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
given that the great circle of a sphere has a radius of 2 feet, find the surface area of the sphere in terms of Pi
Answers
The surface area of a sphere is given by:
\(\begin{gathered} SA=4\pi r^2 \\ SA=4\pi(2^2) \\ SA=16\pi \end{gathered}\)When the two lines are parallel, corresponding angles are ___
a always congruent
b supplementary
c never congruent
Answers
Explanation: if a transversal intersected two parallel lines than both the lines of both angles would be parallel to each other making the angles congruent.
A bouncy ball is dropped such that the height of its first bounce is 4.5 feet and each successive bounce is 73% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
The height of the 10th bounce of the ball will be 0.6 feet.
What is geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
\(\sf T_n=ar^{n-1}\)
Where,
\(\sf T_n\) is the nth term.r is the common ratioa is the first termAccording to the given question.
During the first bounce, height of the ball from the ground, a = 4.5 feet
And, the each successive bounce is 73% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 10\)
\(=\dfrac{73}{100}(10)\)
\(\sf = 0.73 \times 10\)
\(\sf = 7.3 \ feet\)
During the third bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 7.3\)
\(=\dfrac{73}{100}(7.3)\)
\(\sf = 5.33 \ feet\)
Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.73
Therefore,
The sixth term of the geometric sequence is given by
\(\sf T_{10}=10(0.73)^{10-1\)
\(\sf T_{10}=10(0.73)^{9\)
\(\sf T_{10}=10(0.059)\)
\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)
Hence, the height of the 10th bounce of the ball will be 0.6 feet.
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Please helpppp HURYYYYYYY
Answers
Answer:
C
Step-by-step explanation:
Whats the Simplify form of (x^2/y)3
Answers
Answer:
\(\frac{3x^2}{y}\)
Pls help with this pls thanks
Answers
Answer:
The books in the library are 1040
A planner assembles party favor bags filled with glow sticks and temporary tattoos for a client. There are 24 glow sticks and 30 temporary tattoos to divide
evenly among the bags.
If there are no leftover items, what is the greatest number of bags the planner can assemble?
A. 6 bags
B.8 bags
C. 24 bags
D. 30 bags
Answers
Answer:
24
Step-by-step explanation:
you don't have more than 24 glow sticks so thats the most amount of bags you can have
over the weekend, jada made three times as much money babysitting than han did mowing lawns. jada made an additional $27 selling lemonade.
from babysitting and selling lemonade, she has a total of $96.
if the equation 3x+27=96 represents this situation, what does the variable x represent?
A). amount han made mowing lawns
B). amount jada made selling lemonade
C). total amount jada made
Answers
Answer:
23
Step-by-step explanation:
should be 23, start by subtracting 96-27 and from there you can divide that answer by3 to get x
Answer:
B). amount jada made selling lemonade
Step-by-step explanation:
Welcome for the answer. This answer is for good intentions only please don't report unless necessary. Have a great rest of your day!How do I answer,
Graph:
slope=5/3 (0, -2)
Answers
Required line is : \(y+2 = \frac{5}{3} x\)
What do you mean by slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of a linear equation y = mx + c. The values of m as well as c are real numbers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of a location where the line's graph crosses the y-axis.
Given , Slope, m = 5/3
Required line passes through (0,-2) and has slope m = 5/3.
So, Required line is : \(y+2 = \frac{5}{3} x\)
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To join the tennis club, there is a $10.20
initial fee and a $3.90 yearly fee. What
would be the value of the slope in this
situation?
Use this space to write down notes or work through problems
Your teacher will see what you wrate.
Answers
Answer:
10.20
Step-by-step explanation:
Let
y = Total fee
Initial fee = $10.20
Yearly fee = $3.90
Number of years = x
The equation:
y = 3.90x + 10.20
Recall,
y = mx + c
Where,
x = slope
c = y - intercept
Therefore,
The y - intercept from y = 3.90x + 10.20 is 10.20
Is 1.8 repeating rational or irrational number
Answers
Answer:
Irrational number
Step-by-step explanation:
The number 1.8 isn't repeating so it wouldn't be a repeating rational number.
Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
Answers
The gradient of line A is 4/72% or 0.0555.The gradient of line B is -2/6 or -0.3333.
What is value?Value is the worth of something, or the amount of importance, good qualities, or benefits that something has. It is determined by the amount of effort, time, and resources that have been put into it. Value can also refer to a person's moral or ethical principles and standards. It is the measure of worth that someone places on something or someone. Ultimately, value is subjective, as it is based on individual opinion.
The gradients of lines A and B indicate the rate of change of the line in relation to the x-axis. The gradient of line A is positive, which indicates that the line is increasing as it moves along the x-axis. This means that the y-value of the line is increasing as the x-value increases. On the other hand, line B has a negative gradient, which means that the y-value of the line is decreasing as the x-value increases. This means that the line is decreasing as it moves along the x-axis. This is why the gradients of lines A and B are different.
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A regular hexagon has sides of 3 feet. What is the area of the hexagon?
27 √3 ft 2
18 √3 ft 2
9 √3 ft 2
13.5 √3 ft 2
Answers
Answer:
13.5√(3) ft^2
Step-by-step explanation:
In this, question, we are to calculate the area of the hexagon
Mathematically, we can calculate the area of a hexagon using the formula;
A = {3√(3)/2}a^2
where a is the length of the side which is 3 feet
substituting the value of 3 into the formula, we have;
A = 3√3/2 * 3^2 = 27 √(3)/2 = 13.5√(3) ft^2
Answer:
13.5√(3) ft^2
Step-by-step explanation:
Drag the vertices of the triangle below to draw a right triangle with side lengths 10, 24, and 26.
16
15
Answers
Answer:
15 ? :)
Step-by-step explanation:
on average, what percentage of infants born to 45-year-old mothers have down syndrome? on average, what percentage of infants born to 45-year-old mothers have down syndrome? 1% 3% 8% 10% 30%
Answers
The number of infants born to 45-year-old mothers who have Down syndrome on average is approximately 1 in 30 or 3.33%. The Down disorder may be a hereditary clutter that happens when there's an additional duplicate of chromosome 21.
The chance of having a child with Down disorder increments with maternal age. Agreeing to the American College of Obstetricians and Gynecologists, at age 35, the hazard of having an infant with Down disorder is around 1 in 350, or 0.29%. By age 40, the hazard increments to around 1 in 100, or 1%. And by age 45, the chance is around 1 in 30 or 3.33%.
In any case, pre-birth testing can offer assistance distinguish the chance of Down disorder and other hereditary anomalies amid pregnancy. This will offer assistance to hopeful guardians to make educated choices approximately their pregnancy and their baby's wellbeing.
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find the product. give your answer as a simplified fraction. 5/6×5=?
Answers
To solve:
\(\frac{5}{6}\cdot5\)We multiply the denominator by 5:
\(\frac{5\cdot5}{6}=\frac{25}{6}\)To write it as a simplified fraction, we can note that 4 * 6 = 24
Then:
\(\frac{25}{6}=4\frac{1}{6}\)
Combine the methods of row reduction and cofactor expansion to compute the determinant.
∣
∣
−1
0
−3
6
−5
−4
−5
2
−4
−8
−4
2
−1
0
−1
0
∣
∣
The determinant is (Simplify your answer.)
Answers
The determinant of the given matrix, obtained through a combination of row reduction and cofactor expansion, simplifies to 192.
To compute the determinant using a combination of row reduction and cofactor expansion, we can use the following steps:
Step 1: Perform row operations to create a triangular matrix.
We can start by subtracting the first row from the second row multiplied by -5, and subtracting the first row from the third row multiplied by -4. Finally, subtract the first row from the fourth row.
The matrix becomes:
| -1 0 -3 6 |
| 0 -4 2 32 |
| 0 -8 8 10 |
| 0 0 2 6 |
Step 2: Compute the determinant of the triangular matrix by multiplying the elements on the main diagonal.
