V = (edge length)³
Using this formula and keeping in mind the edge length is 1/4 yd, substitute it in the formula.
V = (1/4)³V = 1/64 [4³ = 64]V = 1/64 cubic yards or 0.015625 cubic yardsAnswer:
Volume of the cube is 1/64 yd³.Step-by-step explanation:
Given that, Length of each edge of the cube is 1/4 yard.
Using formula:
\( \: \: \dashrightarrow \: \: { \underline{ \boxed{ \pmb { \sf{ \purple{Volume _{(cube)} = (edge) ^{3} }}}}}} \\ \)
On substituting the value of edge in the above formula, we will get the required volume of the cube.
\( \: \: \dashrightarrow \: \: \rm Volume = \bigg( \dfrac{1}{4} \bigg) ^{3} \\ \)
\(\: \: \dashrightarrow \: \: \rm Volume = \dfrac{1}{4} \times \dfrac{1}{4} \times \dfrac{1}{4} \\ \)
\(\: \: \dashrightarrow \: \: { \underline{\boxed{ \purple{\pmb{ \sf {Volume = \dfrac{1}{64} \: {yd}^{3} }}}}}} \\ \\ \)
Hence,
Volume of the cube is 1/64 yd³helpppppppppppppp please
Answers
Answer:29
so the mini triangle in the corner is a mini model of the entire triangle, all you have to do is take the width or bottom number and find the factor in which it is smaller, then take the height of the smaller triangle and add the factor in which it increases to it. so the factor goes up by 31 1/2--9=22 1/2 and adding the factor in which it increases to the height is 22 1/2+6 1/2=29 because 2 halfs make a whole.
Step-by-step explanation:
mr clean has big brien 0-0
Please help me put the coordinates on and get the slope!
Answers
Answer:
Step-by-step explanation:
Slope
\(m=\frac{y2-y1}{x2-x1} \\\\m= \frac{3/2-(-3/2)}{3/2-(-3/2)}\\\\m=\frac{3/2+3/2}{3/2+3/2}\\ \\m=\frac{3}{3}\\ \\m=1\)
slope: m=1
y=mx+b
y=1x+0
Keira said that if 6 tickets are sold, there should be 2 tickets left. Is Keira correct?
Answers
According to Keira, if 6 tickets are sold, there should be 2 tickets left. However, we don't have any information about the initial number of tickets available.
If the total number of tickets initially was 8, and 6 tickets were sold, then there would indeed be 2 tickets left, supporting Keira's statement.
However, if the total number of tickets initially was less than 8, or if the statement doesn't specify the initial number of tickets, we cannot determine if Keira's statement is correct.
Therefore, without additional information, we cannot determine the accuracy of Keira's statement.
Will give brainliest!!! Please help I am truly stuck on this!!!!!!!!!!!!!
Answers
Answer:
20x⁸y¹⁰
Step-by-step explanation:
I put my explanation above. I hope you can give me brainliest. Thanks
Answer:
\(20x^8y^{10}\)
Step-by-step explanation:
\(\frac{4x^{-2}y^2}{2^{-3}x^2y^7}*(x^{-4}y^{-5})^{-3}-12x^8y^{10}\)
you have to cancel the fraction stuff, distribute the exponent in the second term multiply, simplify like terms and then subtract the last term
it would take a very long time for me to explain all this and type it out so instead copy and paste this into mathpapa.com and it will explain it
\frac{4x^{-2}y^2}{2^{-3}x^2y^7}*(x^{-4}y^{-5})^{-3}-12x^8y^{10}
then let me know if you have any questions in the comments and I will answer
Hope this helps! :)
pls help due tomorrrowwww :(((((
Answers
To find this answer you need to sort all of the numbers and find the 1st Quartile, and the 3rd Quartile.
0,0,0,1,2,2,4,5,7,8,10
The 1st and 3rd quartile in this set of numbers is 0 and 7.
To find inter range you subtract the 1st quartile from the 3rd. This would get you a answer of 7.
IM SO SORRY IF THIS DIDN’T MAKE SINCE!
I need some help for this and the graph won’t let you use decimals as the answer. Tip: 1/3 = 0.3
.
Answers
Answer:
\(\large\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}6&2\\\cline{1-2}12&4\\\cline{1-2}18&6\\\cline{1-2}\end{array}\)
See attachment for the graph of the equation.
