Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Answers
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]Related Questions
You have discovered another alien.
What is the equation of the line that provides the correct path to rescue this alien?
Answers
Answer:
what is the equation of the line that provides the correct path to rescue this alineAnswer:
✔ y = 0x + 0
Step-by-step explanation:yes
The perimeter of a rectangle is to be between 140 and 220 inches. FindThe range of values for its length when its width is 20 inches
Answers
The lower value of the perimeter is 140 inches .
Width of the rectangle is 20 inches .
The length of the rectangle is calculated as ,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Rearranging the terms ,
[tex]\begin{gathered} \text{Length + 20 = }\frac{140}{2} \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}[/tex]The higher value of perimeter is 220 inches .
Width of the rectangle is 20 inches .
The length is calculated as,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}[/tex]Thus the range of values for the length of the given rectangle are 50 and 90 .
X=
/////////////////////
Answers
Answer: [tex]x=15[/tex]
Step-by-step explanation:
By the consecutive interior angles theorem,
[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]
Consider the following trapezoid.
Find the value of X.
(Helpful for math-space users)
Answer; y = 108
Explanation;
x + 72 = 180
X=180-72
Answers
The value that represents the variable x in the trapezoid is 108 degrees
How to determine the value of x?From the question, the trapezoid represents the given parameter
We can see that the trapezoid is an isosceles triangle
This means that the angle x and y are congruent
The sum of angles is a trapezoid is 360 degrees
So, we have the following summation equation
x + x + 72+ 72 = 360
Evaluate the like terms
So, we have
2x + 144= 360
This gives
2x = 216
Divide by 2
x = 108
Hence, the value of x is 108 degrees
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Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles away from the airport and Plane 2 is 200 miles away from the airport. If the 2 planes are 175 miles away from each other, what is the angle measurement from the airport to the 2 planes? (round to the nearest whole number)
Answers
To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:
Then;
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]Since we want to find the measure of angle x, we can use:
c = 175 mi
a = 200 mi
b = 50 mi
C = x
Now, by the Law of Cosines:
[tex]175^2=200^2+50^2-2\cdot200\cdot50\cdot\cos(x)[/tex]And solve:
[tex]30625=40000+2500-20000\cos(x)[/tex][tex]30625-40000-2500=-20000\cos(x)[/tex][tex]\frac{-11875}{-20000}=\cos(x)[/tex][tex]\begin{gathered} x=\cos^{-1}(0.59375) \\ . \\ x\approx53.5764 \end{gathered}[/tex]To the nearest whole number, x = 54°
this is NOT a test or Quiz its a homework pic is below
Answers
From the information given,
Jack wants to eat 2 1/5 of his plate in 1/3 hour. The first step is to convert 2 1/5 to improper fraction. It becomes 11/5
The statement would be
Jack wants to eat 11/5 of his plate in 1/3 hour.
Let x represent how much of his plate that he will eat in 1 hour. Therefore
11/5 = 1/3
x = 1
By cross multiplying, it becomes
x * 1/3 = 1 * 11/5
x/3 = 11/5
x = 11/5 * 3
x = 33/5
Converting to mixed fraction, it becomes
6 3/5
The correct option is the first one
Can someone tell me what x and y is and how to solve for it
Answers
[tex]2x = 76[/tex]
Due to alternate angles
[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]
40°+(y-8)°+76°=180°(sum of angles in a triangle)
[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]
ATTACHED IS THE SOLUTION.
Answer:
x = 38 ; y = 72
Step-by-step explanation:
180 = 76 + 40 + (y - 8)
180 = 108 + y
72 = y
The triangle has parallel lines, so the uppermost right angle is also 90 degrees.
90 - 76 = 14
180 = 90 + 14 + 2x
180 = 104 + 2x
76 = 2x
38 = x
This question has two parts. First, answer Part A. Then, answer Part B.
part A:
Answers
The length of the incline of the ramp will be [h] = 12.0415 ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft
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[This question also has part B. Visit the following link for part B -
https://brainly.com/question/28956732]
a road running north to south crosses a road going east to west at the point pp. cyclist aa is riding north along the first road, and cyclist bb is riding east along the second road. at a particular time, cyclist aa is 3939 hundred meters to the north of pp and traveling at 3232 meters per second, while cyclist bb is 5252 hundred meters to the east of pp and traveling at 2424 meters per second. how fast is the distance between the two cyclists changing? the distance between the two cyclists is increasing by 1925 meters per second.
