![Find The Value Of Interval [0,2pie] Such As That Tan S= -radical3/3](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/miRQUaRKggfUqBZNEqmqdZO5JozBsngo.png)
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The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.
Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
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Related Questions
Beginning in 1995,( 1995= 0 years) the Chicago Cubs decreased its ticket price by a constant amount each year until 2016 when they finally won the World Series. A ticket cost $77.50 in 2005, but only $49.50 in 2012. How much did a ticket cost in 2000?
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The cost of the Chicago Cubs ticket in the year 2000 was $97.50.
What is defined as the constant rate of change?A rate of change is defined as the ratio of change in dependent values as well as outputs to change in independent variables or inputs. The change, also known as the function's slope, describes what numbers change between 2 points on the a coordinate plane.For the given question.
The price of the Chicago Cubs ticket in year 2005 is $77.50.
The price of the ticket reduced in year 2012 as $49.50.
There is a constant amount of decrease in the price.
Thus, difference in years;
= 2012 - 2005
= 7 years.
Difference in amount;
= 49.50 - 77.50
= -28
Price decreased in one year = 28/ 7 = -4 per year.
For the price of the ticket in the years 2000.
= 2005 - 2000
= 5 years.
Price decreased in 5 years is;
= -4 x 5
= -20
The price is 2000 is 77.50 + 20 = 97.50
Thus, the cost of the Chicago Cubs ticket in the year 2000 was $97.50.
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I need help on writing the table and graphing it please !!
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Given:
[tex]f(x)=2-\sqrt[]{x+6}[/tex]Calculate the values for f(x),
[tex]\begin{gathered} \text{for x=-6 , f(-6)=}2-\sqrt[]{-6+6} \\ f(-6)=2 \\ \text{for x=3 ,f(6)=2-}\sqrt[]{3+6} \\ f(3)=2-3=-1 \\ \text{for x=-2 f(-2)=2-}\sqrt[]{-2+6} \\ f(-2)=2-2=0 \\ \text{for x=1, f(1)=2-}\sqrt[]{1+6} \\ f(1)=-0.6 \end{gathered}[/tex]The graph of given function is,
Twenty students choose a piece of fruit from a list of 4 fruits: apple, banana, grape, and pear. The theoretical probability that a student will choose a banana is .25. Only 1 student chooses a banana. How can the experimental probability get closer to the theoretical probability?A. only give two choices of fruitB. use a smaller sample size of studentsC. use a larger sample size of studentsD. provide more choices of fruit
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Total number of student 20.
Total number of fruits are 4.
The theoretical probability that a student will choose a banana is 0.25
The experimental probability is 1/20=0.05.
Thus there is a huge difference in the theoritical probability and experimental probability.
Thus the experimental probability get closer to the theoretical probability is:
A. only give two choices of fruit.
The best way of getting the experimental probability closer to the theoretical value is by taking a larger sample.
Sadly the fruit selection is not random but based on student preferences.
Because the fruit are unlikely to have equal appeal to students, the theoretical probability is not valid.
solve for x and y (2x+7)(x+1)(y+5)(x-4)
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Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
f(x) = 3x² - 5x+20
Find f(-8)
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Answer:
Substitute x = -8 into f(x).
f(-8) = 3(-8)² - 5(-8) + 20
= 3(64) + 40 + 20
= 192 + 60
= 252
Which 3 pairs of side lengths are possible measurements for the triangle?
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SOLUTION
From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC
And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)
So this means
[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]So from the first option
[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]Hence the 1st option is correct, so its possible
The second option
[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]Hence the 2nd option is wrong, hence not possible
The 3rd option
[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]Hence the 3rd option is wrong, not possible
The 4th option
[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]Hence the 4th option is correct, it is possible
The 5th option
AB = BC
This is correct, and its possible
The last option
[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]This is wrong and not possible because AB should be equal to BC
Hence the correct options are the options bolded, which are
1st, 4th and 5th
Money in a particular savings account increases by 6% after a year. How much money will be in the account after one year if the initial amount is $125?
