For questions 1,2, and 3 find intervals of positive and negative r values. 1. r= 1 - 2 cos θ 2. r= 5 sin (3θ) 3. r= 1 - 5 sin θ
Answers
r has negative values when 2 cos θ > 1, and positive values otherwise.
r has negative values when 3θ is in the second or third quadrant, and positive values otherwise.
r has negative values when sin θ > 1/5, and positive values otherwise.
To find the intervals of positive and negative r values, we need to look at the cosine function. Since the cosine function has a maximum value of 1, we have r = 1 - 2 cos θ ≥ -1. Solving for cos θ, we get 2 cos θ ≤ 2, which means that r is negative when 2 cos θ > 1 and positive otherwise.
We can rewrite the polar equation r = 5 sin (3θ) as r = 5(sin θ)(cos^2 θ)(3)^(1/2). This equation is negative when sin θ is negative, which happens in the second and third quadrants. Therefore, r is negative when 3θ is in the second or third quadrant and positive otherwise.
Similarly, we can rewrite the polar equation r = 1 - 5 sin θ as r = 5(cos θ)(sin(π/2 - θ)). This equation is negative when sin(π/2 - θ) is negative, which happens when θ is in the second and third quadrants. Therefore, r is negative when sin θ > 1/5, and positive otherwise.
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Related Questions
The square has sides of length 3 cm and the arcs
have centres at the corners. Find the shaded area.
Answers
Answer:
Shaded area= 5.14 cm² (3 s.f.)
Step-by-step explanation:
Please see the attached picture for the full solution.
Create a function called sensor_value that randomly generates a number between ( 0 and 3 ). Create a new function called Gate_Control that uses the function sensor_value to generate two semaphores: Gate and Counter. The semaphore Gate is passed if the output is 2 . On the other hand the semaphore Counter is passed if the output is 1 , or 3 ). Then create a thread using the Gate_Control function. C should be used and code should be ready to be executed
Answers
We have been able to create a thread that uses Gate_Control function and then shown the code generated.
How to use the Gate Control Function?A thread that uses Gate_Control function and the code generated is as follows:
#include <stdio.h>
#include <stdlib.h>
#include <pthread.h>
#include <semaphore.h>
#include <unistd.h>
sem_t Gate, Counter;
// Function to generate a random number between 0 and 3
int sensor_value() {
return rand() % 4;
}
// Function for the Gate_Control thread
void* Gate_Control(void* arg) {
while (1) {
int value = sensor_value();
if (value == 2) {
// Passing the Gate semaphore
sem_post(&Gate);
}
if (value == 1 || value == 3) {
// Passing the Counter semaphore
sem_post(&Counter);
}
usleep(1000000); // Wait for 1 second
}
return NULL;
}
int main() {
srand(time(NULL));
// Initialize semaphores
sem_init(&Gate, 0, 0);
sem_init(&Counter, 0, 0);
// Create the Gate_Control thread
pthread_t gateControlThread;
pthread_create(&gateControlThread, NULL, Gate_Control, NULL);
// Main thread waits for the Gate semaphore
while (1) {
sem_wait(&Gate);
// Gate semaphore passed
printf("Gate semaphore passed\n");
}
// Cleanup and exit
sem_destroy(&Gate);
sem_destroy(&Counter);
return 0;
}
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Number 8 find the value x so that l//m state the converse used
Answers
The converse of l//m is the reverse statement that if x has a certain value, then l and m have a certain value. In this case, it is stated that if x = 4, then l = 6 and m = 2.
What is reverse statement?Reverse statement, also known as a converse statement, is a logical statement that switches the order of the terms in an original statement. It is used to express the opposite of the original statement in a logical, meaningful way. For example, the statement "all dogs have four legs" can be reversed to "if something has four legs, then it is a dog".
Let x = 4 and let l = 6 and m = 2.
The converse statement is: If x = 4, then l = 6 and m = 2.
The converse of l//m is the reverse statement that if x has a certain value, then l and m have a certain value. In this case, it is stated that if x = 4, then l = 6 and m = 2.
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limx²-9x+20
x->4 x-4?
