What is the range of the function y= cot(x)?
A. all real numbers
B. all real numbers except pi/2 + n(pi), where n is any integer
C. all real numbers except n(pi)/2, where n is any integer
D. all real numbers except n(pi), where n is any integer
Answers
Answer:
all real numbers
Step-by-step explanation:
Given : y = cot(x)
To Find: Range.
Solution:
Refer the attached graph.
The domain of the function [tex]y=cot(x)=\frac{cos(x)}{sin(x)}[/tex] is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n .
The range of the function is all real numbers.
Referring the graph we can say that the range of the given function y = cot(x) is all real numbers .
Hence Option A is correct.
Related Questions
What are the factors of x^2-64
Answers
a^2 - b^2 = a^2 - b^2
so
x^2-64
=x^2 - 8^2
= (x + 8)(x - 8)
The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).
Explanation:The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:
x^2 - 64 = (x - 8)(x + 8)
This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.
I WILL MARK BRAINLIEST TO A CORRECT AND EXPLAINED ANSWER!!!!
Look at points C and D on the graph:
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
A. 4.54 units
B. 5.00 units
C. 5.83 units
D. 34.00 units
Answers
D(1:0)
Image the right triangle between C, D and the point A(-4,0)
CA is 3-0=3; AD is 1-(-4)=1+4=5
CD is √3²+5²=√34=5.8309...
Answer:
Option C.
Step-by-step explanation:
Coordinates of the points C and D are (-4, 3) and (1, 0)
We have to find the distance CD.
Distance CD = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
CD = [tex]\sqrt{(1+4)^{2}+(0-3)^{2}}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34}[/tex]
= 5.83 units
Therefore, Option C. distance CD = 5.83 units is the answer.
what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Answers
Answer:
[tex](30\sqrt{3}-21\sqrt{6})[/tex]
Step-by-step explanation:
We have to find the product of the expressions.
[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]
= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)
= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]
= [tex]15\sqrt{12}-21\sqrt{6}[/tex]
= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]
= [tex]30\sqrt{3}-21\sqrt{6}[/tex]
= [tex](30\sqrt{3}-21\sqrt{6})[/tex]
Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.
Answers
A correlation can be called association when it can be ascertained that the result in one variable is as a result of the result of the other variable. Though correlation is a condition for causation, but correlation does not imply causation.
Therefore, given that there were a strong correlation between the variables n and p, the true statement is "n may cause p".
A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease
A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?
Answers
[tex]P(X) = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of success we want
p = probability of success
Therefore, since the problem tells you that X is the number of subjects who test positive for the disease, you will have:
[tex]P(X) = \frac{30!}{0!(30-0)!} 0.02^{0} (1-0.02)^{30-0} [/tex]
= 1 · 1 · 0.98³⁰
= 0.5455
Hence, the probability of none of the 30 subjects testing positive to the desease is 54.55%
B) In a binomial distribution, the mean is given by the formula:
μ = n · p
= 30 · 0.02
= 0.6
And the standard deviation is given by the formula:
σ = √[n·p·(1-p)]
= √[30·0.02·0.98]
= √0.588
= 0.77
Hence, the mean is 0.6 and the standard deviation is 0.77
C) This test is not very viable: 30 subjects are a sample too small compared to the population (millions of people who need to be tested), the probability of finding that all the 30 subjects are healty is only a little bit over 50%, the standard deviation is too high compared to the mean, and 2% of false positive is a percentage too high to consider the test viable.
please help asap 50 pts
Answers
Your answer should be C.
[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]
suzie divided a 3-pound bag of apples into 2 equal piles. How many lbs of apples are in each pile
Answers
3 pounds divided by 2 piles = 1.5 pounds per pile
Suzie's 3-pound bag of apples divided into two equal piles will result in each pile weighing 1.5 pounds. This is a basic arithmetic problem often referred to as equal distribution.
Explanation:Suzie is dividing a 3-pound bag of apples into two equal piles. This is a simple division problem where the total weight of apples (3 pounds) is distributed equally into two piles. Therefore, we simply divide the total weight by the number of piles.
To calculate the weight of apples in each pile, we divide the total weight (which is 3 lbs) by the number of piles (which is 2). So, 3 lbs ÷ 2 = 1.5 lbs. Each pile would weigh 1.5 lbs.
This type of problem is often referred to as an equal distribution problem in mathematics. It falls under the category of basic arithmetic and is typically taught in lower grades.