Step-by-step explanation:
Given equation:
\(y=\dfrac{1}{3}x\)
To complete the table, find the corresponding values of y by substituting each given value of x into the equation.
\(x=6 \implies y=\dfrac{1}{3}(6)=\dfrac{6}{3}=2\)
\(x=12 \implies y=\dfrac{1}{3}(12)=\dfrac{12}{3}=4\)
\(x=18 \implies y=\dfrac{1}{3}(18)=\dfrac{18}{3}=6\)
Therefore the completed table is:
\(\large\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}6&2\\\cline{1-2}12&4\\\cline{1-2}18&6\\\cline{1-2}\end{array}\)
To graph the equation, plot the ordered pairs on the given coordinate plane:
(6, 2)(12, 4)(18, 6)Draw a straight line through the points. (See attachment).
A school track is shown.
The track is made up of two semi-circles and a rectangle. Find the perimeter of the track. Use 3.14 for \piπ .
Answers
Answer:
2232.36m
Explanation:
since the perimeter of two semicircles adds up to that of one circle, the perimeter of the track would be the perimeter of the circle + the length of the rectangle.
we can find the perimeter of the circle using the formula of π × diameter, which would be:
π × diameter
= 3.14 × 74
= 232.36
now, we can add this to the given length of the rectangle:
232.36 + 1000 + 1000 = 2232.36
thus, the perimeter of the track is 2232.36m.
i hope this helps! :D
English is the predominant language spoken in Chile. Question 1 options: True False
whoever answers first gets the crown
Answers
Answer: The answer is false!
Step-by-step explanation: You may think its true but NO, its not true!
Answer: false
Step-by-step explanation:
the correct answer is a dialect of spanish, chilean spanish.
If you toss three coins, what are the odds in favor of getting exactly two tails and one head?
A. 3:8
B. 3:5
C. 5:3
D. 8:3
(Explaination needed)
Answers
Therefore 2 tails and 1 head appears 3 times over the possible outcome 8.
Pls help me in math, I need this tomorrow, thx :)
Answers
Answer: Range and mean = 8 of both
variance of Set X= 4.7
variance of Set Y= 4.6
Step-by-step explanation:
Two sets of data, set X and set Y are given
a.) Range is the difference of the highest value and the lowest value,
Therefore, Range of set X = 12-4=8
Range of set Y = 12-4=8
Now, Mean of a given data set is the average of all the terms present in the given data set
Mean of set X= Σxif/n = (4+5+6+7+16+18+24)/10 = 8
Mean of set Y= (4+5+7+32+20+12)/10= 8
Therefore, both the data sets has same range and mean.
b.) Standard deviation tells about the variability of the date and is given by,
S.D= σ = √∑ ( X − μ )^2/n
S.D of set X= √(16+9+4+1+0+1+16)/10= √4.7
S.D of set Y= √(16+9+1+0+4+16)/10= √4.6
Variance is the square of S.D, that is, σ^2
Therefore, variance of set X=4.6
variance of set Y= 4.7
c.) The calculated variances of set X and set Y are 4.7 and 4.6 respectively. It implies that the data is more distributed or varied in set X than in set Y. In the other words, data in set Y is more consistent data than of set X.
To learn more about S.D and variance,
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Answer: Range and mean = 8 of both
variance of Set X= 4.7
variance of Set Y= 4.6
Step-by-step explanation:
We know
a.) Range is the difference of the highest value and the lowest value,
Therefore, Range of set X = 12-4=8
Range of set Y = 12-4=8
Now, Mean of a given data set is the average of all the terms present in the given data set
Mean of set X= Σxif/n = (4+5+6+7+16+18+24)/10 = 8
Mean of set Y= (4+5+7+32+20+12)/10= 8
also
b.) Standard deviation tells about the variability of the date and is given by,
S.D= σ = √∑ ( X − μ )^2/n
S.D of set X= √(16+9+4+1+0+1+16)/10= √4.7
S.D of set Y= √(16+9+1+0+4+16)/10= √4.6
Variance is the square of S.D, that is, σ^2
Therefore, variance of set X=4.6
variance of set Y= 4.7
c.) The calculated variances of set X and set Y are 4.7 and 4.6 respectively. It implies that the data is more distributed or varied in set X than in set Y. In the other words, data in set Y is more consistent data than of set X.
Yeah, get into this work problem