Answers
Answer:
-1
Step-by-step explanation:
lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.
So the limit is 4-5=-1
What is the answer? Please help. Urgent.
Answers
Given:
A figure that contains a right triangular prism and cuboid.
To find:
The volume of the figure.
Solution:
The dimensions of cuboid are 16 in, 7 in and 3 in.
So, the volume of the cuboid is:
\(V_1=Length\times Width \times height\)
\(V_1=16\times 7 \times 3\)
\(V_1=336\)
The base of the prism is a right angle with base 3 in and height 5 in, and the length of the prism is 6 in. So, the base are of the prism is
\(B=\dfrac{1}{2}\times Base\times Height\)
\(B=\dfrac{1}{2}\times 3\times 5\)
\(B=7.5\)
The volume of a prism is:
\(V_2=Bh\)
Where, B is the base area and h is the height of the prism.
\(V_2=(7.5)(6)\)
\(V_2=45\)
The volume of combined figure is:
\(V=V_1+V_2\)
\(V=336+45\)
\(V=381\)
Therefore, the volume of the figure is 381 cubic in.
Y=2x+1
Y=4x-1
Indicate the point if intersection if it exists
Answers
For given linear equations, The point of intersection is (1,3).
What is a linear equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
After drawing given linear lines Y=2x+1, Y=4x-1 on graph we can see from the graph that the point of intersection is (1,3).
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A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. \( 87,87,215,154,288,235,231 \) Find the median number of newspapers sold.
Answers
The median number of newspapers sold over seven weeks is 223.
The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.
The formula for the median is as follows:
Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)
We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288
The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.
Median = (215 + 231)/2
= 446/2
= 223
In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.
Hence, the median number of newspapers sold over seven weeks is 223.
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Find the value of x
Answers
Answer:
A) 33
Step-by-step explanation:
180 - 105= 75
75 + 72 + x = 180
147 + x = 180
x= 33
One number is 2 less than 3 times another. If the sum of the two number is 14, find the numbers.
Answers
Solution:
Given:
A word problem.
To solve the question, we develop the statements into mathematical equations.
Hence,
Let the two numbers be represented by x and y
where;
x is one number
y is another number
\(\begin{gathered} \text{One number is 2 less than 3 times another.} \\ \text{Mathematically means;} \\ x=3y-2 \\ R\text{earranging, th}e\text{ equation becomes; }x-3y=-2\ldots\ldots\ldots\ldots.(1) \\ \text{The sum of the two numbers is 14.} \\ \text{Mathematically means;} \\ x+y=14\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}\)
Solving both equations generated simultaneously, using the elimination method, we subtract equation (1) from equation (2).
That is equation (2) - equation (1);
\(\begin{gathered} x-3y=-2\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ x+y=14\ldots\ldots\ldots\ldots\ldots\text{.}(2) \\ \text{equation (2)-(1);} \\ x-x+y-(-3y)=14-(-2)_{} \\ y+3y=14+2 \\ 4y=16 \\ \text{Dividing both sides by 4,} \\ y=\frac{16}{4} \\ y=4 \end{gathered}\)
Substituting the value of y gotten into equation (2) to solve for x,
\(\begin{gathered} x+y=14 \\ x+4=14 \\ x=14-4 \\ x=10 \end{gathered}\)
Hence, the solution to the equations is;
\((x,y)=(10,4)\)Therefore, the numbers are 10 and 4.
Betsy earns $15.50 per hour working as a hairdresser. Each week, she earns an
average of $150 in tips. Write an equation to determine how many
hours Betsy worked in a week where she was paid a total of $739
Answers
Answer:So you subtract 150 from 739 which is 598 and then you divide 589 with 15.50 which is 38. The answer is 38 hours
Step-by-step explanation:
739-150=589
589/15.50 is 38
The answer is 38 hours
Provide the missing statement and reasons for the following proof: Given: m∠X+m∠Y=m∠W Prove: m∠Z+m∠X+m∠Y=180°
Answers
Answer:
R3. Definition of Linera Pair
S4. m∠3 +m∠4 =180°
R5. Substitution Property of Equality
I'm not sure if it's right but I tried :/
lmk if it's wrong
this is due tomorrow pls help
Answers
The angle that is a vertical angle to AEB is CED.