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Mind helping someone out?
I've kinda been stuck on this problem and it's my last math problem for the day.
Answers
What is the remainder when the positive integer n is divided by 12 ? (1) when n is divided by 6, the remainder is 1. (2) when n is divided by 12, the remainder is greater than 5?
Answers
The number n would be 31. In this case you could divide it by 6 and get 5 with a 1 remainder and then divide it by 12 and get 2 with a 7 remainder.
multiply and simplify. 5x^2 / y^3 * 4y^2 / 10x
Answers
[tex] \frac{5x^2}{y^3} * \frac{4y^2}{10x} [/tex]
Rewriting the expression we have:
[tex]\frac{20x^2y^2}{10xy^3} [/tex]
Then, simplifying and by properties of exponents we have:
[tex]{2x^{2-1}y^{2-3}} {2xy^{-1}}[/tex]
Rewriting we have::
[tex] \frac{2x}{y} [/tex]
Answer:
The simplified expression is given by:
[tex] \frac{2x}{y} [/tex]
using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. the telescope is positioned so that the line of sight to the eagle forms a 38 degree angle of elevation. the telescope sits 1.3 m above the ground and the base of the telescope is 116 m away from the base of the cliff. to the nearest tenth of a meter, how high above the ground is the eagle?
Answers
Find the surface area of each right regular pyramid. a pentagonal pyramid with base sides 1.5 meters, base area 3.9 m2, and slant height 4 meters
Answers
since the base area is 3.9 m2, we could just add that to the total at the end.
since the base edge is 1.5 m and the height is 4m, we could find the area of the face by doing (1.5 times 4)/2 which would give us 3m2.
Since there are 5 faces(pentagonal), we would multiply 3 times 5, and would get 15m total for all the triangle faces.
so to get the total surface area, you would add 15 + 3.9 (which was the base area) and get 18.9m2....
....;);) hope this helps
Share 450 in the ratio of 4:5
Answers
4n + 5n = 450
9n = 450
n = 50
Now we multiply into the ratio:
200:250
Or
200 and 250
450 : 9 = 50
4 · 50 = 200
5 · 50 = 250
Answer: 200 and 250.
What is the area of a regular hexagon with a side length of 12 cm
Answers
More exactly would be 374.12.
Hope this helps!
The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit
Answers
To calculate the area, multiply 15 and 6, then divide the product by 2.
15 × 6 = 90
90 ÷ 2 = 45
The area of this triangle is 45.
New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?
Answers
Am I correct in thinking that the answer to this derivative problem is B?
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1
Answer is actually choice C (not choice B)
note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative
-----------------------------------------------------
Checking the answer:
y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression
x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before
So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.
A group of 12 people attend a meeting. Every pair of people shook hands with each other. How many handshakes were there?
Answers
So there will be 11+10+9+8+7+6+5+4+3+2+1=66 handshakes.
Hope this helped!
Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.
Answers
[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}\\\\S_{10}=4\cdot \dfrac{(-\frac{1}{2})^{10}-1}{-\frac{1}{2}-1}=4\cdot \dfrac{(\frac{1}{1024}-1)}{(-\frac{3}{2})}\\\\=\dfrac{8}{3}\cdot \dfrac{1023}{1024}=\dfrac{341}{128}[/tex]
The sum is approximately 2.66.
What is the measure of the angle?
Answers
Measure of the angle=65°+90°=155°
We can conclude that the measure of the bigger angle in the picture is 155°
So the angle is 90 degrees + 65 degrees = 155 degrees
The fourth one is the answer
Given v=(6,3) and w=(1,-2), what is the result of v-w
Answers
I don't believe you need the word "result" here. At first I thought you'd meant "resultant." Here you're finding the "difference" v less w.
The result of v - w is (5, 5).
Explanation:To find the result of v - w, we need to subtract the corresponding components of the two vectors. Given v = (6, 3) and w = (1, -2), we subtract their x-components and their y-components separately.
v - w = (6 - 1, 3 - (-2))
Therefore, v - w = (5, 5).
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Daniel’s tennis team made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64. What expression would model the amount of money each player would receive if the money is divided equally?
Answers
The answer would be
1. (582.85 - 64)/p Or D
And
2. 64.85 Or A
The expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).
What is division?
Division is a operation in mathematics which is used to divide a specific number into equal parts of specific magnitude.
