Answers
θ = 5π/6 is the polar equivalent to the equation y= -√3x.
To determine the polar equivalent of the equation y = -√3x, we need to convert it from rectangular coordinates (x, y) to polar coordinates (r, θ).
In polar coordinates, r represents the distance from the origin to the point, and θ represents the angle from the positive x-axis to the point.
To convert the equation, we need to substitute x and y in terms of r and θ. We can rewrite the given equation as:
r sin(θ) = -√3 r cos(θ)
Simplifying, we can divide both sides by r:
sin(θ) = -√3 cos(θ)
Using trigonometric identities, we can rewrite this equation as:
tan(θ) = -√3
Now, we need to find the value of θ that satisfies this equation.
The value of θ that satisfies tan(θ) = -√3 is θ = 5π/6 or 150 degrees.
Therefore, the polar equivalent of the equation y = -√3x is:
θ = 5π/6 (or 150 degrees)
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Answer:
\(\theta =\dfrac{2\pi }{3}\)
Step-by-step explanation:
The polar equivalent refers to the representation of a mathematical equation, point, or shape in polar coordinates (r, θ) instead of Cartesian coordinates (x, y).
In Cartesian coordinates, the relationship between a point (x, y) and its polar coordinates (r, θ) can be described by the following equations:
\(\boxed{\begin{aligned}x &= r \cos \theta\\y &= r \sin \theta\end{aligned}}\)
where:
r represents the distance of the point from the origin (0, 0).θ represents the angle formed by the line connecting the point and the positive x-axis in polar coordinates.By substituting these expressions into the equation \(y = -\sqrt{3}x\), we get:
\(r \sin \theta=-\sqrt{3} \:r\cos \theta\)
Divide both sides of the equation by r:
\(\dfrac{r \sin \theta}{r}=\dfrac{-\sqrt{3} \:r\cos \theta}{r}\)
\(\sin \theta=-\sqrt{3} \cos \theta\)
Divide both sides of the equation by cos θ, and apply the trigonometric identity tan θ = sin θ / cos θ:
\(\dfrac{\sin \theta}{\cos \theta}=\dfrac{-\sqrt{3} \cos \theta}{\cos \theta}\)
\(\tan \theta =-\sqrt{3}\)
Solve for θ:
\(\theta =\tan^{-1}\left(-\sqrt{3}\right)\)
\(\theta =\dfrac{2\pi }{3}+\pi n\)
Therefore, the polar equivalent to the equation \(y = -\sqrt{3}x\) is:
\(\boxed{\theta =\dfrac{2\pi }{3}}\)
Related Questions
Evaluate the expression when x = 3.
6) 21-X
Answers
Answer: 18
Step-by-step explanation: You would substitute x for 3 in the expression. This would equal 21-3, or 18 when simplified
Helppppp pleaseeeeee
Answers
Answer:Godo luck!
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph with the correct cosine function based on its period.
Graph shows a sinusoidal function plotted on a coordinate plane. A curve enters quadrant 2 and it goes through (0, 1), (1.5, 0), (3, minus 1), (5, 0), (6.5, 1), (7.5, 0), It follows the same pattern.
Graph shows a sinusoidal function plotted on a coordinate plane. A curve enters quadrant 2 and it goes through (0, 1), (3, 0), (6, minus 1), (9.5, 0). It follows the same pattern.
Graph shows a sinusoidal function plotted on a coordinate plane. A curve enters quadrant 2 and it goes through (0, 1), (0.5, 0), (1, minus 1), (1.5, 1), (2, 0), (2.5, minus 1), (3, 0). It follows the same pattern.
Graph shows a sinusoidal function plotted on a coordinate plane. A curve enters quadrant 2 at (minus 1, 0) and goes through (0, 1), (1, 0), (3, 1), (4, 0), and (4.5, minus 1) and curve follows the same pattern on X-axis.
Graph shows a sinusoidal function plotted on a coordinate plane. A curve enters quadrant 2 and it goes through (0, 1), (6, 0), and (12, minus 1). It follows the same pattern.
y=cos x/2 arrowRight
y=cos x arrowRight
y=cos x/4 arrowRight
y=cos x/4arrowRight
Answers
The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)
Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:
Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.
Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.
Graph 4: (Not used)
Graph 5: (Not used)
Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.