What is a vertical angle to AEB?When we have the intersection of two lines, we define the vertical angles as the pair of angles that share a vertex and don't share sides.
So these angles are only connected by the vertex.
So a vertical angle to AEB should also have the vertex E, and no common sides to AEB, the only angle that meets that requiriment is CED.
Then we conclude that the vertical angle to AEB is CED.
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Micah is at a donut shop and wants to choose his own dozen. There are ample glazed,
chocolate and jelly donuts. If Micah wants at least two jelly donuts, how many different
combinations of donuts can Micah use to create a box of a dozen donuts?
Answers
Answer:
Well lets label them
There are 4 choices
And the 4 choices can make up a dozen
He wants at least 2 jelly donuts
So instead of drawing over a 100 different combinations of donuts and checking them we can Do it like this
Well we know there has to be at least 2 jelly donuts out of the dozen so at least 2 of the donuts are jelly. Now you have 10 donut spaces left
So 1/4*1/4*1/4*1/4 since 4 options is 1/288 Now you have 1/288.
So 288 spaces? I’m not sure haven’t done this in a while just search up probability calcualtions
Each side of a square office is 9 feet long. It will cost $7.37 per square foot to replace the carpet in the office. What would be the total cost to replace the carpet?
$______
Answers
81*7.37=596.97
So your answer is $596.97
Answer: $596.79
Step-by-step explanation:
9*9=81 square feet
81*7.37=596.79 dollars worth of carpet
A sample is selected from a population with a mean of μ = 65 and a standard deviation of σ = 15. if the sample has n = 9 scores, what are the expected value of m and the standard error of m?
Answers
The Expected value of M is 65
The Standard error of M is 5
The mean of the distribution of sample means is called the expected value of M.The standard deviation of the distribution of sample means is called the standard error of M.Given,
The sample score, n = 9
The Standard deviation, σ = 15
Population mean, μ = 65
Then,
The Expected value of M = μ
∴ The Expected value of M = 65
The Standard error of M = σ/\(\sqrt{n}\)
\(=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5\)
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These problems are called exponents or something. I just want to make sure I got it right and please solve it.
Answers
Answer:
you have all of them right just make sure for number six you have 1/3125. you have all the work im not sure what i should solve.
Next consider a different scenario. Instead of Mexico experiencing rapid economic growth suppose that Canada experiences rapid and prolonged economic growth. Consider the affect of Canada economic growth on the economic growth of various us states. Move states that should grow quickly
Answers
The correct answer to this open question is the following.
Although the question does not include references, under that context we can say that if Canada experiences rapid and prolonged economic growth, instead of México, this would affect Canada's economic growth for the better and it will have a direct impact in various US states, basically, the border states to Canada.
This would mean more trade relations and people border crossing activity due to the increase of trade and businesses.
However, let's have in mind that México, Canada, and the United States have signed a new trade agreement that substitutes the North American Free Trade Agreement (former NAFTA). The new agreement is called USMCA, the United States, México, and Canada Agreement, and creates tight trade bonds between the three countries.
Answer:
grow quickly: michigan minnesota new york
not impacted: texas n. carolina
Step-by-step explanation: states that border canada are expected to gain from trade easier.
An investment will pay you $15,000 in 9 years. The appropriate discount rate is 8 percent compounded daily. What is the present value?
Answers
The present value of an investment that will pay you $15,000 in 9 years, with an appropriate discount rate of 8 percent compounded daily, is $7,638.61.
This is calculated using the following formula:
\(\begin{equation}PV = \frac{FV}{(1 + r)^n}\end{equation}\)
\(\begin{equation}PV = \frac{15000}{(1 + 0.08)^{3285}} = 0.00001059\end{equation}\)
Present Value = $7,638.61
The number of years is 9 years multiplied by 365 days per year, which is 3285 days. The interest rate is 8 percent divided by 365 days per year, which is 0.0002191780822.
In other words, if you invest $7,638.61 today at 8 percent compounded daily, you will have $15,000 in 9 years.
