The solution of the given trigonometric expression is x = 2π/3.
Use the concept of trigonometric ratio defined as:
Trigonometric ratios depend on the value of the ratio of sides of a triangle which is right-angled and contains the values of all trigonometric functions.
The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as it's trigonometric ratios.
The given expression is:
2 cos x + 1 = 0
Where,
0 ≤ x ≤ 2π
To solve it,
Subtract both sides,
2 cos x = - 1
Divide by 2 on both sides,
cos x = -1/2
Take cos inverse on both sides,
[tex]x = cos^{-1} (\frac{1}{2})[/tex]
Since cos(2π/3) = -1
x = 2π/3
Now since 2π/3 lies between 0 ≤ x ≤ 2π
Hence,
The solution of the given expression is x = 2π/3
To learn more about trigonometric ratios visit:
https://brainly.com/question/29156330
#SPJ4
Which expression is equivalent to .02m(n-5)-.02(m+10)
Answer:
thank you
Step-by-step explanation:
Help! WHAT IS THE VALUE OF X, and can you show how you got it please?
What are three consecutive odd integers that have a sum of 39?
A certain arithmetic sequence has the recursive formula an = an-1 + d. If the common difference between the terms of the sequence is -13, what term follows the term that has the value 13?
The fourth term of a sequence is 14. Each term of the sequence is 8 less than the previous term. Which recursive formula represents the situation?
Please pretty please help me fast
Two cubes have surface areas of 72 square feet and 98 square feet. what is the ratio of the volume of the small cube to the volume of the large cube?
Answer:
Ratio of the volumes of the cubes = 216 : 343
Step-by-step explanation:
Since surface area of a cube is represented as 6a² where a is the side of a cube.
Let a is one side of large cube and b is the side of smaller one.
Ratio of their surface area = [tex]\frac{6a^{2} }{6b^{2}}=\frac{72}{98}[/tex]
[tex](\frac{a}{b})^{2}=\frac{36}{49}[/tex]
[tex]\frac{a}{b}=\sqrt{\frac{36}{49}}[/tex]
[tex]\frac{a}{b}=\frac{6}{7}[/tex]
Now ratio of the volumes = [tex]\frac{a^{3} }{b^{3}}=(\frac{1}{b})^{3}[/tex]
Ratio = [tex](\frac{6}{7})^{3}=\frac{216}{343}[/tex]
Therefore, ratio of the volumes of the cubes = 216 : 343
the weight of 1in ^3 of water is 0.036 pounds. A container contains
528.768 pounds of water. what is the volume of water in the container
The volume of the water in the container is calculated by dividing the total weight of water (528.768 pounds) by the weight of one cubic inch of water (0.036 pounds), resulting in 14688 cubic inches.
To find the volume of water in the container, we first consider the weight of 1 cubic inch of water, which is given as 0.036 pounds. We know that the container holds 528.768 pounds of water. To find the volume, we divide the total weight of water in the container by the weight of one cubic inch of water.
Volume = Total Weight / Weight per Unit Volume
Volume = 528.768 pounds / 0.036 pounds/in³
Volume = 14688 cubic inches
If you need the volume in other units, such as gallons, you must convert cubic inches to gallons using the appropriate conversion factor.
Simplify the equation 7.5+N+9.63
Add 7.5+9.63 which would be 17.13
17.13+N
Sally goes out to lunch and has the option of a soup or a salad and then a turkey, ham, or club sandwich. Which tree diagram correctly shows all of her choices?
Someone please help me?
Y=|x| vertically stretched by a factor of 5
Which of the following proportions can be used to prove AE || DK in the proof below? Select all that apply.
the pictures in order are
a
b
c
d
and the last picture is a figure if an awnser is missing please tell me if that one is the correct one
Answer: DA:FA=KE:EF, DF:DA=KF:KE and FA:DA=EF:KE are correct.
Explanation: Since, [tex]\triangle EFA[/tex] and [tex]\triangle KFD[/tex] are similar triangles.
Because, [tex]\angle FAE= \angle FDK[/tex] and [tex]\angle FEA= \angle FKD[/tex] (because EA and KD are parallels. And, [tex]\angle F[/tex] is common angle for these triangles.
Therefore, according to the property of similar triangles.
FE:EK= FA:AD, FE:FK=FA:FD and DF:DA=KF:KE .
Thus, first, second and third options are correct.
A card is being drawn from a standard deck of playing cards. Find each probability.
1.P(Jack or ten)
2.P(red or black)
3.P(queen or club)
4.P(red or ace)
5.P(diamond or black)
6.P(face card or spade)
if the number of bacteria in a colony double every 330 minutes and there is currently a population of 1100 bacteria what will the population be 990 minutes from now
please help type the integer that represents the correct answer the absolute value of 7
Assume that the line passes through the point (−2,4) and is parallel to the line through the points ( −4,4) and (−5,−1).find the equation of this line in slope intercept form.
Company A charges a $120 annual fee plus $7 per hour car share fee. Company B charges $100 plus $9 per hour. What is the minimum number of hours that a car share needs to be used per year to make company A a better deal?
Answer:
11
Step-by-step explanation:
The Tran Family drove 1,246 miles during a vacation that lasted 14 days. How many miles on average did they drive each day? :3
Which of the following describes the probability distribution below?
A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.
B.) The mean is greater than the median, and the majority of the data points are to the right of the mean.
C.) The median is greater than the mean, and the majority of the data points are to the left of the mean.
D.) The median is greater than the mean, and the majority of the data points are to the right of the mean.
Answer: A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.
It is clear that most of the data (around 75%) is consist of value 1, which is the leftmost part of the data. Since it was more than 50% of the data, the median should be 1.
if 75% data is 1, it need 25% data with value at least 5 to make the means equal to 2. The means would be bigger than 1 but less than 2, so most(75% data is 1) of the data would be on the left of the mean
If we draw a normal distribution bell curve as shown in the attachment, we can see that the bell curve is skewed to the right . This means it has a right tail. This means few points are to the right of the mean. In other words, we can say that majority of the data points are to the left of the mean
Since the majority of the data points are to the left, the median will also be to the left of the mean which indicates median is lesser than mean . In other words, mean is greater than median
So, answer is: A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.
Which table represents a direct variation function?
x y x y x y
-3 -4.5 -5.5 -3 -3 -7.5
-1 -3.0 -5.5 -1 -1 -2.5
2 -1.5 -5.5 2 2 5.0
5 0.0 -5.5 5 5 12.5
10 1.5 -5.5 10 10 25.0
x y
-5.5 10
-4.5 8
-3.5 6
-2.5 4
-1.5 2
The answer to this question is B Ed
The table that represents a direct variation function is
x y
-3 -7.5
-1 -2.5
2 5.0
5 12.5
10 25.0
How to determine the table?For a table to represents a direct variation, the following must be true
k = y/x
Where k represents the constant of variation
In table 3, we have:
k = 25.0/10 = 12.5/5 = 5.0/2 = -2.5/-1 = -7.5/-3
This gives
k = 2.5
The value of k is the same for all input and output values
Hence, the table that represents a direct variation function is the table 3
Read more about direct variation at:
https://brainly.com/question/6499629
Will give brainliest-H(t)=-16t^2+28t
T is time in seconds.
How long will it take for the dolphin to make one jump, show your work.
Simplify: (3 + 4i) + (2 - 3i) - (5 - 6i)
Three consecutive numbers that have a sum of 159. What are the numbers?
The angle of depression from point R to point S is angle .
The question involves high school level mathematics, specifically geometry and trigonometry, discussing the angle of depression, cross-sectional area, angles, distances, and congruent triangles.
Explanation:The question relates to the angle of depression and concepts of geometry involving angles and distances. In the context provided, the angle of depression from point R to S is being discussed, but not enough information is given to define the angle. The references to cross-sectional area, small-angle approximation, and congruent triangles touch on topics in geometry and trigonometry that are critical to understanding the properties of shapes, sizes, and angles in mathematical problems.
In the mathematical equations provided, 'S' is used as a variable representing a stress value, with reference to pressure units of N/m², and 'r' represents a radius which is then used to calculate an area. The references to a graph with a slope and 'y = mx + b' appear to relate to linear equations and representations in coordinate geometry.
The descriptions involving angle vector, position vector, arc length vector, and angle of distance between two points separated by an angle further contribute to the idea that this question falls under the Mathematics category, addressing high school level concepts in geometry and trigonometry.
With a quick explanation please
If cosine x is approximately.9511 what is the measurement of x to the nearest degree? Approximately what is the sine of the angle that is complementary to x
Sin(x) = .2588 Given
ARCSin (x) = x = ARCSin(.2588) Using the calculator = 14.9988 degrees ( ~ 15 degrees)
COMPLIMENTARY angle is the angle which added to 'x' will equal 90 so the COMPLIMENTARY Angle is 75 degrees
Using the calculator again cos (75) = .2588 The same as the complimentary angle's SIN !!!
A girl scout sells 3 boxes of cookies during week 1. She has a goal to sell twice as many cookies each week as she did the week before. If she succeeds in doing this during weeks 2, 3, 4, and 5, how many boxes will she sell all together? a0
x(t) = t^3 - 12t^2 + 36t
Velocity = x'(t) = 3y^3 - 24t + 36 = 0
x'(t) = t^2 - 8t + 12 = 0
x'(t) = t^2 - 6t - 2t + 12 = 0
x'(t) = t(t - 6) - 2(t - 6) = 0
x'(t) = (t - 2)(t - 6) = 0
t = 2 and t = 6 must be the roots.
Is my answer of D "2 and 6" correct based on this work?
The perimeter of a parallelogram is 30 ft and its length is 5 ft. What is the length of the other side?