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on a scale drawing of the park the sandbox is 2 inches wide actual sandbox is 8 feet wide what is the scale of the drawing
Answers
9514 1404 393
Answer:
1 : 48
Step-by-step explanation:
The scale is ...
drawing : world =
2 in : 8 ft = 2 in : 96 in
= 2 : 96 = 1 : 48
please help asap!!!
Answers
Answer:
\( w = 6 \)
Step-by-step explanation:
ST = w + 6,
PR = w
From the diagram given, we can deduce that PR is the midsegment of ∆QST. Therefore, according to the midsegment theorem:
PR = ½ of ST
Plug in the values into the equation and solve for w.
\( w = \frac{1}{2}(w + 6) \)
\( w = \frac{w}{2} + 3 \) (distributive property of equality)
\( w - 3 = \frac{w}{2} \) (subtraction property of equality)
\( 2(w - 3) = \frac{w}{2}*2 \) (multiplication property of equality)
\( 2w - 6 = w \)
\( 2w - 6 - 2w= w - 2w \) (subtraction property of equality)
\( - 6 = - w \)
Divide both sides by -1
\( 6 = w \)
\( w = 6 \)
Round 5 2/3 to the nearest whole number then subtract
Answers
this rounds to 6
1 1/4=5/4=1.25
this rounds to 1
6-1=5
40% of what number is 36?
Answers
40/100*36
36*100/40
=90
2. A(n) is NOT an example of an agreement. (1 point)
O lease
O month-to-month
O annual
O fine print
Answers
An Annual is not an example of an agreement.
Type < or > to make this statement true -a___-b
Answers
The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 19. 17 < 23 20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)
To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.
To indicate that the first value is less than the second value, write <.
Alternatively, to indicate that the first value is greater than the second value, write >.
Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36
To determine the direction of inequality, we need to compare the values.
We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.
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The correct question would be as
Write > or < to make each statement true.
11. -5 0
12. 9 -8
13. -7 7
14. 55 -75
15. -32 -24
16. 89 73
17. -58 -51
18. -32 4
19. 17 23
20. 18 -36
Students were surveyed about their favorite color is 1/4 of the students preferred red 1/8 of the students preferred blue and 3/5 of the remaining students preferred Green and 15 students preferred Green how many students were surveyed
Answers
There were 40 students surveyed.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let us assume total number of students were surveyed be x.
1/4 of x students preferred red = 1/4 x.
1/8 of of x students preferred blue = 1/8 x
Remaining students = (x - 1/4 x - 1/8 x)
So, 3/5 of the remaining students chose green that is 3/5 of (x - 1/4 x - 1/8 x).
15 students preferred green.
So, we can setup an equation:
We also know that 3/5(x - x/4 -x/8) = 15
3x - 3x/4 - 3x/8 = 75
5x = 200.
Dividing both sides by 5, we get
x= 40.
Therefore, 40 students were surveyed.
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A random sample of 10 fields of corn has a mean yield of 37.1 bushels per acre and standard deviation of 5.91 bushels per acre. Determine the 98% confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
The critical value of that used in constructing the confidence interval is (42.512 , 31.688)
We have the following information from the question:
Sample mean, x(bar) = 37.1 bushels per acre
Sample size, n = 10
Alpha, α = 0.05
Sample standard deviation, s = 5.91 bushels per acre
Degree of freedom = n - 1 = 9
We have to determine the 98% confidence interval for the true mean yield.
We use the formula:
x(bar) ± \(t_c_r_i_t_i_c_a_l\)\(\frac{s}{\sqrt{n} }\)
Plug all the values in above formula:
37.1 ± 2.896\((\frac{5.91}{\sqrt{10} } )\)
37.1 ± 5.412 = (42.512 , 31.688)
Hence, The critical value of that used in constructing the confidence interval is (42.512 , 31.688).
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HELP PLEASE FAST!!!!!
Answers
Answer: first choice is correct
Step-by-step explanation:
\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)
22/9 = 2.44
Therefore Point A is 22/9, Point B is \(\sqrt{10}\), Point C is \(\sqrt{13}\)
Factor 36+21. Write your answer in the form a(b+c) where a is the GCF of 36 and 21.
Answers
Answer:
3(12 + 7)
Step-by-step explanation:
To find the GCF of 36 and 21, list out their factors.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
21: 1, 3, 7, 21
The greatest factor which both numbers share is 3.
Therefore, you can factor 36 + 21 as 3(12 + 7)
A high school robotics club sold cupcakes at a fundraising event.