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a data set consists of 145 observations that range from 56 to 490. what size class interval would you recommend? (round up to the next whole number.)
Answers
The size class interval recommend is 30.
Assume that the observations are more or less evenly distributed across the range, and you should get about 5 observations per class.
It also presumes that your interest in the observations is uniform: you are equally interested in values close to 60 as you are in values close to 480. If you were only interested in values above 450, you could group all values from 56 to 449 into one large class and divide the rest into smaller classes.
It is also necessary to check to see if the distribution is uniform. If it is skewed in either direction, it makes more sense to have smaller classes where the observations are dense and larger classes where they are sparse.
Therefore, the size class interval recommend is 30.
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A pair of boots normally sales for $89.00,it is on sale for $50 what’s the sale percent?
Answers
Answer:
Your answer
43.8 %
Mark it as Brainlist. Follow me for more answer.
Step-by-step explanation:
you find
Write an equation of the line in point-slope form
that passes through the given points.
7. (4, 2) and (1,6)
Answers
Answer:
Step-by-step explanation:
slope=(6-2)/(1-4)=4/-3=-4/3
eq. of line is y-2=-4/3(x-4)
Which equation represents the same linear function in the table below? E. y = -x +7 F. y = 4x +3 G. y=8x+7 H. y=x+8
Answers
Answer:
F. y = 4x +3
Explanation:
Comparing the values in the table and the given function, the equation that represents the same linear function in the table is:
\(y=4x+3\)Check
\(\begin{gathered} \text{When x=1} \\ y=4(1)+3=7 \end{gathered}\)\(\begin{gathered} \text{When x=3} \\ y=4(3)+3=12+3=15 \end{gathered}\)A Construction worker needs to pour a rectangular slab 29 feet long 16 feet wide and 6 inches thick how many cubic yards of concrete does the worker need
Answers
We have a rectangular slab.
The volume of concrete is equal to the volume of this rectangular prism.
The volume of this prism is equal to the product of its length, width and thickness.
Then, we can write:
\(\begin{gathered} V=L\cdot W\cdot t \\ V=29ft\cdot16ft\cdot6in \\ V=29ft\cdot16ft\cdot(6in\cdot\frac{1ft}{12in}) \\ V=29\cdot16\cdot\frac{6}{12}ft^3 \\ V=232ft^3 \end{gathered}\)We convert the thickness from inches to feet by multiplying it by a unit ratio 1 ft / 12 inches, which has a value of 1, as 1 ft = 12 inches, but let us change the units from inches to feet.
When we have all the measures in feet we can have the volume in cubic feet.
Answer: 232 cubic feet.
Which table contains the values that satisfy equation y=0.5×+12
Answers
Answer: 6
Step-by-step explanation:
Maybe
Missy has 4 times as many trading cards as her friends ashe and caleb combined. Ashe has 17 cards . Missy has 156 cards.
How many trading cards does caleb have ?
The eqaution that repsents this problem _____
Solving the equation gives x= ____
Caleb has ___ trading cards.
Answers
There are 22 cards in the Caleb trading card deck.
What is the division of the 52 playing cards?A deck of playing cards contains 52 total cards. Each of the four suits contains 13 playing cards. These are the diamonds, clubs, hearts, and spades. Although hearts and diamonds are red, spades and clubs are black.
In total, Missy has 156 cards. We split 156 by 4 since she has four times as many as they have.
156/4= 39
Ashe possesses 17 cards, while Caleb's number is still a mystery. They each have 39 cards, thus to determine how many cards Caleb has, we must take Ashe's cards away.
39-17=22
presently going over our work
Caleb has 22 cards in his hand.
Ashe is holding 17 cards.
They each have 39.
Which is 4 times less than how many cards Missy has
Missy has 156 cards.
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what is equivalent to 8 1/2?