Given is Daniel’s tennis team which made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64.
Assume that there are [x] players in the team.
Now, the money left after spending on food = 582.85 - 64 = 518.85
Each player, when divided equally, would receive = y = (518.85/x)
Therefore, the expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).
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Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answers
For this case we must find the set of ordered pairs that form an exponential function.
When observing, the last set of ordered pairs is an exponential function of the form:
[tex]y = 3 ^ x[/tex]
For x = 0:
[tex]y = 3 ^ 0 = 1[/tex]
We have the ordered pair:
[tex](x, y): (0, 1)[/tex]
For x = 1:
[tex]y = 3 ^ 1 = 3[/tex]
We have the ordered pair:
[tex](x, y): (1, 3)[/tex]
For x = 2:
[tex]y = 3 ^ 2 = 9[/tex]
We have the ordered pair:
[tex](x, y): (2, 9)[/tex]
For x = 3:
[tex]y = 3 ^ 3 = 27[/tex]
We have the ordered pair:
[tex](x, y): (3, 27)[/tex]
Answer:
The set of ordered pairs that form an exponential function is:
[tex](0, 1), (1, 3), (2, 9), (3, 27)[/tex]
Answer:
D
Step-by-step explanation:
What is sin (51)?
Answer Choices : 1.23 , 0.63 , 0.51 , 0.78
Answers
Make sure your calculator is in degrre mode when doing these.
so the answer is 0.78
Bob can type 2 letters in 4 hours while Bill can do it in 6. How many hours would it take them, working together, to type six letters?
Answers
r1 = 2/4 = 1/2 letter / hour
The production rate of Bill is given by:
r2 = 2/6 = 1/3 letter / hour
Thus, the production rate of both is:
r1 + r2 = 1/2 + 1/3 = 5/6 letter / hour
Then, the production of 6 letters is given by:
rate * time = letters
(5/6) t = 6
t = (6/5) 6
t = 36/5 = 7 1/5 hours = 7hr 12 min
Answer:
it would take them, working together, to type six letters about:
7hr 12 min
Answer:
It would take them 7.2 hours.
The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form? Show your work.
8 square units
20 square units
24 square units
28 square units
Answers
we know that
surface area=area A +area B+area C+area D+area E+area F
area A=area F
area B=area area D
area C=area E
so
surface area=[2*1]+[4*2]+[4*1]+[4*2]+[4*1]+[2*1]----> 28 units²
the answer is
28 units²
Answer:
the answer is d:)
Step-by-step explanation:
i took the quiz on edge and got 100:D
Maria works at a bookstore. On Wednesday, she sold three times as many books as she did on Tuesday. On Thursday, she sold 8 fewer books than she did on Wednesday. During the three days, Maria sold 20 books. Create an equation that can be used to find m, the number of books Maria sold on Tuesday.
Answers
Tuesday - m
Wednesday - 3m
Thursday - 3m - 8
Show all of these in an addition problem with a total of 20 and simplify.
m + 3m + (3m - 8) = 20
7m - 8 = 20; You can solve this equation to find the number of books Maria read.
Quick need the answer!
Answers
Find the area of the following rectangle in square feet. 44 ft 2 11 ft 2 14.7 ft 2 132 ft 2
Answers
we know that
area of rectangle=base*height
in this problem
base is 22 ft
height is 2 yd
convert yd to ft
1 yd is equal to 3 ft
2 yd--------> 2*3-----> 6 ft
area of rectangle=22*6-----> 132 ft²
the answer is
132 ft²
Answer:
132
Step-by-step explanation:
Write the expression 5x+4x^2(2x+7)-6x^2-9x as a polynomial in standard form
Answers
5x + 8x³ + 28x² - 6x² - 9x
8x³ + 22x² - 4x
This can be simplified to:
2x(4x² + 11x - 2)
I don't know which of those answers you are looking for.
Answer:
8x^3 + 22x^2 - 4x
Step-by-step explanation:
5x+4x^2(2x+7)-6x^2-9x
Open the bracket
5x + 8x^3 + 28x^2 - 6x^2 - 9x
= 8x^3 + 28x^2 - 6x^2 - 9x + 5x
= 8x^3 + 22x^2 - 4x
In standard form, the polynomial 5x+4x^2(2x+7)-6x^2-9x is 8x^3 + 22x^2 - 4x