Which function is an odd function?
A. f(x) = cos(-2pi x)
B. f(x) =csc(-3pi/2 x)
C. f(x) = sec (5pi/3 x)
D. f(x) = cos(6pi/5 x)
Answers
Answer:
B. f(x) =csc(-3pi/2 x)
Step-by-step explanation:
Got it right on Edmentum.
The function \(f(x)=csc(-\frac{3\pi}{2x} )\) is an odd function.
The correct answer is an option (B)
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is odd function?"A function f(x) is odd function if f(-x) = -f(x) "
For given question,
We know, cos(-x) = cos(x)
This means, cos function is an even function.
Consider, f(x) = sec (5pi/3 x)
We know,
\(sec(\theta)=\frac{1}{cos(\theta)}\)
\(\Rightarrow f(x) =sec (\frac{5\pi}{3x} )\\\\\Rightarrow f(x)=\frac{1}{cos(\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=\frac{1}{cos(-\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=\frac{1}{cos(\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=sec(\frac{5\pi}{3x} )\\\\\Rightarrow f(-x)=-f(x)\)
This means, f(x) = sec (5pi/3 x) is an even function.
We know, sin(-x) = -sin(x)
\(\Rightarrow f(x)=csc(-\frac{3\pi}{2x} )\\\\\Rightarrow f(x)=\frac{1}{sin(-\frac{3\pi}{2x} )}\\\\ \Rightarrow f(-x)=\frac{1}{sin[(-\frac{3\pi}{2x} )]} \\\\\Rightarrow f(-x)=\frac{1}{-sin(-\frac{3\pi}{2x} )}\\\\\Rightarrow f(-x)=-csc(-\frac{3\pi}{2x} )}\\\\\Rightarrow f(-x)=-f(x)\)
Therefore, the function \(f(x)=csc(-\frac{3\pi}{2x} )\) is an odd function.
The correct answer is an option (B)
Learn more about odd function here:
https://brainly.com/question/14264818
#SPJ2
Related Questions
PLEASE HELP direct vs inverse variation graphs
Answers
A direct variation graph is a linear graph with a positive slope that increases in a straight line, while an inverse variation graph is a curved graph with a negative slope that decreases over time.
What is variation?Variation is the act of changing something slightly or the result of such a change. In biology, variation is the differences between individuals of the same species or the differences between species. In genetics, variation is the result of mutations in the genetic code, which can create different phenotypes. Variation can also refer to the differences in traits caused by the environment or cultural differences. In economics, variation refers to the changes in the supply and demand of a particular good or service. Variation can also refer to the differences in the performance of different organizations or people.
The inverse variation graph has a different shape than the direct variation graph, and the ratio of the two variables is inversely proportional.
To learn more about variation
https://brainly.com/question/25215474
#SPJ1
Evaluate 2 to the ninth power. Help plz
Answers
2^9 = 2 x 2 x2 x 2 x 2 x 2 x2 x 2 x 2 = 512
2 ^9 = 512
The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
Answers
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
Learn more about the tangent line:
https://brainly.com/question/30162650
#SPJ1
Enter the decimal equivalent of the following:
Nine hundred eight and seven hundredths
_
Answers
Answer:
908.07
Step-by-step explanation:
We know there is nine hundered and eight so lets put that.
908.
Then we know that there are seven hundredths, one number to the right of a decimal is a tenth, so lets go one more to the right. We put seven to the right of the tenth decimal place. Now we have:
908.07
3x - 8 - 7x= 2x + 8 + 2x
Answers
Simpify the equation.
\(\begin{gathered} 3x-8-7x=2x+8+2x \\ -4x-8=4x+8 \\ -4x-4x=8+8 \\ x=\frac{16}{-8} \\ =-2 \end{gathered}\)The value of x is -2. So the solution of equation is x=-2.
Please look at the photo. Thank you!
Answers
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
#SPJ1
Lookout station A is 12 miles from the fire. Lookout station B is 39 miles from station A. The angle at station A is 52°. Find the distance between Station B and the fire.
Answers
Therefore, in order to find out the distance from station b to the fire, we must use the sine formula, as we know that sine is the opposite side divided by the hypotenuse.
We want to find out the opposite side and we already have the hypotenuse that is 12 miles.
So:
\(\begin{gathered} \sin52=\text{ }\frac{x}{12} \\ 12(\sin52)=x \\ 12(0.788)=x \\ 9.456=x \end{gathered}\)Therefore, station B i 09.456 miles from the fire.
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answers
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
\(v(t) = v(0)*e^{rt}\)
Applying data from the problem gives us:
\(v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4\)
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
Choose the system of inequalities that best matches the graph below.