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If g(x)=f(x)−1, then g(x) translates the function f(x) 1 unit _[blank]_.Which word correctly fills in the blank in the previous sentence?A. upB. leftC. downD. right
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To answer this question, we need to remember the rules of transformations of functions, the rules are shown below:
From the table, we notice that if we subtract a number we are performing a vertical translation down.
Therefore, the correct word to fill the blank is down and the correct option is C.
From the origin of the coordinate plane, how many units does one travel along the y-axis to find the point with the coordinates (1,8)?
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Solution:
Let's recall that in a coordinate plane, we consider (0, 0) as the origin because this is the point where the x and y-axes intersect.
Therefore, the unit you travel along the y-axis from the origin is:
8 - 0 = 8 (Value of y given - Value of y at the origin)
The answer is 8 units
Student unresponsive. No interaction at all. Session ended by tutor.
i neeeeeeeeeeed the aseer :D
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Answer:
Step-by-step explanation:
21
y=x-6y=x+2 how to solve this problem
Answers
No solutions
Explanation
[tex]\begin{gathered} y=x+6\text{ Eq(1)} \\ y=x+2\text{ Eq(2)} \end{gathered}[/tex]
Step 1
replace Eq(1) in Eq (2)
[tex]\begin{gathered} y=x+2\text{ Eq(2)} \\ x+6=x+2 \\ \end{gathered}[/tex]Step 2
subtract x in both sides
[tex]\begin{gathered} x+6=x+2 \\ x+6-x=x+2-x \\ 6=2 \end{gathered}[/tex]6=2 is false, it means there is not solution for both equations,
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answers
Answer:
2/3
Step-by-step explanation:
y = xk
6 = 72K Solve for k Divide both sides by 72
[tex]\frac{1}{12}[/tex] = k
y = xk
y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]
y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4
y = 2/3
What is the slope of the line in the graph?A. 2/3B. -2/3C. 3/2D. -3/2
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
slope of the line:
we must analyze the graph to find the solution.
point 01 (0, 8)
point 02 (12, 0)
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{0-8}{12-0}=\frac{-8}{12}=\frac{-2}{3}[/tex]The answer is:
m = - 2/3
Use one or more transformations to transform the pre-image (purple) onto the image (white). helppp
Answers
The transformation required to transform the preimage in purple to the image in white is
Rotation 180 degreesTranslation to the right 14 unitsTranslation down 4 unitsWhat is transformation?Transformation is the term used to describe when a body is repositioned or makes some movement.
Some of the movements involved in transformation are:
Rotation Translation and so onHow to transform the pre- image to the imageThe movement can start in several ways however we stick to this as described
The first movement is rotation by 180 degrees about the topmost edge at the left side.The next step is translation 14 units to the right. This gets the preimage exactly on top of the imageFinally, translation 4 units downLearn more about translation at: https://brainly.com/question/29042273
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what is the volume of a pipe that has a diameter of 8 meters and a height of 3 meters of water, round to the nearest tenth
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The pipe is in the form of cylinder.
[tex]\begin{gathered} d\text{ = 8 m} \\ r\text{ = 4 m} \\ h\text{ = 3 m} \end{gathered}[/tex]The volume of the pipe is calculated as,
[tex]\begin{gathered} \text{Volume = }\pi\times r^2\times h \\ \text{Volume = 3.14 }\times\text{ 4}\times4\times3 \\ \text{Volume = 150.72 }\approx150.70m^3 \end{gathered}[/tex]Thus the volume of water is 150.70 cubic m .
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator).
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Given the system of equations
[tex]\begin{gathered} x+4y-z=20-----1 \\ 3x+2y+z=8-----2 \\ 2x-3y+2z=-16-----3 \end{gathered}[/tex]We can solve for x, y and z below.