The determinant of an upper triangular matrix is the product of its diagonal elements.
det(A) = (-1) * (-4) * 8 * 6 = 192
Step 3: Calculate the sign of the determinant by multiplying (-1) raised to the power of the number of row swaps made during the row reduction. In this case, no row swaps were made, so the sign remains positive.
Step 4: Simplify the answer.
The determinant of the given matrix is 192.
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Alewuya invests a total of $29,000 in two accounts paying 15% and 6% annual interest, respectively. How
much was invested in each account if, after one year, the total interest was $2,685.00. $__was invested at 15% and
$__ invested at 6%.
Answers
1,611 will be your investment for the 6%
Multiplying by a positive number will give a positive product. TrueFalse
Answers
Answer:
true
Step-by-step explanation:
step by step please <3
Answers
Answer: 5/8 pounds
Step-by-step explanation:
\(\displaystyle\\\frac{15}{16} (\frac{2}{3} )=\\\\\frac{15(2)}{16(3)}=\\\\\frac{(3)(5)(2)}{(2)(8)(3)}=\\\\\frac{5}{8} \ pounds\)
a bar chart might be used for
Answers
When presenting chunks of information, bar charts should be used. As long as there aren't too many categories to contrast, vertical bar charts can be useful for comparing several discrete or categorical variables, such as age groups, courses, and schools. For time series data, they are also highly beneficial.
Why would one use a bar chart?
To show a frequency distribution for qualitative data, bar charts are frequently employed.
The axis used to measure the bars should always begin at zero, unless there is a valid reason for doing otherwise.
Otherwise, the axis can be stretched to magnify differences in the lengths of the bars. A title and the axis labels are required for bar charts.
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For each equation, determine whether it is linear.
Equation
(a) y=x-6
(b) y=2x²-1
(c) y=6x
(d) y=-x³
Is the equation linear?
Yes
No
Answers
Answer:
Step-by-step explanation:
For an equation or function be linear, it should be in the form:
Y= mX +b
then
a) YES Linear
b) NO linear
c) YES Linear
d) NO linear
The cost of three tickets to a movie is at least $20. Write and solve an inequality that represents the situation.
Answers
x>20/3
x>6.67 so the price of one ticket is at least 6.67 $
(Mark me the brainliest if this was helpful)
If 60% of all women areemployed outside the home, find the probability that in a sample of20 women,
a. Exactly 15 are employed outside the home.
b. At least 10 are employed outside the home.
c. At most 8 are employedoutside the home
Answers
The probability of exactly 15 are employed outside the home is 0.209, at least 10 are employed outside the home is 0.9726, and at most 8 are employed outside the home is 0.12020.
Given that, 60% of all women are employed outside the home. Let P (E) be the probability of employed women.
Then P(E) = 60 / 100 = 0.6 We need to find the probability that in a sample of 20 women,
Exactly 15 are employed outside the home.
At least 10 are employed outside the home.
At most 8 are employed outside the home.
a. To find the probability of exactly 15 employed women, we use the Binomial distribution.
The probability of exactly r successes in n independent Bernoulli trials is P (X = r) = nCr (p)^r (q)^(n-r)
Here, n = 20, r = 15, p = 0.6, q = 0.4
So, P (X = 15) = nCr (p)^r (q)^(n-r)= 20C15 (0.6)^15 (0.4)^5= 0.209
b. To find the probability of at least 10 employed women,
we use the complement of P(X ≤ 9).P(X ≥ 10) = 1 – P(X ≤ 9)So, P(X ≥ 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=9)] = 1 - F(9)
Here, F(9) is the cumulative probability when x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Using the binomial distribution formula,
we find: F(9) = P(X ≤ 9) = ΣP(X = i) = ΣnCi (p)^i (q)^(n-i) i=0 to 9Now, n = 20, p = 0.6, q = 0.4
Hence, P(X ≥ 10) = 1 - F(9) = 1 - P(X ≤ 9) = 1 - ΣnCi (p)^i (q)^(n-i) i=0 to 9= 1 - (0.00045 + 0.00604 + 0.04162 + 0.15580 + 0.35131 + 0.42331 + 0.26801 + 0.08722 + 0.01525 + 0.00121)= 0.9726
c. To find the probability of at most 8 women employed outside the home,
we use the binomial distribution formula, and P (X ≤ 8).P(X ≤ 8) = ΣP(X = i) = ΣnCi (p)^i (q)^(n-i) i=0 to 8
Now, n = 20, p = 0.6, q = 0.4So, P(X ≤ 8) = ΣnCi (p)^i (q)^(n-i) i=0 to 8= 0.00015 + 0.00257 + 0.01831 + 0.07151 + 0.17355 + 0.29002 + 0.33539 + 0.22957 + 0.07832= 0.12020
Therefore, the probabilities are as follows:
a. Exactly 15 are employed outside the home = 0.209
b. At least 10 are employed outside the home = 0.9726
c. At most 8 are employed outside the home = 0.12020
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Type the correct answer in each box. spell all words correctly.
