find sin B and cos B, given that cos2b=1/8, 540<2b<720.
Answers
The value of sinB and cosB are as follows:
sin(B) = ±1/2
cos(B) = ± sqrt(3/8)
We can use the identity cos(2B) = cos^2(B) - sin^2(B) to relate cos(2B) to sin(B) and cos(B).
Given that cos^2(2B) = 1/8, we have:
cos^2(B) - sin^2(B) = 1/8
We can also use the Pythagorean identity sin^2(B) + cos^2(B) = 1 to relate sin(B) to cos(B).
Solving for cos(B) in the first equation, we get:
cos^2(B) = (1/8 + sin^2(B))/2
Taking the square root of both sides, we get:
cos(B) = ±sqrt((1/8 + sin^2(B))/2)
Using the Pythagorean identity, we can write:
sin^2(B) = 1 - cos^2(B)
Substituting this into the expression for cos(B), we get:
cos(B) = ±sqrt((1/8 + 1 - sin^2(B))/2)
Simplifying, we get:
cos(B) = ±sqrt((9/8 - sin^2(B))/2)
Squaring both sides, we get:
cos^2(B) = (9/8 - sin^2(B))/2
Substituting the expression for cos^2(B) from the first equation, we get:
(1/8 + sin^2(B))/2 = (9/8 - sin^2(B))/2
Solving for sin^2(B), we get:
sin^2(B) = 1/4
Taking the square root, we get:
sin(B) = ±1/2
Substituting this into the expression for cos(B), we get:
cos(B) = ±sqrt((1/8 + 1/4)/2) = ±sqrt(3/8)
Therefore, we have:
sin(B) = ±1/2
cos(B) = ±sqrt(3/8)
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Related Questions
Seven decreased by three times a number is 40
Answers
Your equation would be 7-3x=40. Subtract 7, divide by -3, and your answer is -11
Wilson's Woodworking Shop produces wood chairs and sells them for $250. The company's weekly profit, (y), depends on the number of $1.50 price increases (x) for each chair. Use the graph below to answer the question.
Graph of function with the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 300), increases to (40, 1100), and then decreases through (86.904, 0).
What is the approximate value of the maximized profit?
200
800
1000
1100
Answers
The approximate value of the maximized profit include the following: D. 1100.
What is profit?In Economics, profit can be defined as a measure of the amount of money (revenue) that is generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
Mathematically, the profit function P(x) of a company simply refers to the revenue function R(x) minus the cost function C(x):
P(x) = R(x) - C(x)
Where:
R(x) represents the revenue or the amount of money generated.C(x) represents cost or the amount of money spent.Based on the graph of the company's weekly profit, (y), we can logically deduce that its maximized profit would occur at point (40, 1100) because this is the vertex of profit function P(x).
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hellooo how are you ??
Answers
Answer:
doing really good
Step-by-step explanation:
brainiest please.
somebody pls helpp meee
Answers
Answer:
1 and 3
Step-by-step explanation:
+ 3 & 1 belong to the solution
What is the name of the segment inside the large triangle?
1. Perpendicular bisector
2.Midsegment
3.Angle Bisector
4.Median
Answers
The name of the segment inside the large triangle is called the: 3. angle bisector.
What is an Angle Bisector?The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.
The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.
A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.
Therefore, we can state that the name of the segment is: 3. angle bisector.
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Could someone explain
Answers
Answer:
top one =75
bottom one=65
Step-by-step explanation:
all angles should equal to 180
so 180-40=140
the sum of th eother two angles will be 140
so 4x-5+3x+5=140
now solve for x
x=20
subsitute for x
4(20)-5=75
3(20)+5=65
please mark brainliest if correct
8 x 10^5 in standard form
Answers
Answer:
8×10 5=800,000
Step-by-step explanation:
Warning: In different part of the world "standard form" means different things. In some places
8.0×105 is considered "standard form"
Find the value of f(3) for the function.
f(a) = 7(a + 1) - 5
F(3)=?
Answers
f(3) = 7(3+1) - 5 = 7(4) - 5 = 28 - 5 = 23.
f(3) = 23
Answer:
F(3)=23
Step-by-step explanation:
F(3)= 7(3+1)-5
F(3)=7(4)-5
F(3)=28-5
F(3)= 23
you always want to do the problem in the parenthesis first. and you replace a with 3
Given triangle ABC with ordered pairs:
A - (1, -3)
B - (3, 0)
C - (4, -2)
Rotate ABC 180 degrees about the origin and then reflect it over the y-axis. Determine the points of A', B', and C'.