Answers
The distance between the two cyclists changing exists 38.4 meters per second.
What is meant by differential equation?A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others.
There exists at least a couple of ways to work this. One exists to write the equation for the distance between the cyclists and differentiate it.
d² = (3900 + 32t)² + (5200 + 24t)²
simplifying the above equation, we get
(2d)d/dt = 2(3900 + 32t)(32) +2(5200 + 24t)(24)
At t = 0,
dd/dt = (32·3900 + 24·5200)/√(3900² + 5200²)
simplifying the above equation, we get
= (124800 + 124800)/√(15210000 + 27040000)
= 249600/6500 = 38.4 meters per second
Therefore, the distance between the two cyclists changing exists 38.4 meters per second.
The complete question is:
A road running north to south crosses a road going east to west at the point P. Cyclist A is riding north along the first road, and cyclist B is riding east along the second road. At a particular time, cyclist A is 39 hundred meters to the north of P and traveling at 32 meters per second, while cyclist B is 52 hundred meters to the east of P and traveling at 24 meters per second. How fast is the distance between the two cyclists changing?
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Jim sits on a seesaw. If Jim weighs 100 pounds, what mass in kilograms does the person on the other side need to be for the seesaw to be balanced?
Answers
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
The teacher recommends that students read for 20 minutes each night how many pages will the students complete
Answers
The number of pages read by the student at the constant rate in 20 minutes is 10 pages.
What is termed as the constant rate?In math, a constant rate is the exclusion of acceleration. A function with such a constant rate, in general, has a second derivative of 0. The function would be a straight line if plotted on standard graph paper because the change in y (or rate) would've been constant. Whenever the value of x increases, a value of y does not change.That is, the y value does not change, and the graph is just a horizontal line.For the given question,
The rate at which the student reads the book is given by equation;
y = (1/2)x.
Consider the data from the table given.
For 1 minutes the pages read is 0.5.
From the recommendation of 20 pages by the teacher.
Thus, for 20 min, put the value x = 20 in the equation.
y = (1/2)×20
y = 10 pages.
Thus, the number of pages read by the student at the constant rate in 20 minutes is 10 pages.
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The complete question is-
A student reads at a constant rate in her chapter book, Where the Red Fern Grows. This can be described by the equation
y = (1/2)x. The chart above is complete. The teacher recommends that students read for 20 minutes each night. How many pages will the student complete?
Please help me I only have 3 minutes left to do this
Answers
486lb of grass seed is required to cover the field on the right.
What is Area of Rectangle?The area of Rectangle is length times of width
Let us find the areas of two rectangle larger and smaller.
Area of the larger rectangle:
60×90=5400 square feet.
Now divide the larger square area by the smaller square area:
Area of the smaller rectangle
40×50=200 square feet.
Now divide larger rectangle with smaller
5400/200 =27
27 is the ratio of the difference
27×18=486 lb.
Hence 486lb of grass seed is required to cover the field on the right.
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63 ÷ 5 = 12 R3 solve the problem
Answers
Answer:
12r^3
Step-by-step explanation:
If Susie's age is 8 less than 3 times her brother's age, and Susie is 13. How old is her brother?
Answers
Answer:
correct me if im wrong but my answer is x=7, or in other words, 7.
Step-by-step explanation:
Answer:
7 years old
Step-by-step explanation:
You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13
The Answer, 7 years old
What is the simple interest rate on an account that earned $56.25 in interest after two and one-half years on a principal balance of $300? please show work
Answers
The rate of interest on the given principal is 7.5%.
Given that, simple interest = $56.25, principal = $300 and time period = [tex]2\frac{1}{2}[/tex] years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 56.26 = (300 × R × 2.5)/100
⇒ 5625 = 750R
⇒ R = 7.5%
Therefore, the rate of interest on the given principal is 7.5%.