Answers
Answer: D
Step-by-step explanation:
Hope it helps
Answer the mixed number as a decimal 8 9/10
Answers
Answer:
8.9
Step-by-step explanation:
Answer:
8.9
Step-by-step explanation:
8 9/10=8+9/10
=8/1+9/10
=(8/1×10/10)+9/10
=80/10+9/10=8 9/10
We know that
89/10
is the same as
89÷10
Then using
Long Division for 89 divided by 10
gives us
=8.9
Line segment AB is equal to 40cm. What is the length of the middle part in terms of x?
Answers
Answer:
Step-by-step explanation:
40/30=409
If x = 8 units, y = 5 units, and h = 3 units, then what is the area of the parallelogram shown above?
Answers
Answer:
Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....
Using Diagonals: A = ½ × d1 × d2 sin (y)
Using Base and Height: A = b × h
Using Trigonometry: A = ab sin (x)
Which best describe an angle biscector
Answers
Step-by-step explanation:
I hope this helps : ) I added an attachment for your answer.
here is 93 points but answer this please If x = 4, what is the value of x3 + x - 5?
Answers
Answer:
11
Step-by-step explanation:
x3+x-5
3*4=12
12+4-5
16-5=11
pls i REALLY need brainliest
Clarence walks 3.1 miles around Lake Johnson every day for five days.
If it takes him a total of 6 hours to walk the 15.5 miles, what is his
average time per day?
minutes per day.
Answers
Answer:
Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day
Step-by-step explanation:
To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.
Let's calculate his average time per day:
Average time per day = Total time / Number of days
Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:
Average time per day = 6 hours / 5
Average time per day = 1.2 hours per day
To convert hours to minutes, we'll multiply the average time per day by 60:
Average time per day = 1.2 hours * 60 minutes
Average time per day = 72 minutes per day
Therefore, Clarence's average time per day is 72 minutes.
what is the constant in 8b + 3.2
Answers
Elizabeth changes 300 Canadian dollars she has $230.05 in American dollars. What was $1 worth in Canadian dollars Number 401
Answers
ANSWER:
1.3 Canadian dollars.
STEP-BY-STEP EXPLANATION:
We can calculate the equivalence of a Canadian dollar, through the following proportion:
\(\frac{300}{230.05}=\frac{x}{1}\)We solve for x:
\(\begin{gathered} x=\frac{300}{230.05} \\ x\approx1.3 \end{gathered}\)Which means that $1 is approximately equal to 1.3 Canadian dollars.
In a coordinate plane, plot the points and sketch
angle. Write the coordinates of a point that lies in the interior of the
angle and the coordinates of a point that lies in the exterior of the
angle.
A(-5,0)
B(-1,-4)
C(4,2)
Answers
Answer:
A.
Step-by-step explanation:
Points A and B are on opposite sides of a lake. Another point, C. is 94.4 meters from Angle A. The measure of Angle A is 72° and the measure of Angle C is 30°. Find the distance between A and B.
Answers
To find the distance between points A and B, we can use trigonometry and the given information.
Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.
Using trigonometry, we can use the tangent function to find the value of "d".
tan(72°) = d / 94.4
To solve for "d", we can rearrange the equation:
d = tan(72°) * 94.4
Using a calculator, we can evaluate the expression:
d ≈ 4.345 * 94.4
d ≈ 408.932
Therefore, the distance between points A and B is approximately 408.932 meters.
Round 52.476 to the nearest tenth.
Answers
Explanation: The 4 is in the tenths spot. The next digit over is 7, which fits the "5 or more" category. We'll bump the 52.4 up to 52.5 and ignore every other digit.
Answer:
52.5
Step-by-step explanation:
Tenths are the first decimal place to the right of the decimal.
Rounding to the nearest tenth means you have to look at the hundredth place, which is seven.
The rule is if your place value is five or more, you race the value up.
So rounding four up will be five
Lastly, get rid of any other place values on the right of your place
Therefore, your new number is 52.5
In Problem, p is in dollars and q is the number of units.
(a) Find the elasticity of the demand function
p2 + 2p + q = 49 at p = 6.
(b) How will a price increase affect total revenue?
Answers
Answer:
-14
Explanation:
Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.
Formula for calculating price elasticity is: change in price/change in quantity =dq/dp
Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:
2p+2+dq/dp=0
dq/dp=-2p-2
Given p =6, we substitute:
dq/dp=-2×6-2
dq/dp=-12-2
dq/dp=-14
With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.
The graph of g(x) = ax^2 opens downward and is narrower than the graph of f(x) = x^2. Which of the following could be the value of a?