Answers
The points A', B', and C' are (1, 3), (3, 0) and (4, 2) respectively. The solution has been obtained by using the concept of transformation.
What is transformation?
On a coordinate plane, forms can be translated, rotated, and reflected thanks to transformations. Any line, any point, and any vector can be reflected, rotated, and translated.
We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).
Now, we need to rotate the triangle 180 degrees about the origin.
We know that the rotation rule for rotating 180 degrees about the origin is that (x, y) becomes (-x, -y).
So, we get the new coordinates as
A' (-1, 3)
B' (-3, 0)
C' (-4, 2)
Now, on reflecting it over the y - axis, we get
A' (1, 3)
B' (3, 0)
C' (4, 2)
Hence, the points A', B', and C' are (1, 3), (3, 0) and (4, 2) respectively.
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(2,n) and (0,8) Slope is -2 what is n?
Answers
Answer:
n = 4-------------------
Use slope equation:
m = (y₂ - y₁)/(x₂ - x₁), where m - slope, (x₁, y₁) and (x₂, y₂) are pointsSubstitute coordinates and solve for n:
- 2 = (8 - n)/(0 - 2)- 2 = (8 - n)/ (-2)8 - n = (-2)*(-2)8 - n = 4n = 8 - 4n = 4Write the equation of a line that is parallel to the given line and passes through the given point.
y=1/3x+1 (-3,4)
Answers
Answer:
\(y=\frac{1}{3}x +5\)
Step-by-step explanation:
Linear equations are typically formatted in slope-intercept form:
\(y=mx+b\) where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
Parallel lines will always have the same slope. Therefore, this line will also have a slope of \(\frac{1}{3}\). Plug this into our equation:
\(y=\frac{1}{3} x+b\)
2) Determine the y-intercept (b)
To solve for the y-intercept (b), plug the given point (-3,4) into our equation and isolate b.
\(4=\frac{1}{3}(-3)+b\\4=\frac{-3}{3}+b\\4=-1+b\)
Add 1 to both sides
\(4+1=-1+b+1\\5=b\)
Therefore, the y-intercept is 5. Plug this back into our original equation with the slope:
\(y=\frac{1}{3}x +5\)
I hope this helps!
what is the answer to 6x+9=2x-7
Answers
Answer:
x= -4
Step-by-step explanation:
Answer:
x=-4
Step-by-step explanation:
6x-2x=-7-9
4x=-16
x=-16/4
x=-4
Does 2 times 36 equal 3 times 24
Answers
Answer:
Yes
Step-by-step explanation:
\(2 * 36 = 72\\ 3 * 24 = 72\)
Answer:
Yes.
Step-by-step explanation:
2 times 36 = 72 and 3 times 24 = 72
Hope this helped! ^-^
If there is 0.25 probability that a child in New York gets the flu and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu?If there is 0.25 probability that a child in New York gets the file and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu? O 0.075 O 0.275 O 0.25 O 0.55
Answers
Answer:
(.25)(.30) = .075 probability that both children will get the flu
The probability that both a youngster in New York and a kid in Los Angeles will get this season's virus can be determined by duplicating the singular probabilities. Consequently, the likelihood that both will get influenza is 0.075.
To find the probability of the two occasions happening, we duplicate the probabilities of every occasion. Considering that the probability of a kid in New York getting this season's virus is 0.25 (or 25%) and the probability of a youngster in Los Angeles getting influenza is 0.30 (or 30%), we multiply these probabilities: 0.25 * 0.30 = 0.075. This implies there is a 0.075 probability, or 7.5%, that both a youngster in New York and a kid in Los Angeles will get influenza.
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Find the greatest
7/16٫ 3/8٫ 11/24٫ 10/21٫ 21/46
Answers
What does the intersection of the two
functions mean?
Answers
♡Answer:♡
it means when the planes cross each other it is perpendicular to each other i think.
♡Step-by-step explanation:♡
♡ ∩_∩
（„• ֊ •„)♡
┏━∪∪━━━━┓
♡ good luck 。 ♡
┗━━━━━━━┛
Weiming receives a weekly pocket money of $28. If he decides to save 20% of it, find his saving in a year and spendings in a year
Answers
Welming's spending is $1164.8 and his savings is $291.2
How to determine the savings and the spending?The given parameters are:
Weekly pocket = $28
Save = 20%
There are 52 weeks in a year.
So, the yearly pocket is:
Yearly pocket = $28 * 52
Evaluate
Yearly pocket = $1456
He saves 20%.
So, we have:
Savings = 20% * $1456
Evaluate
Savings = $291.2
His spending is then calculated as:
Spending = $1456 - $291.2
Evaluate
Spending = $1164.8
Hence, Welming's spending is $1164.8 and his savings is $291.2
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Please provide an explanation for this problem, thank you!Car A (traveling north at 70 mph) and car B (traveling west at 50 mph) are heading toward the same intersection. Car A is 5 miles from the intersection while car B is 6 miles from the intersection. Find parametric equations that describe the motion of cars A and B.A) Car A: x = 0, y = 70t-5; Car B: x = 6 - 50 t, y = 0B) Car A: x = 0, y = 50t - 6; Car B: x = 70t - 5, y = 0C) Car A: x = -70t + 5, y = 0; Car B: x = 6 - 50t, y = 0D) Car A: x = 50t - 6, y = 0; Car B: x = 0, y = 50 - 70t
Answers
The correct parametric equations for the motion of Car A and Car B are: Car A: x = 70t, y = 5 + 70t; Car B: x = 6 - 50t, y = 50t. Option C is correct.
Car A is traveling north at a speed of 70 mph. Therefore, its velocity vector can be represented as <0, 70>.
Car B is traveling west at a speed of 50 mph. Therefore, its velocity vector can be represented as <-50, 0>.
Let's assume that at time t = 0, Car A is at position (0, -5) and Car B is at position (6, 0).
Then, the position vectors for Car A and Car B at any time t can be given as:
Position of Car A = <0, -5> + t<0, 70> = <0, 70t-5>
Position of Car B = <6, 0> + t<-50, 0> = <6-50t, 0>
Therefore, the parametric equations for the motion of Car A and Car B are:
Car A: x = 0, y = 70t-5
Car B: x = 6 - 50t, y = 0
So, option C is the correct answer.
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(-2, 8), (r, 4), m = -1/2
Answers
represent the number of books a student buys at the next book fair. what is the expected value of
Answers
The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.
How to determine a discrete probability distribution's expected value?The sum of each result of a discrete probability distribution times its corresponding probability is the distribution's anticipated value.The distribution is stated as follows based on the histogram provided by the picture just at end of the answer:P(X = 1) = 0.285P(X = 2) = 0.333P(X = 3) = 0.168P(X = 4) = 0.136P(X = 5) = 0.063P(X = 6) = 0.015The random variable b's expected value is then calculated as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X) = 2.404 books.
Thus, the expected value of discrete probability distribution is 2.404 books.
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The graph for the question is attached.
kid had 10 apples and he gic
Answers
Answer:
The meal cost $14.51 per person.
Step by step explanation:
Meal cost: 46.72
Sales tax: 8%
Then.
then we take out 8% of the value
\(46.72\text{ x 0.08 =3.74}\)\(46.72+3.74\text{ = 50.46}\)Tip : 15% (meal and sales tax)
\(50.46\text{ x 0.15 = 7.57}\)\(50.46\text{ + 7.57 = 58.03}\)There are 4 people.
\(\frac{58.03}{4}=14.51\)A restaurant offers pizzas with 2 types of crust, 7 different toppings, and in 5 different sizes. how many different pizzas could be ordered?
Answers
There are 70 different types of pizzas could be ordered
A permutation is an act of arranging the objects or numbers in order.
Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter
Given,
Number of options on crust=2
Number of options on topping= 7
Number of options on size= 5
Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes
The total number ways of ordering pizza=2×7×5=70
Hence, there are 70 different types of pizzas could be ordered
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The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There is one dot above 2, 4, 8, and 9.There are two dots above 6 and 7. There are three dots above 3.
Which measure of center is most appropriate to represent the data in the graph, and why?
Answers
The mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.
The most appropriate measure of center to represent the data in the given line plot is the mode.
The mode is the value or values that occur most frequently in a dataset. In this case, we can observe the frequencies of the data points on the line plot:
There is one dot above 2, 4, 8, and 9.
There are two dots above 6 and 7.
There are three dots above 3.
Based on this information, the mode(s) of the dataset would be the values that have the highest frequency. In this case, the mode is 3 because it appears most frequently with a frequency of three. The other data points have frequencies of one or two.
The mode is particularly appropriate in this scenario because it represents the most common or frequently occurring value(s) in the dataset. It is useful for identifying the central tendency when the data is discrete and there are distinct peaks or clusters.
While the median and mean are also measures of center, they may not be the most appropriate in this case. The median represents the middle value and is useful when the data is ordered. However, the given line plot does not provide an ordered arrangement of the data points. The mean, on the other hand, can be affected by outliers and extreme values, which may not accurately represent the central tendency of the dataset in this scenario.
Therefore, the mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.
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Please help me ASAP!!!
Answers
1. 7:4 = 21:x; what is the value of x?
A. 12
B. 10
C. 8
D. 6
E. 4
8.
Answers
Answer:
x = 12
I hope it's helps you
PLEASE I WLL GIVE BRAINLIEST JUST HELPS MEEEEE OMG IM ON MY SECOND ATTEMPT PLS PLS PLS HELP
Answers
Answer:
\( \purple { \bold{ \frac{ (x - 3)}{3x - 18} }}\)
Step-by-step explanation:
\( \frac{x + 3}{ {x}^{2} + 7x + 12 } . \frac{ {x}^{2} + x - 12}{3x - 18} \\ \\ = \frac{x + 3}{ {x}^{2} + 4x + 3x + 12 } . \frac{ {x}^{2} + 4x - 3x - 12}{3(x - 6)} \\ \\ = \frac{x + 3}{ {x}(x + 4) + 3(x + 4) } . \frac{ {x}(x + 4) - 3(x + 4)}{3(x - 6)} \\ \\ = \frac{ \cancel{(x + 3)}}{ (x + 4) \cancel{(x + 3)} } . \frac{ (x + 4) (x - 3)}{3(x - 6)} \\ \\ = \frac{1}{ \cancel{ (x + 4)} } . \frac{ \cancel{ (x + 4)} (x - 3)}{3(x - 6)} \\ \\ \red{ \bold{= \frac{ (x - 3)}{3x - 18} }}\\ \\ \)
Find the derivative of the following function at x = 12. f(x) = 7x2
Answers
\(\text{Given that,}\\\\f(x) = 7x^2\\\\f'(x) = 7\cdot 2 x = 14x\\\\\text{At x = 12,}\\\\f'(12) = 14 \times 12 = 168\)
Complete the sentence.
The horizontal asymptote of f(x) = 0.8x is y = 0.
The horizontal asymptote of h(x) = 0.8x– 10 is y =
Answers
The functions are not fractions and do not have a denominator so there is no horizontal asymptote.
The answer is 0
Answer: the answer is -10
Step-by-step explanation:
the asymptote is always k
y = f(x+k) or y = f(x-k)
Use a trigonomic ratio to find the value of x
Answers
The value of side x in of the right triangle is 4.8 unit.
What is the value of x?The figure is in the image is a right triangle.
Given that;
Angle θ = 40°Adjacent to angle θ = xOpposite to angle θ = 4To determine the value of x, we use trigonometric ratio
Tangent = Opposite / Adjacent
tan( 40 ) = 4 / x
x = 4 / tan( 40 )
x = 4.8
Therefore, the measure of side x is 4.8 units.
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a 10-question multiple-choice exam offers 5 choices for each question. jason just guesses the answers, so he has probability 1/5 of getting any one answer correct. you want to perform a simulation to determine the number of correct answers that jason gets. what would be a proper way to use a table of random digits to do this? one digit from the random digit table simulates one answer, with 5
Answers
By using a table of a random number in this manner, you can simulate the number of correct answers Jason might get on a 10-question multiple-choice exam with 5 choices for each question.
To perform a simulation using a table of random digits to determine the number of correct answers Jason gets on a 10-question multiple-choice exam, follow these steps:
1. Assign each answer choice a digit from 0 to 4. For example, A=0, B=1, C=2, D=3, and E=4.
2. Determine the correct answers for each question and note down the corresponding digits. For example, if the correct answers are A, B, C, D, and E for the first five questions, the correct answer digits would be 0, 1, 2, 3, and 4.
3. Select a starting point in the table of random digits. You can choose any point, as long as you use a consistent method to move through the table.
4. For each question, compare the random digit in the table to the correct answer digit. If the digits match, that means Jason guessed the answer correctly.
5. Move to the next random digit in the table for the next question, until you have simulated all 10 questions.
6. Count the number of correct answers based on matching digits and record the result.
7. Repeat steps 3 to 6 multiple times to get a more accurate estimate of Jason's expected number of correct answers. You can use different starting points in the table for each repetition.
8. Calculate the average number of correct answers from all the repetitions to estimate Jason's performance when guessing the answers.
By using a table of a random number in this manner, you can simulate the number of correct answers Jason might get on a 10-question multiple-choice exam with 5 choices for each question.
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