Which values represent solutions to Cosine (StartFraction pi Over 4 EndFraction minus x) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction sine x, where x Is an element of [0, 2Pi)?
Left-brace 0, pi right-brace
Left-brace 0, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace pi, StartFraction 3 pi Over 2 EndFraction
Answers
Answer:
C.
Step-by-step explanation:
got it right on edge :)
The given trig function consist of trig values of common angles;
The values that represent the solution to \(\mathbf{cos \left(\dfrac{\pi}{4} - x\right)} = \dfrac{\sqrt{2} }{2} \cdot sin \, x\), x ∈ [0, 2·π) are;
\(x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}\)
Reason:
The given function is presented as follows;
\(cos \left(\dfrac{\pi}{4} - x\right) = \dfrac{\sqrt{2} }{2} \cdot sin \, x\)
Where;
x ∈ [0, 2·π)
We have;
cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)
\(cos \left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}, \ sin\left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}\)
Which gives
\(cos \left(\dfrac{\pi}{4} - x\right) =\dfrac{\sqrt{2} }{2} \cdot cos \, x + \dfrac{\sqrt{2} }{2} \cdot sin \, x\)
Therefore, we get;
\(\dfrac{\sqrt{2} }{2} \cdot cos \, x = \dfrac{\sqrt{2} }{2} \cdot sin \, x - \dfrac{\sqrt{2} }{2} \cdot sin \, x = 0\)
cos x = 0
\(cos \left(\dfrac{\pi}{2} \right) = 0\)Therefore;
The possible solutions (x-values) to cos x = 0 are; \(0 \leq \dfrac{n \cdot \pi}{2} \leq 2 \cdot \pi\)Where;
n = 1, 3, 5, ...
x ∈ [0, 2·π)
We get;
\(x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}\)Learn more here:
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Related Questions
A researcher believes that on average, the span (distance from thumb to finger) of a person’s dominant hand is greater than that of their non-dominant hand. To investigate her belief, she randomly sampled 35 individuals for the study. She measured and recorded the spam (in centimetres) of both the dominant and the non-dominant hands of each of the individuals in the study. WHICH of these statistical techniques would be the MOST appropriate?
A researcher believes that on average, the span (distance from thumb to finger) of a person’s dominant hand is greater than that of their non-dominant hand. To investigate her belief, she randomly sampled 35 individuals for the study. She measured and recorded the spam (in centimetres) of both the dominant and the non-dominant hands of each of the individuals in the study. WHICH of these statistical techniques would be the MOST appropriate?
ANOVA
Paired samples t test
Independent samples t test
Wilcoxon’s matched pairs sign rank test
Mann-Whitney U test
Answers
The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.
To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.
The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.
The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:
- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.
- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.
- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.
Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.
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What does Thanksgiving have in common with Halloween?
Answers
Answer:
They are both Holidays. People also put up decorations for both.
Thanksgiving has in common with Halloween are:
- They are both celebrated in the fall season.
- They often involve gathering with family and friends.
What are cultural events?Cultural events are social gatherings or activities that celebrate or showcase the values, traditions, beliefs, and customs of a particular community or society.
We have,
Thanksgiving and Halloween:
Both are holidays celebrated in the United States, but they are very different in terms of their origins and traditions.
- One thing they have in common is that they are both celebrated in the fall season.
Halloween is celebrated on October 31st, while Thanksgiving is celebrated on the fourth Thursday of November.
- Another thing they have in common is that they often involve gathering with family and friends.
On Thanksgiving, people often have large family meals and give thanks for their blessings.
On Halloween, people may have costume parties or go trick-or-treating with friends and family.
Thus,
Thanksgiving has in common with Halloween are:
- They are both celebrated in the fall season.
- They often involve gathering with family and friends.
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the value of “y” varies directly with “x”. if y= 56, then x= 4
Answers
The opposite of the sum of -7 and y
Please help!!
Answers
Answer:
7 - y
Step-by-step explanation:
The sum of -7 and y: -7 + y
The opposite of the sum: -(-7 + y) = 7 - y
Step-by-step explanation:
The sum of -7 and y:-7+ y
The opposite of the sum: -(-7 + y) = 7 - y
fast pls? evaluate sin30 + tan45 - cosec60 / sin30 + cos45 + cot45
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\( \frac{ \sin(30) + \tan(45) - \csc(60) }{ \sin(30) + \cos(45) + \cot(45) } = \\ \)
\( \frac{ \frac{1}{2} + 1 - \frac{1}{ \frac{1}{2} } }{ \frac{1}{2} + \frac{ \sqrt{2} }{2} + 1 } = \\ \)
\( \frac{ \frac{1}{2} + \frac{2}{2} - 2 }{ \frac{1}{2} + \frac{ \sqrt{2} }{2} + \frac{2}{2} } = \\ \)
\( \frac{ \frac{3}{2} - \frac{4}{2} }{ \frac{3 + \sqrt{5} }{2} } = \\ \)
\( \frac{ - \frac{1}{2} }{ \frac{3 + \sqrt{2} }{2} } = \\ \)
\( - \frac{1}{3 + \sqrt{2} } \\ \)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
how to get easy points: make two acounts, on the second acount answer random question to get points, then make questions that have a lot of points, on the first acount answer the questions that you made. repeat.