Answers
Answer:
Hi
Please mark brainliest ❣️
Thanks
Step-by-step explanation:
8 1/2 is equivalent to 17/2 and 8.5
Reason
Change 8 1/2 to improper fraction which is 17/2
Then to decimal which is 8.5
Hope I helped
Don't forget to Mark ❣️ brainliest and leave a like
Solve for x: (5x + 28)° (4x + 30)°
Answers
Answer:
x = 2
Step-by-step explanation:
The 2 angles are vertical and congruent, thus
5x + 28 = 4x + 30 ( subtract 4x from both sides )
x + 28 = 30 ( subtract 28 from both sides )
x = 2
Let a=2 and b=1, find the value of 2a + 3b
Answers
Answer:
7 is a answer
Step-by-step explanation:
2a+3b
2×2+3×1
4+3
7
hope it helps....
\( \sf a = 2,\: b = 1\)
\( \sf Q) \:2a + 3b = {?}\)
\( \sf \implies 2a + 3b\)
\( \sf \implies 2(2) + 3(1)\)
\( \sf \implies 4 + 3\)
\( \sf \implies 7\) is the required answer.
Question 16 30. Scenario 3-1 How many many blooms are on the peony plants at Bouquet Farms? In previous years, you know that each plant on average would produce 30 blooms. You are interested if your y
Answers
Mean number is less than 30 represents reject H₀ Null hypothesis if Tstat < -1.6604 for significance level of 0.05.
t-statistic falls below -1.6604, reject Null hypothesis and conclude there is evidence to suggest mean number is indeed less than 30.
The Null hypothesis is that the mean number is equal to 30 (μ = 30).
The alternative hypothesis would be that the mean number is less than 30 (μ < 30).
Calculate the test-statistic (Tstat) using the sample data.
Sample data provided is the number per plant in a random sample of 100 plants.
Based on decision rule, which is to reject H₀ if Tstat < -1.6604,
Compare the calculated test-statistic to the critical value of -1.6604.
If the calculated Tstat is less than -1.6604, we reject the null hypothesis.
The critical value of -1.6604 is associated with a significance level of 0.05.
This means that if the Null hypothesis is true (μ = 30),
There is a 5% chance of observing a test statistic smaller than -1.6604.
Therefore, Tstat falls below -1.6604 sufficient evidence to reject Null hypothesis and conclude mean number is likely less than 30.
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The above question is incomplete, the complete question is:
How many many blooms are on the peony plants at Bouquet Farms? In previous years, you know that each plant on average would produce 30 blooms. You are interested if your yield this year is smaller because the past few months have been cold and wet. Suppose a random sample of 100 plants yielded the following data on the number of blooms per plant: X=25, S= 8.
You are interested in determining whether there is evidence that the mean number of blooms is less than 30.
Referring to Scenario 3-1, state the correct decision rule for a -0.05.
Reject H₀ if Tstat > 1.6604
Reject H₀ if Tstat < -1.96
Reject H₀ if Tstat < 1.6604
Reject H₀ if Tstat < -1.6604
The width of a box is two-thirds of it's length and height is one-third of it's length. If the volume of the box is 48m³, find the are of the base of the box.
Please teach it step by step
Answers
Volume = length x (2/3 length) x (1/3 length)
We also know that the height is one-third of the length, so we can replace "height" with "1/3 length": Volume = length x (2/3 length) x (1/3 length) = 48m³
Now we can simplify this equation by multiplying the lengths together:
(2/3 length) x (1/3 length) = 2/9 length² So the equation becomes: Volume = length x (2/9 length²) = 48m³
We can solve for the length by dividing both sides by (2/9 length²):
length = 3∛144 = 6m
Now that we know the length of the box is 6m, we can find the width and height: width = 2/3 length = 4m
height = 1/3 length = 2m
Finally, we can find the area of the base of the box by multiplying the length and width:
Area of base = length x width = 6m x 4m = 24m²
* Therefore, the area of the base of the box is 24m²
Answer:
Step-by-step explanation:
\(V=48,w=\frac{2}{3} l,h=\frac{1}{3} l,l=l\)
\(V=whl\)
\(48=\frac{2}{3} l\times \frac{1}{3} l \times l\)
\(48=\frac{2}{9} l^3\)
\(l^3=216\)
\(l=\sqrt[3]{216}\)
\(l=6\)
So length = 6m, width = 4m, height = 2m
Area of base = length x width = 24\(m^2\)