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3x+y-77=0
Can anyone help me with this question it would really help me out
Answers
the answer is in the photo I took of solving it
Pick one of the remaining choices and explain on the lines below, why thatchoice contains two expressions that are not equivalent for any value of r.
Answers
If two expressions have the same coefficients of the variable, then the variable can be any number
For the first choice
3(3r + 3) = 9r + 9 === 1st expression
6r + 6 ===== 2nd expression
If we equate them
9r + 9 = 6r + 6
If we solve the equation we will find just one value of r
9r + 9 - 6r = 6r - 6r + 6
3r + 9 = 6
3r + 9 - 9 = 6 - 9
3r = -3
r = -1
But in the other choices, the two expressions have the same coefficients of r
Then when we equate them they will cancel each other
Then r can be any value
Because it does not affect the equation
What percentage of the numbers from 1 to 20 contain the digit 2?
Answers
3/20 = 0.15
Answer: 15%
you constructed a pairwise ranking of four events w, x, y, and z and came up with the following assessment: x is more likely than z y is more likely than x w is more likely than x what needed information is missing that prevents you from completing this analysis?
Answers
The relation between the events Y and W prevents us from completing the analysis.
The relation between the events Y and W prevents us from completing the analysis.
Case 1: W is more likely than Y then we have the following analysis:
Z, X, Y, and W are arranged in ascending order of more likeliness.
Case 2: Y is more likely than W then we have the following analysis:
Z, X, W, and Y are arranged in ascending order of more likeliness.
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Subtract.
−3−6−(−1) = ?
Answers
Answer:
-8
Step-by-step explanation:
An acorn fell from a branch 20 feet high and landed on a branch 7 feet high. How long did it
take the acorn to fall?
Answers
It will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
What is defined as the speed of object?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.For the given question,
An acorn fell from a branch 20 feet high.
An acorn landed on a branch 7 feet high.
The total distance travelled by and acron is 20 - 7 = 13 feet.
Let the final velocity of an acron is 'v'.
The initial velocity of an acron 'u' is zero.
Using third equation of straight line.
v² = u² + 2gsu = 0g = 9.8 /sec²s = 13 feetPut the values.
v² = 2×9.8×13
v = 15.96 ft/sec
Put the value in first equation of straight line.
v = u + gt
15.96 = 0 + 9.8×t
t = 15.96/9.8
t = 1.62 seconds.
Thus, it will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
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Can you write a quadratic function that does not have a y-intercept?
Answers
Answer:
The graph of a quadratic function will always have one y-intercept
Step-by-step explanation:
suppose the number of hours of sleep students get per night has a unimodal and symmetric distribution with a mean of 7 hours and a standard deviation of 1.5 hours. approximately what percent of students sleep more than 8.5 hours per night?
Answers
Approximately 34% of people sleep more than 8.5 hours per night.
According to the Empirical Rule states for a normally distributed random variable: 68% of the measures are within 1 standard deviation of the mean, 95% of the measures are within 2 standard deviations of the mean and 99.7% of the measures are within 3 standard deviations of the mean. According to the question, Mean = 7 and Standard deviation = 1.5. Also, in the question the normal distribution is symmetric, which means that 50% of the measures are below the mean and the rest 50% are above the mean. Now, the mean is 7 and 8.5 is 1 one standard deviation above the mean. So, by the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (more than 8.5 hours). So, we get
0.5*0.68 = 0.34 which is equal to 34%.
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WILL GIVE BRAINLIEST!!! solve the problem fill in the blanks to show your work
Answers
By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The four mathematical operations are functions that take input values, or numbers, and turn them into output values, or yet another number. They are multiplication, division, addition, and subtraction.So, the values in the blank will be:
= - 1.2(2/5) ÷ -2= -1.2(0.4) ÷ -2= - 0.48 ÷ -2= 0.24Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
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Mike had 28 books. His brother Joseph decided to give one third of his books to Mike. After that, Joseph and Mike had the exact same number of books. How many books did they have altogether?