Answers
Answer:
the bro ik
Step-by-step explanation:
yup yup yup bri
Answer:
heyyyy
Step-by-step explanation:
What is the image point of (9,0) after a translation left 2 units and up 5 units?
Answers
Answer:
(7, 5)
Step-by-step explanation:
9-2=7 x-coordinate
0+5=5 y-coordinate
a woman whose mother is colorblind and whose father has hemophilia a is pregnant with a boy. what is the probability that her son will have normal vision and normal blood clotting? enter as a probability value between 0 and 1.
Answers
The required probability of the son with normal vision is 0.50 and for the normal blood clotting is 0.
If mutations is present on one of the X chromosome then it is capable of developing the condition which is called X-linked disorder.Generally men are affected by this disorder because they carry one copy of the X chromosome.If women carry one copy of the chromosome, then it is consider that they are carriers of disease and if they have both the copies affected then they are affected by disorder.Colorblind woman with a normal man is in position to produce 2 carrier females and 2 males colorblind.In the condition of a carrier woman with colorblindness marries a hemophilic man, progeny mentioned below phenotypes are produced:Parent phenotype Carrier woman
Affected man (Hemophilic) (colorblindness)
Parents X^h Y XX^C
Gametes X^h, Y X, X^C
Progeny X X^h X^C X^h X^C Y, XY
Total outcome = 100
Favourable outcomes for a son with normal vision is= 50
Probability of a son with normal vision = 50/100
= 0.50
probability of a son with normal blood clotting = 0 / 100
= 0
Therefore, the probability of the son with normal vision and normal blood clotting is 0.50 and 0 respectively.
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A recent college graduate is looking to begin saving for retirement. option a is a savings account with 3.5% annual simple interest. option b is a savings account with 3.5% annual interest compounded monthly. if the principal investment is the same for both options, which account would have a larger balance after 10 years?
Answers
Option B, the savings account with 3.5% annual interest compounded monthly, would have a larger balance after 10 years.
Simple interest is calculated by multiplying the principal investment by the annual interest rate.
Compound interest is calculated by adding the interest earned in each compounding period (in this case, each month) to the principal balance, and then calculating the interest on the new balance for the next compounding period.
This means that compound interest earns interest on the interest earned in previous compounding periods, leading to a larger balance over time compared to simple interest.
To calculate the balance of the savings account with 3.5% annual interest compounded monthly after 10 years, we can use the formula:
A = P * (1 + r/n)^(nt)
where A is the balance after t years, P is the principal investment, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years.
For this savings account, n = 12 (since the interest is compounded monthly), t = 10, and r = 0.035.
Plugging these values into the formula, we get:
A = P * (1 + 0.035/12)^(12 * 10)
The balance of the savings account with simple interest after 10 years can be calculated by multiplying the principal investment by the annual interest rate and then multiplying by the number of years:
A = P * (1 + 0.035 * 10)
Comparing the two formulas,
it is clear that the balance with compound interest will be larger after 10 years, as the balance grows faster due to the interest earned on the interest in each compounding period.
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A rectangle where the ratio of the width to length is 5 : 9.
If the perimeter of the rectangle is 448 in, find the length and width.
Steps to solve please
Answers
Answer:
length=80m
breadth=144m
hope it is helpful for you
Breadth 144
(3 points) how many bit strings of length 7 are there? 128 how many different bit strings are there of length 7 that start with 0110? 8 how many different bit strings are there of length 7 that contain the string 0000?
Answers
there are 128 different bit strings of length 7. To calculate the number of bit strings of length 7, we need to consider that each position in the bit string can either be 0 or 1.
Since there are 7 positions in the string, we have 2 options (0 or 1) for each position. Therefore, the total number of bit strings of length 7 is 2^7 = 128.To calculate the number of bit strings of length 7 that start with 0110, we need to fix the first four positions as 0110. The remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that start with 0110 is 2^3 = 8.
To calculate the number of bit strings of length 7 that contain the string 0000, we need to consider the possible positions for the string 0000. It can occur in five different positions: at the beginning, at the end, or in any of the three middle positions. For each position, the remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that contain the string 0000 is 5 * 2^3 = 40. However, we need to subtract the cases where the string 0000 occurs in both the beginning and end positions, as they were counted twice. So, the final answer is 40 - 24 = 16.