Explanation
Step 1: Find the value of z using the substitution method
[tex]\begin{gathered} \begin{bmatrix}x+4y-z=20\\ 3x+2y+z=8\\ 2x-3y+2z=-16\end{bmatrix} \\ Isolate\text{ for x in equation 1} \\ x=20-4y+z \\ \mathrm{Substitute\:}x=20-4y+z\text{ in equation 2 and 3} \\ \begin{bmatrix}3\left(20-4y+z\right)+2y+z=8\\ 2\left(20-4y+z\right)-3y+2z=-16\end{bmatrix} \\ sinplify \\ \begin{bmatrix}-10y+4z+60=8 \\ -11y+4z+40=-16\end{bmatrix} \\ Isolate\text{ for y in}-10y+4z+60=8 \\ -10y=8-4z-60 \\ y=\frac{8-4z-60}{-10} \\ y=\frac{-4z-52}{-10} \\ y=\frac{2\left(z+13\right)}{5} \\ \mathrm{Substitute\:}y=\frac{2\left(z+13\right)}{5}\text{ in }-11y+4z+40=-16 \\ \begin{bmatrix}-11\cdot \frac{2\left(z+13\right)}{5}+4z+40=-16\end{bmatrix} \\ simplify \\ \begin{bmatrix}\frac{-2z-286}{5}+40=-16\end{bmatrix} \\ multiply\text{ through by 5} \\ -2z-286+200=-80 \\ isolate\text{ for z} \\ -2z=-80-200+286 \\ -2z=6 \\ z=\frac{6}{-2} \\ z=-3 \end{gathered}[/tex]Step 2: Find y
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3\text{ in}\mathrm{\:}y=\frac{2\left(z+13\right)}{5} \\ y=\frac{2(-3+13)}{5} \\ y=\frac{2(10)}{5} \\ y=4 \end{gathered}[/tex]Step 3: Find z
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3,\:y=4\text{ in }x=20-4y+z \\ x=20-4\cdot \:4-3 \\ x=1 \end{gathered}[/tex]Answer: The solutions to the system of equations are
[tex]x=1,\:z=-3,\:y=4[/tex]The ratio of boys to girls in a school is 5:4. if there are 500 girls , how many boys are there in the school?
Answers
Answer:
The number of boys in the school is;
[tex]625[/tex]Explanation:
Given that the ratio of boys to girls in a school is 5:4;
[tex]5\colon4[/tex]And there are 500 girls in the school.
The number of boys in the school will be;
[tex]\begin{gathered} \frac{B}{G}=\frac{5}{4} \\ G=500 \\ B=\frac{5\times G}{4}=\frac{5\times500}{4} \\ B=625 \end{gathered}[/tex]Therefore, the number of boys in the school is;
[tex]625[/tex]State all integer values of X in the interval that satisfy the following inequality.
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Solve the inequality
-5x - 5 < 8
for all integer values of x in the interval [-4,2]
We solve the inequality
Adding 5:
-5x - 5 +5 < 8 +5
Operating:
-5x < 13
We need to divide by -5, but we must be careful to flip the inequality sign. It must be done when multiplying or dividing by negative values
Dividing by -5 and flipping the sign:
x > -13 / 5
Or, equivalently:
x > -2.6
I am here, I'm correcting the answer. the interval was [-4,2] I misread the question. do you read me now?
Any number greater than -2.6 will solve the inequality, but we must use only those integers in the interval [-4,2]
Those possible integers are -4, -3, -2, -1, 0, 1, 2
The integers that are greater than -2.6 are
-2, -1, 0, 1, 2
This is the answer.
The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the sh Ay 10 00 6 water 4 shore |(2, 1) swimmer 19 -2 2 1 3 4 5X N -2 An equation that represents the shortest path is y=
Answers
Answer:
Explanation:
From the graph, we ca
Eric takes classes at both Westside Community College and Pinewood Community College. At Westfield class fees are $98 per credit hour and at Pinewood, class fees are $115 per credit hour. Eric is taking a combined total of 17 credit hours at the two schools. Suppose that he is taking W credit hours at Westside. Write an expression for the combined total dollar amount he paid for class fees. Total paid ( in dollars) =
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Let W = number of credit hours at Westside
Since the total credit hours is 17, the number of credit hours at Pinewood is :
[tex]17-W[/tex]To find the expression for the combined total dollar amount for both class.
Multiply each hours by the corresponding fees.
The expression will be :
[tex]\begin{gathered} 98(W)+115(17-W) \\ =98W+1955-115W \\ =1955-17W \end{gathered}[/tex]The correct answer is :
1955 - 17W
What’s the last number in row 8 for the new number triangle I made
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We have the sequence, shown as a number triangle, where in each step we add 5 (that is the constant difference).