They charged $2.00 for a single cupcake, and $4.00 for a package of 3 cupcakes.
They sold a total of 350 cupcakes, and the total sales amount was $625.
The system of equations below can be solved for , the number of single cupcakes sold, and , the number of packages of 3 cupcakes sold.
Multiply the first equation by 2. Then subtract the second equation. What is the resulting equation?
x + 3y = 350
2x + 4= 625
Type your response in the box below.
$$
Answers
The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:
-5y = -375
1. Given equations:
- x + 3y = 350 (Equation 1)
- 2x + 4y = 625 (Equation 2)
2. Multiply Equation 1 by 2:
- 2(x + 3y) = 2(350)
- 2x + 6y = 700 (Equation 3)
3. Subtract Equation 2 from Equation 3:
- (2x + 6y) - (2x + 4y) = 700 - 625
- 2x - 2x + 6y - 4y = 75
- 2y = 75
4. Simplify Equation 4:
-2y = 75
5. To isolate the variable y, divide both sides of Equation 5 by -2:
y = 75 / -2
y = -37.5
6. Therefore, the resulting equation is:
-5y = -375
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Let h(t) =-161+ 5t + 1. What is h(1)?
Answers
Answer:
It is putting 1 at the place of t
so h(1)=161+5×1+1
h(1)=167
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
Answers
The possible values of B in the number line are option A, C, D and E
Number LineA number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
In this problem, the value of B is between 3 and 2 since B is located between them.
Checking the given options;
A = 2.5
This is possible because B can be at the middle between 2 and 3
B = 2/5
This fraction isn't possible because the value of B is greater than this.
C = 5 / 2
This fraction is possible because the decimal value is 2.5 which is the same as option A
D = 25 / 10
This fraction is also possible because the decimal value is 2.5 which is same as option A and C
E = 2.49
This is also a likely possibility as this can be approximated to 2.5
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a. calculate the percent extension and lengthening (in meters) for the deformed rock layers. assume a 1:5,000 scale. (2.5 pts.)
Answers
The percent extension and lengthening (in meters) for the deformed rock layers is 20%.
Percent extension refers to the amount of stretching that has occurred in a rock layer, expressed as a percentage of its original length.
To calculate percent extension, we would subtract the original length from the current length (120 - 100 = 20) and then divide that difference by the original length (20/100 = 0.2).
Finally, we would multiply by 100 to get the percent extension (0.2 x 100 = 20%).
Therefore, the percent extension of the rock layer would be 20%.
In summary, percent extension and lengthening are important concepts in geology that help us understand how rocks have been deformed over time.
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find the number of occurrences
Answers
Some definitions - note that the "bi-" frequencies are a bit ambiguous:
• Weekly = 1/week, i.e. something is done once every week
• Biweekly = 1/(2 weeks)
• Quarterly = 1/(3 months)
• Semimonthly = 2/month
• Bimonthly = 1/(2 months)
• Annually = 1/year
• Monthly = 1/month
"Biweekly" is sometimes used to mean "twice per week", but I've looked up "semimonthly" and it seems to strictly mean "once per half-month" or "twice per month". So to avoid ambiguity, I'll take "bimonthly" and "biweekly" to mean "once every two months" and "once every two weeks".
Some conversion factors:
• 1 year = 12 months = 52 weeks
1. Weekly for 1 year:
1/week • 52 weeks = 52 times
2. Biweekly for 2 years:
1/(2 weeks) • 104 weeks = 52 times
3. Quarterly for 4 years:
1/(3 months) • 48 months = 16 times
4. Semimonthly for 1 year:
2/month • 12 months = 24 times
5. Bimonthly for 2 years:
1/(2 months) • 24 months = 12 times
6. Annually for 25 years:
1/year • 25 years = 25 times
7. Monthly for 1/2 year:
1/month • 6 months = 6 times
8. Weekly for 1.5 years:
1/week • 78 weeks = 78 times
9. Semimonthly for 2.5 years:
2/month • 30 months = 60 times
helpppppppppppppppppppppppppppppppppppppp
Answers
Answer:
the last one
Step-by-step explanation:
there is no rhythm
One of the specialties at Dixie’s Cafe is vegetable stew, which simmers over a low flame all day. Since the cooking time is so long, Dixie must decide in the morning how many servings of the stew to cook for that night’s dinner service. Moreover, the stew cooked on a given day cannot be served the next day; it must be thrown away. Vegetable stew is the highest-profit item on the menu at Dixie's Cafe. It earns Dixie a profit of $8. Demand for in-flight meals Cumulative d Probability f(d) Probability F(d) 40 0.01 0.01 41 0.03 0.04 42 0.04 0.0843 0.05 0.1344 0.08 0.2145 0.09 0.346 0.12 0.42 47 0.13 0.55 48 0.17 0.7249 0.12 0.8450 0.08 0.9251 0.03 0.95 52 0.02 0.9753 0.02 0.01 54 0.99 1 serving, whereas all the other items earn a profit of $4. Customers who want stew but find it out of stock will order one of these other items. The ingredients for one serving of stew cost the Cafe $2.50. A) First suppose that the demand for stew on a given evening is normally distributed with a mean of 18 and a variance of 16. How many servings of stew should Dixie prepare in the morning? (Fractional servings are OK). What is the expected cost (ingredients and lost profit) of the optimal solution? B) Now suppose that the demand is distributed as an exponential random variable with mean 18. How many servings should Dixie prepare?