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The following figure was drawn using a straightedge and a compass. Where was the point of the compass located in order to make the arcs?
1. points X and Y
2. point D
3. point C
4. points A and B
The slopes of the sides of quadrilateral ABCD are shown in the table below. Which statement describes the relationships between the sides of the quadrilateral?
1. AD¯¯¯¯¯¯¯¯ is not parallel to BC¯¯¯¯¯¯¯¯, and AB¯¯¯¯¯¯¯¯ is not parallel to CD¯¯¯¯¯¯¯¯.
2. AB¯¯¯¯¯¯¯¯ is parallel to CD¯¯¯¯¯¯¯¯, but AD¯¯¯¯¯¯¯¯ is not parallel to BC¯¯¯¯¯¯¯¯.
3. AB¯¯¯¯¯¯¯¯ is parallel to CD¯¯¯¯¯¯¯¯, and AD¯¯¯¯¯¯¯¯ is parallel to BC¯¯¯¯¯¯¯¯
4. AD¯¯¯¯¯¯¯¯ is parallel to BC¯¯¯¯¯¯¯¯, but AB¯¯¯¯¯¯¯¯ is not parallel to CD¯¯¯¯¯¯¯¯
Answers
Statement which describes the relationships between the sides of the quadrilateral ABCD is AD is not parallel to BC, and AB is not parallel to CD.
What is a quadrilateral?A quadrilateral in geometry is a four-sided polygon with four sides and four corners (vertices). The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name. In reference to other polygons, it is also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). An anagram of "angle," "gon" is sometimes referred to as a quadrangle or 4-angle.ABCD is sometimes used to indicate a quadrilateral with the vertices A, B,C, and D.There are two types of quadrilaterals: simple (not self-intersecting) and complex (self-intersecting, or crossed). Convex or concave quadrilaterals are simple quadrilaterals.A simple (and planar) quadrilateral ABCD's internal angles sum up to 360 degrees of arc.That is, ∠A+∠B+∠C+∠D=360°Hence, statement which describes the relationships between the sides of the quadrilateral ABCD is AD is not parallel to BC, and AB is not parallel to CD.
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Statement which describes the relationships between the sides of the quadrilateral ABCD is AD is not parallel to BC, and AB is not parallel to CD.
What is a quadrilateral?A quadrilateral in geometry is a four-sided polygon with four sides and four corners (vertices).The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.In reference to other polygons, it is also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon).An anagram of "angle," "gon" is sometimes referred to as a quadrangle or 4-angle.ABCD is sometimes used to indicate a quadrilateral with the vertices A, B,C, and D.There are two types of quadrilaterals: simple (not self-intersecting) and complex (self-intersecting, or crossed).Convex or concave quadrilaterals are simple quadrilaterals.A simple (and planar) quadrilateral ABCD's internal angles sum up to 360 degrees of arc.That is, ∠A+∠B+∠C+∠D=360°
Hence, statement which describes the relationships between the sides of the quadrilateral ABCD is AD is not parallel to BC, and AB is not parallel to CD.
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Josie walks 3/4 mile in 1/5 hour. What is Josie's speed in miles per hour?
Answers
Find the area of hexagon DEFGHI.
Answers
Step-by-step explanation:
Break it up into two trapezoids as shown
area = trap1 + trap2
= 2 * (7+3) / 2 + 3 * ( 7 + 3) / 2 = 10 + 15 = 25 units^2
The population of weights of a particular fruit is normally distributed, with a mean of 535 grams and a standard deviation of 13 grams. If 8 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.
Answers
Pn(Z>zp)=1−p%
Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a
is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:
\(z=\frac{x-\mu}{\sigma}\)
The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.
The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.
Pn(Z>zp)=1−p%
Here Pn is the probability for the standard normal variable.
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can you guys please help me on this?
Answers
x= -5
Step by step:
Multiply both sides by 5
-20 = 3x - 5
Add 5 to both sides
-15 = 3x
Divide both sides by 3
-5 = x
And that’s all
Hope this helps!
Kamal is 17 years older than Gina. Gina is 3 years younger than Rachelle. If the sum of their ages is 77, how old is Gina?
Answers
Answer:
Answer : Gina's age is 19 years.
Step-by-step explanation:
Kamal is 17 years older than Gina. Gina is 3 years younger than Rachelle.
Let Gina's age be x years
So Kamal’s age will be = x + 17
Rachelle’s age = x + 3
the sum of their ages is 77, Accordingly
x + x + 17 + x + 3 = 77
3x + 20 = 77
3x = 77 - 20
3x = 57
x = 57/3
x = 19
Thus Gina's age is 19 years,
Kamal’s age x + 17 = 19 + 17 = 36 years
Rachelle’s age x + 3 = 19 + 3 = 22 years
Gina = 19 years old
If f(1) = 0, what are all the roots of the function ? use the remainder theorem.