Answers
The value of a should be less than -1.
Equation of parabola,The equation of a parabola is given by the following function,
\(y=f(x)=\pm a(x-h)^2+k\)
where,
(h, k) denotes the coordinates of its vertex,
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us,\(f(x) = x^2\)
\(g(x)=ax^2\)
SolutionFor the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.
Hence, the value of a should be less than -1.
Learn more about Equation of parabola:
https://brainly.com/question/4443998
rewrite the following expression as a single logarithm 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
Answers
The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).
What is the rewritten form of the expression?The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;
2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)
= log {(x+3)²(x-2)^5}/(x-7)³(x²)
Read more on logarithm;
https://brainly.com/question/237321
#SPJ1
Joe has 16 pounds of fertilizer for his three gardens. He uses ⅜ of the fertilizer in his first garden and ¼ of the fertilizer in his second garden. What fraction of the fertilizer is left for the third garden? *
Answers
Answer:
3/8
Step-by-step explanation:
3/8 of 16 is 6
1/4 of 16 is 4
6+4 = 10
16-10 = 6
3/8 of 16 = 6
You deposit $5000 in an account earning 3% interest compounded continuously. How much will you have in the account in 5 years?
Answers
Answer:
$5809.17
Step-by-step explanation:
Using the formula for continuous compound interest \(P(t)=Pe^{rt}\) We can plug in our values \(P(t)=5000e^{0.03*5}\) and solve.
plese help im in 2nd grade and this is really hard all the kids in my class know it but me
Answers
Answer:
This isn't in second gradee- x-x
Step-by-step explanation:
Answer: For x such that 0<x<(pie/2), the expression:
[square-root(1-cos^2(x)]/sinx + [square-root(1-sin^2(x)]/cos(x)
is equivalent to,
F. 0
G. 1
H. 2
J. -tan(x)
K. sin2x
The answer is H.
Step-by-step explanation:
Write the equivalent decimal for each
fraction shown.
9/10
37/100
8 5/100
Answers
Answer:
The equivalent decimals for the given fractions are:
9/10 = 0.9
37/100 = 0.37
8 5/100 = 8.05
Step-by-step explanation:
The diameter of a cylindrical construction pipe is 4 ft, and its
length is 18 ft.
Answer the parts below.
Answers
Answer:
72π ft³226.19 ft³Step-by-step explanation:
(a) The figure shows the diameter of the pipe is 4 ft, so its radius is 2 ft. The equation for the volume of a cylinder is ...
V = πr^2·h
Filling in r=2 and h=18, we have ...
V = π(2 ft)^2(18 ft) = 72π ft^3
The exact volume is 72π ft³.
__
(b) Using a sufficiently accurate value of pi, the numerical value of the volume is ...
72π ft^3 ≈ 226.19 ft^3
The approximate volume is 226.19 ft³.
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.The probability of a student scoring less than 19 is(Round to four decimal places as needed.)(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.The probability of a student scoring between 17.7 and 27.1 is. -(Round to four decimal places as needed.)(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.The probability of a student scoring more than 33.1 is(Round to four decimal places as needed.)(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.OA. None of the events are unusual because all the probabilities are greater than 0.05.OB. The event in part (c) is unusual because its probability is less than 0.05.OC. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.D. The event in part (a) is unusual because its probability is less than 0.05.Help me solve thisView an example
Answers
Given
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1.
To find:
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
Explanation:
It is given that,
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1.
That implies,
a) Consider x=19.
Then,
\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ =\frac{19-22.4}{5.1} \\ =-0.6667 \end{gathered}\)Therefore,
The probability of a student scoring less than 19 is,
\(\begin{gathered} P(x<19)=P(z<-0.6667) \\ =0.25249 \\ =0.2525 \end{gathered}\)Hence, the probability of a student scoring less than 19 is 0.2525.
b) Consider x=17.7 and 27.1.
Then,
\(\begin{gathered} P(17.7Hence, the probability of a student scoring between 17.7 and 27.1 is 0.6433.c) Consider x=33.1.
Then,
\(\begin{gathered} P(x>33.1)=P(z>\frac{33.1-22.4}{5.1}) \\ =P(z>2.0980) \\ =1-P(z<2.0980) \\ =1-0.9821 \\ =0.0180 \end{gathered}\)Hence, the probability of a student scoring more than 33.1 is 0.0180.
d) Since, a probability of 5%, or 0.05, is considered unusual.
Then, the unusual event is,
Option B),
The event in part (c) is unusual because its probability is less than 0.05.
Suppose the given confidence level is 85%, what is the corresponding z critical value?