Answers
SOLUTION
Given the question in the question tab, the following are the solution step to get the number of books they have altogether.
Step 1: Write the notations for Joseph's and Mike's books
[tex]\begin{gathered} \text{let j represents the number of books Joseph has,} \\ \text{let m represents the number of books Mike has} \end{gathered}[/tex]Step 2: Write the statements in a mathematical form
[tex]\begin{gathered} m=28---\text{statement 1} \\ \frac{1}{3}of\text{ j was given to Mike to have }m+\frac{j}{3}=28+\frac{j}{3} \\ \text{After that, }28+\frac{j}{3}=\frac{2j}{3} \end{gathered}[/tex]Step 3: Solve to get the value of j by using substitution method
[tex]\begin{gathered} \\ m=28+\frac{j}{3} \\ 28+\frac{j}{3}=\frac{2j}{3} \\ \text{ multiply through by 3} \\ 84+j=2j \\ 84=2j-j \\ 84=j \\ j=84 \end{gathered}[/tex]Therefore, Joseph had 84 books initially.
Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially
[tex]\begin{gathered} m=28,j=84 \\ \text{Total}=28+84=112 \end{gathered}[/tex]Hence, they both had 112 books altogether.
I need help with math identify the vertex of the parabola
Answers
The vertex of a parabola is the extreme point (maximum or minimum, depending on the the sign of the quadratic coefficient).
In the graph, we can see that the x-coordinate of the vertex is x=-1 and the y-coordinate is y=3.
Then, we can write the coordinates of the vertex as (h,k) = (-1,3)
Answer: The coordinates of the vertex are (-1,3)
si cada 8.33 minutos me dan 10 dolares cuantos dolares tendria en 6 horas ademas cuantos dolares ganaria cada 30 minutos
Answers
The payment for each 6 h is equal to $ 432.2 while the payment for each 30 min would be $ 36.01.
Rule of ThreeIt's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.
Conversion Unit TimeIn the International System Units (SI), the standard unit for time is the second (s). For solving any exercise, you need to know the relation between the units of the time. See below:
1h=60 min = 3600s
1 min = 60 s
Now you can solve the question from the rule of three for finding the payment in dollars.
The question gives: an each 8.33 min, the payment is 10 dollars. Thus, from this relation you can write:
For 6 hFirst, you should convert 6h to minutes, then,
1 h ----- 60 min
6h ----- x
x=60*6=360 min
After that, you should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
360 min ------- x
8.33x=360*10
8.33x=3600
x= $ 432.2
For 30minYou should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
30 min ------- x
8.33x=30*10
8.33x=300
x= $ 36.01
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dentify ALL pairs of parallel and perpendicular lines in the image below.
Answers
Step 1: redraw the figure given
Step 2: State the relationship between the lines
It can be observed that
(i) line XY is perpendicular to line PS
[tex]\text{line XY}\perp line\text{ PS}[/tex](ii) line XY is perpendicular to line QT
[tex]\text{line XY}\perp lineQT[/tex](iii) line PS is parallel to line QT
[tex]\text{line PS}\parallel lineQT[/tex]Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.
A heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope. What are the horizontal and vertical components of the force?
Answers
The vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
What is the resolution of the forces?Resolution of forces is the process of separating a force into two or more pieces so that the combined effect on the body is the same as if it had been a single force. We can analyze motion individually in different directions thanks to the resolution of forces.
Given that a heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope.
The vertical component and the horizontal component will be calculated as:-
Vertical component = 80sin60=69.28 N
Horizontal component = 80cos60 = 40 N
Therefore, the vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
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Evaluate without any table 3log2 +log20 - log 1.6
Answers
The value of 3log2 +log20 - log 1.6 is 2.
What is logarithm?
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. or
logarithm is the exponent or power to which the base must be raised to be raised to yield a given number.
Given,
3log2 +log20 - log 1.6
we can write it as
log[tex]2^{3}[/tex]+log20 - (log 1.6)
= log 8+ log20 - (log 1.6) (property of logarithm)
= log (8×20/1.6)
=log 100
=2
Hence, the value of 3log2 +log20 - log 1.6 = 2
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