We can write:
1
6 11
16 21 26
31 36 41 46
51 56 61 66 71
76 81 86 91 96 101
106 111 116 121 126 131 136
141 146 151 156 161 166 171 176
Answer: The last number in row 8 is 176.
Answer:
thr last number in row eight is 176
Given a function described by the table below, what is y when x is 5?XY264859612
Answers
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9
A crowbar 28 in. Long is pivoted 6 in. From the end. What force must be applied at the end in order to lift a 400-lb object at the short end?
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What you are trying to do is balance the “moments" about the fulcrum (pivot).
We will calculate moment at the pivot (M1) due to weight (W):
• L1 = length of the bar = 6in
[tex]M1=W\times L1=400\cdot6=2400in\cdot lb_f[/tex]The moment (M2) at the pivot due to your applied force (Fa) on the other end of the bar must equal M1.
• LT = total lenght = 28in
,• L2 = LT - L1 = 28 - 6 = 22in
,• M2 = M1 = 2400in lbf
[tex]\begin{gathered} M2=Fa\times L2 \\ Fa=\frac{M2}{L2}=\frac{2400inlb_f}{22in}=109.09lb_f \end{gathered}[/tex]Answer: 109.09lbf
A force of 109.091 pounds would have to be applied to move the load.
need help with this problem answer in a quick and clear response
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Answer:
A system of inequalities with parallel boundaries doesn't have a solution when the regions for each inequality don't intersect. This region depends on the sign of inequality, so the signs of inequality determine if the system has solutions.
what is the slope of the line represented by y = -5 + 2?
Answers
Question:
Find the slope of
[tex]y=-5x+2[/tex]Answer:
Remember that when we have the equation of a line in the form
[tex]y=mx+b[/tex]The slope of the line is the number that accompanies x (A.K.A Coefficient)
Therefore, the slope of the line is -5
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Answers
Given angles are corresponding angles, they are congruent (have the same measure):
[tex](2x+20)=(3x-10)[/tex]Use the equation above to solve x;
[tex]\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}[/tex]You use the value of x=30 to find the measure of corresponding angles:
[tex]\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}[/tex]Then, the meaure of the corresponding angles is 80°molly has 12 stickers 1/3 of her stickers are blue exactly how many stickers are not blue
Answers
Answer:
8 stickers
Step-by-step explanation:
beacuse 1/3 =4 4x3 =12 12-4=8 here you go:)
The triangles are similar, solve for the question mark. A Z с ? 15 10 12 B X D E 8 8 18 12.5 0 24
Answers
Answer:
18
Explanation:
The triangles are similar if their sides are proportional. It meant that the ratio of AB to CD is equal to the ratio of AE to CE, so we can write the following equation:
[tex]\begin{gathered} \frac{AB}{CD}=\frac{AE}{CE} \\ \frac{15}{10}=\frac{AE}{12} \end{gathered}[/tex]So, we can solve for AE as:
[tex]\begin{gathered} \frac{15}{10}\cdot12=\frac{AE}{12}\cdot12 \\ 18=AE \end{gathered}[/tex]Therefore, the measure of AE is 18
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 57 inches, and standard deviation of 7.3 inches.What is the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
Answers
0.834
Explanations:The formula calculating the z-score is expressed as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Given the following parameters
• x1 = 49.55
,• x2 = 73.35
,• mean μ = 57inches
,• standard deviation σ = 7.3in
Convert the x-values to z-score
[tex]\begin{gathered} z_1=\frac{x_1-\mu}{\sigma} \\ z_1=\frac{49.55-57}{7.3} \\ z_1=-\frac{7.45}{7.3} \\ z_1=-1.02 \end{gathered}[/tex]For z2;
[tex]\begin{gathered} z_2=\frac{73.35-57}{7.3} \\ z_2=\frac{16.35}{7.3} \\ z_2=2.24 \end{gathered}[/tex]Determine the required probability
[tex]\begin{gathered} P(-1.02Hence the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches is 0.834Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
Answers
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