Answers
Answer:
what the hell i cant under stand u need to press enter more
Step-by-step explanation:
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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Which of these expressions is equivalent to 18+24r ?
Answers
Answer:
it will be 322 because 8 + 4 is 12 and 1+2 is 3
If ABCD is dilated by a factor of 3, the
coordinate of B' would be:
-5 -4
MA
А
B
3
26
1
-2 -10
-1
-2.
-3
C
2 3 4 5
D
B' = ([?], [])
Enter
Answers
If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.
Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:
Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).
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Suppose f ( x ) = 7 ( 2.5 ) x and g ( x ) = 52 ( 1.5 ) x . Solve f ( x ) = g ( x ) for x .
Answers
The value of x in when we equate the functions f(x) = g(x) is 0
FunctionsA function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
A function in mathematics is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input. A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as; y = f(x)
Where x is an independent variable and y is a dependent variable.
In the question given;
f(x) = 7(2.5)xg(x) = 52(1.5)xf(x) = g(x)
7(2.5)x = 52(1.5)x
Solving for x
x = 0; This is because they both cancel each other out.
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Which word describes the slope of the line?
O positive
O negative
zero
O undefined
Answers
The slope of a horizontal line is always zero.
What is slope?
The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.
By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:
slope = change in y / change in x = 0 / (any non-zero value of x) = 0
So, the slope of a horizontal line is always zero.
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what does 14a and 5b and 2a and 10b mean
Answers
Answer:
16a+15b
Step-by-step explanation:
Just like addition
Answer:
They are variables
Step-by-step explanation:
zhsineidhwvd
Susie is visiting Greece from the U.S. One day she stopped by a market and found a stall selling tomatoes for 1.92 euro per kilogram. If 1 euro was worth 1.09 dollars that day, how much did the tomatoes cost in dollars per pound?
Answers
can you help me this 4^x x ^8^x^+^1 = 2⁴
Let g(x) be the indicated transformation of f(x) = −|3x| − 4. Stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
Answers
The final rule for g(x) is g(x) = 3|3x| + 12.
To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.
So, the rule for g(x) is g(x) = 3f(x).
Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:
g(x) = 3f(x)
g(x) = 3(-|3x| - 4)
g(x) = -3|3x| - 12
This is the expression for g(x), which represents the transformed graph.
To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.
Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.
Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.
The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).
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QUICK!!
Convert r = 6cscθ to rectangular form.
Answers
Answer:
x2+y2−6y=0
Step-by-step explanation:
Done
AA
savvasrealize.com
46 astigment
ratiquent is past 6 (01/09/21 116
Design An art class is making a mural for their school which has a triangle drawn in the middle. The
length of the bottom of the triangle is x. Another side is 5 more than three times the length of the
bottom of the triangle. The last side is 3 more than the bottom of the triangle. Write and simplify an
expression for the perimeter of the triangle.
What is the expression for the perimeter of the triangle?
(Simplify your answer.)
Answers
Answer:
Expression for perimeter of triangle = 5x+8
Step-by-step explanation:
Given that:
Length of bottom of triangle = b = x
Length of other side = a = 3x + 5
Length of last side = c = x + 3
Perimeter of triangle = a + b + c
Perimeter = (3x+5)+x+(x+3)
Perimeter = 3x+5+x+x+3
Perimeter = 5x + 8
Hence,
Expression for perimeter of triangle = 5x+8