what are the different computer hardware components that entrepreneurs must be familiar with?
entrepreneurs must have sound knowledge of computer hardware and its three components: input devices, output devices, and
(blank) or system units.
Answers
Entrepreneurs must have a solid understanding of computer hardware and its essential components.
These components include input devices, such as keyboards and mice, which allow users to provide commands and data to the computer. Output devices, like monitors and printers, display or produce the results of computer processing. Additionally, entrepreneurs should be familiar with the central processing unit (CPU) or system unit, which serves as the "brain" of the computer, executing instructions and performing calculations.
The CPU consists of the motherboard, memory modules, and the processor itself. Having knowledge of these hardware components enables entrepreneurs to make informed decisions regarding their computing needs, troubleshoot issues, and effectively utilize technology to support their business operations.
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Write the following fraction as a decimal.
one and four-tenths
1.14
1.04
1.4
0.14
Answers
Answer: 1.4
Step-by-step explanation:
[Question 1] You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium. During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population. F
Answers
:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.
During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.
According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes
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I have attached a picture of the question.
Answers
Answer:
B: 1
Step-by-step explanation:
I'm not sure what kind of given information that is, but here is my explanation:
f(x) = g(x) and values for both are given, so we combine their contents into one function: 3 - 6x = 5x - 8. Add 6x on both sides then add 8 on both sides, that'll get you 11x = 11. Divide both sides by 11 and you'll get x = 1.
What does 2x-9=7x-44
Answers
Answer:
Isolate the variable by dividing each side by factors that doesn't contain the variable.
Exact form: x = 154/9
Decimal form: x = 17.1
Mixed number form: x = 17 1/9
Step-by-step explanation:
hope that helps...
have a good day
On a certain hot summer's day, 360 people used the public swimming pool. The daily prices are $1.50 for children and 2.25 for adults. The receipts for admission totaled How many children and how many adults swam at the public pool that day?
Answers
Using a system of equations, the number of children who swam at the public pool that day was 268 while adults were 92.
What is a system of equations?A system of equations involves two or more equations solved simultaneously.
It is known as a system of equations or simultaneous equations.
The total number of people who used the public swimming pool = 360
Children's ticket = $1.50
Adult's ticket = $2.25
Total receipts on that day = $609
Let's form the following equations:
Let the number of children = x
Let the number of adults = y
x + y = 360 ... equation 1
1.50x + 2.25y = 609 ... equation 2
From equation 1, y = 360 - x ... equation 3
In equation 2, replace y = 360 - x and solve:
1.5x + 2.25(360 - x) = 609
1.5x + 810 - 2.25x = 609
-0.75x = -201
x = 268
In equation 3, replace x = 268 to find y:
y = 360 - 268
y = 92
Check:
Equation 2:
1.50x + 2.25y = 609
1.50(268) + 2.25(92) = 609
402 + 207 = 609
609 = 609
Thus, with our simultaneous equations, we can conclude that 268 children and 92 adults graced the swimming on that hot summer's day.
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Question Completion:The admission receipts totaled $609.