Answers
By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.
A root of a function is a value for x that makes the function equal to zero.
In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.
The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.
So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.
Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.
The roots of f(x) will be the values of x that we used as factors in each step of the division process.
This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.
Complete Question
If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.
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Find the gradient vector field of f. f(x, y, z) = x cos 5y/z
Answers
So, the gradient vector field of f is (∇f) = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2).
To find the gradient vector field of the function f(x, y, z) = x cos(5y/z), we need to calculate the partial derivatives with respect to each variable and combine them into a vector.
The gradient vector is defined as:
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Taking the partial derivatives of f(x, y, z) with respect to each variable:
∂f/∂x = cos(5y/z)
∂f/∂y = -5x sin(5y/z)/z
∂f/∂z = 5xy sin(5y/z)/z^2
Putting these partial derivatives together, we have:
∇f = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2)
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Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?
One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.
Answers
Answer:
A. One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
Hope this Helps!
Answer:
you answer is A
Step-by-step explanation:
i got it right on the quiz
Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(7n+0.9)
Answers
Answer:
-7n - .9
Step-by-step explanation:
By distributing the - to the parentheses, you must add a - sign to each number in the parentheses. This makes the positives turn negative.
-7n-0.9=0
-7n=0.9
-n=7.78
n=7.78
A bakery has 40 different flavored muffins
Answers
Answer:
nice
Step-by-step explanation:
In a basketball game, Alison made 6 of 13 free shots.
Madhu made 5 of 9 free shots. Who played better? Explain.
Answers
Answer:
Madhu played better.
Step-by-step explanation:
Change both fractions to where they have the same denominator to see which one is bigger. The smallest possible denominator between the two fractions is 117.
To get the 13 in 6/13 to become 117, you had to multiply it by 9. Whatever you do to the denominator, you must do to the numerator.
6 x 9 = 54.
Allison's fraction is now 54/117.
To get the 9 in 5/9 to become 117, you had to multiply the 9 by 13. Whatever you do to the denominator, you must do to the numerator.
5 x 13 = 65
Madhu's fraction is now 65/117
By looking, 65 is larger than 54, so Madhu had a larger number of shots compared to shots not made than Allison.
i need help with this
Answers
Answer:
ok what here are u meant to do
classify the expression by both degree and terms 2x4 - x +5
Answers
Answer:
x=3
Step-by-step explanation:
Convert the following fraction to a decimal 3/10
Answers
Answer:
Step-by-step explanation: 0.3
Answer:
Step-by-step explanation:
1. The answer is 0.3.
1Q _____is neither a prime number nor a composite number
2Q the only even prime number is ______.
3Q A prime number has only_____ factors,______and_______.
4Q _______is the smallest prime number is_____.
5Q there are ______ prime numbers less then 20.
Answers
Answer for 2) Two
Answer for 3) A prime number has only two factors, one and two.
Answer for 4) Two is the smallest prime number [I don’t understand that wording so that’s the best I can come up with]
Answer for 5) There are eight prime numbers less than 20.
By first calculating the angle of LMN, calculate the area of triangle MNL. You must show all your working.
Answers
Answer:
16.66cm²
Step-by-step Explanation:
Given:
∆LMN with m<N = 38°
Length of side NL = 7.2cm
Length of side ML = 4.8cm
Required:
Area of ∆MNL
Solution:
Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b
Where sin(A) = Sin(M) = ?
a = NL = 7.2cm
sin(B) = sin(N) = 38°
b = ML = 4.8cm
Thus,
Sin(M)/7.2 = sin(38)/4.8
Cross multiply
4.8*sin(M) = 7.2*sin(38)
4.8*sin(M) = 7.2*0.6157
4.8*sin(M) = 4.43304
Divide both sides by 4.8
sin(M) = 4.43304/4.8
sin(M) = 0.92355
M = sin-¹(0.92355) ≈ 67.45°
Step 2: Find m<L
angle M + angle N + angle L = 180 (sum of angles in a triangle)
67.45 + 38 + angle L = 180
105.45 + angle L = 180
Subtract 105.45 from both sides
Angle L = 180 - 105.45
Angle L = 74.55°
Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)
Where,
a = NL = 7.2 cm
b = ML = 4.8 cm
sin(C) = sin(L) = sin(74.55)
Thus,
Area of ∆MNL = ½*7.2*4.8*0.9639
= ½*33.31
= 16.655
Area of ∆MNL ≈ 16.66cm²
PLEASE HELP ASAP!! PLEASE
Answers
Answer:
21 km
Step-by-step explanation:
I am not too sure if i did answer that correctly but the distance should not change even if it is in different directions
The volume of a sphere is 5000pi m^3 What is the surface area of the sphere to the nearest square meter?
Answers
Answer:
2nd chioce
Step-by-step explanation: