What restriction should be applied to y = tanx for y = arctanx to be defined?
Look at the picture below for the choices.
Answers
Answer:
its c on edge
Step-by-step explanation:
restrict the domain to (-pi/2,pi/2)
The restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The graph below shows the functions tan(x) and arctan(x) that is tan^-1(x)
In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.
A restricted domain gives an inverse function because the graph is one to one and able to pass the horizontal line test.
Thus by restricting the domain [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] we can obtain the function [tex]tan(x)[/tex] as [tex]tan^{-1} (x)[/tex].
Hence we can conclude that the restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.
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Related Questions
Which of the following is an obtuse triangle?
Triangle A
Triangle B
Triangle C
Triangle D
Answers
Answer:
triangle B
Step-by-step explanation:
It is the only triangle with an angle wider than 90
Find the present value of an annuity of $120 at the end of each month put into an account yielding 4.8% compounded monthly for 5 years.
Answers
Answer:
Yyyy
Step-by-step explanation:
The sum of two consecutive odd integers is 72 what are the integers
Answers
Since -72 is the sum of two integers, your answer will be approximately -36 and -36 (or ).
Kelly can type 120 words in 3 minutes. At that rate, how many words can she type in 5 minutes?
Answers
Solve the system of linear equations by graphing. x+y=27
y=x+3
Answers
Answer:
X=12 Y=15
Step-by-step explanation:
X+Y=27 (1)
Y=X+3 (2)
substitute (2) into (1)
X+X+3=27
2X=24
X=12
substitute X=12 into (2)
Y=12+3
Y=15
The solution to the problem as shown in the graph is at A(12, 15):
A linear equation is in the form:
y = mx + b;
where m is the slope, b is the y intercept and y, x are variables.
Given the linear equations:
x + y = 27
y = x + 3
Plotting the equations using Geogebra online graphing tool, the solution to the problem as shown in the graph is at A(12, 15):
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helppp me please!!!
Answers
Answer:
18 hdhb
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
21/1 x 6/7
21 x 6 = 126
1 x 7 = 7
126 / 7 = 18
PLEASEE HELP ME AS FAST AS POSSIBLE! According to the fundamental theorem of algebra, how many solutions does this polynomial have?
Btw sorry about the bad lighting
Answers
2, because there are 2 different factors with x in it.
x could be 0, or 4.
Hope this helps
The number of the solution of the polynomial is 2. And the solutions of the polynomial are 0 and 4.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The polynomial is given below.
y = 3x(x - 4)
The factors of the polynomial are 3x and (x - 4).
For the solution of the polynomial, put each factor equals to zero.
Then the solution of the polynomial will be
3x = 0
x = 0
x - 4 = 0
x = 4
The number of the solution of the polynomial is 2.
And the solutions of the polynomial are 0 and 4.
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what number is rational?
Answers
Answer:
0.33333333333333
Step-by-step explanation:
Can someone help me out ? Please ?
Answers
Answer:B
Step-by-step explanation:mark me as brainliest
Daniel and Paul went exploring in the woods. On the first day Daniel saw 3 rabbits and Paul saw 8 deer. On the second day Daniel saw 4 rabbits and Paul saw 7 deer. On which day of hunting did Daniel and Paul catch a higher ratio of rabbits to deer?
Answers
Answer:
first day when they say 3 rabbits and 8 deers 3:8
Simplify -9/6 divided by -3/2
Answers
An negative times a negative is a positive
So the new prob is 9/6 times 2/3
you multiply across and you get 18/18
18/18 is equal to 1
there’s you answer hope it helps ✨
Cheryl has $100 on her subway gift card. Each week she buys the same lunch for $10. She wants to continue using the card until the balance remaining is $40. Write an equation to represent the situation
Answers
Answer:
100-60=40
Step-by-step explanation:
Answer:
In 6 weeks she will have $40.
Step-by-step explanation:
$100 - $10 - $10 -$10 - $10 - $10 - $10.
Or $100 - $60.
1. What is the surface area of the polyhedron? Explain your reasoning.
Answers
Answer:
24
Step-by-step explanation:
i counted the square me good at counting
Which set of ordered pairs does not represent a function?
\{(5, -6), (-1, -2), (2, -9), (-8, -2)\}{(5,−6),(−1,−2),(2,−9),(−8,−2)}
\{(-5, 7), (-4, -9), (-5, -4), (2, -6)\}{(−5,7),(−4,−9),(−5,−4),(2,−6)}
\{(-4, 2), (-2, 8), (-1, 6), (5, 6)\}{(−4,2),(−2,8),(−1,6),(5,6)}
\{(2, 2), (-4, 9), (9, -3), (-3, 2)\}{(2,2),(−4,9),(9,−3),(−3,2)}
Answers
Answer:
the 1st, 2nd, and 4th one because those ordered pairs, the y axis is the same . sooo thats what makes it a non function .
Question 1 of 2
15 Points
A report revealed that the average no. of months that an employee stays in a factory is 36
months. Assuming that the no. of months of an employee tenure in the factory is normally
distributed with a standard deviation of 6 months, find the probability that a certain employee
will stay
a. More than 30 months
b. Less than 24 months
c. Between 24 to 48 months
Answers
Answer:
Step-by-step explanation:
Given the following :
Mean(m) = 36 months
Standard deviation (s) = 6 months
A) probability of staying more than 30 months :
Zscore = ( x - m) / s
x = 30
Zscore = (30 - 36) / 6
Zscore = - 6/6
= - 1
P(Z > - 1) = 1 - p(Z < - 1) ; p(Z < - 1) = 0.1587
1 - p(Z < - 1) = 1 - 0.1587 = 0.8413
2)less than 24 months :
Zscore = ( x - m) / s
x = 24
Zscore = (24 - 36) / 6
Zscore = - 12/6
= - 2
P(Z < - 2) = 0.0228
3.) between 24 to 48 months
For 24 months : from above = 0.0228
48 months :
Zscore = ( x - m) / s
x = 48
Zscore = (48 - 36) / 6
Zscore = 12/6
= 2
P(Z < 2) = 0.9772 ( from z table)
Hence,
0.9772 - 0.0228 = 0.9544
HELP!!! DUE IN 38 MINUTES 11:22 due at 11:59pm pst
Answers
Answer:
(1,2)
(-1,2)
(1,-2)
(-1,-2)
Marcella bought 3 packages of balloons and 4 packages of favors for $14.63.
Rupert bought 2 packages of balloons and 5 packages of favors for $16.03. Find
the price of a package of balloons.
Answers
Answer:
$1.29 for balloons
Step-by-step explanation:
3b + 4f = 14.63
2b + 5f = 16.03
2b = 16.03 - 5f
b = (16.03/2) - 5/2f
3b + 4f = 14.63
3[(16.03/2) - 5/2f] + 4f = 14.63
48.09/2 - 15/2f + 4f = 14.63
24.045 - 15/2f + 8/2f = 14.63
24.045 - 7/2f = 14.63
-7/2f = -9.415
-3.5f = -9.415
f = 2.69 = $2.69 for favors
2b + 5(2.69) = 16.03
2b + 13.45 = 16.03
2b = 2.58
b = 1.29 = $1.29 for balloons
Solve -8 =2(z-18) for z
Answers
Answer:
z=14
Step-by-step explanation:
-8=2(z-18)
-8=2z-36
+36 +36
28=2z
28/2=14
z=14
Answer:
z=14. 2(14-18)=2(-4)=-8=-8
P.s.
please give me brainliest for my next rank
help!!!
3 Peter measured the width of a room as 28 feet
and the length as 17 feet. About how many
square feet does the room cover?
Area = length X width
Answers
Area = length X width 28x17= 476
Use the distributive property to find an expression that is equivalent to
2x(x + 7)-(3x +1)
Answers
Given expression:
2x(x + 7)-(3x +1);
To distribute implies to spread a process equally in an expression. Often times, the distributive property is used for expressions inside parentheses;
2x(x + 7)-(3x +1)
Distribute 2x over the first parentheses;
the negative sign distributes over the second part
= (2x² + 14x) - 3x -1
= 2x² + 14x -3x -1
Add like terms;
= 2x² + 11x -1
This expression 2x² + 11x -1 is equal to the given one
Which inequality is graphed below?
Answers
Answer:
the first one
x is greater than or equal to - 4
Step-by-step explanation:
$15 per hour is the basic rate at a factory. After a 48 hour basic work week, overtime is paid time and a half. If no one worked overtime and the factory paid $15840 in wages one week how many workers are in the factory
Answers
There are 22 workers are available in the factory.
What is Wages?Wages is the payment for work based on hours worked (or sometimes per day or per amount of work done).
Here, Let the number of workers in the factory be x.
Basic rate = $15
Working hours in a week = 48 hours
Total wages in a week = $ 15840
If no overtime is to be paid then according to question,
Amount paid to 1 worker = 48 X 15 = $ 720
Amount paid to x worker = 720x
15840 = 720x
x = 15840/720
x = 22
Thus, There are 22 workers are available in the factory.
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do you like ainme\dislike
Answers
Answer:
I like anime, do u?
Step-by-step explanation:
Answer:
Yes I love it
Step-by-step explanation:
If we increase our food intake, we generally gain weight. Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 nonobese adults, aged 25 to 36 years, were fed 1000 calories per day in excess the calories needed to maintain a stable body weight. The subjects maintained this diet for 8 weeks, so they consumed a total of 56,000 extra calories. According to theory, 7700 extra calories will translate into a weight gain of 1 kilogram. Therefore, we expect each of these subjects to gain 56000/7700=7.3 kilograms. The weights in kilograms before and after the 8-week period are shown below:
ID: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Before: 55.7 54.9 59.6 62.3 74.2 75.6 70.7 53.3 73.3 63.4 68.1 73.7 91.7 55.9 61.7 57.8
After: 61.7 58.8 66.0 66.2 79.0 82.4 74.3 59.3 79.1 67.0 73.4 76.9 93.1 63.0 68.3 60.3
(1) For each subject, manually calculate the weight gain subtracting the weight before from the weight after.
Answers
Given: A = {(2, 3), (5, 1), (-3, -2), (0, 3)}
What is the domain of A?
Answers
A 33 pound bag of grass seed holds 2 pounds less than 5 smaller bags of seed. Find the weight of the smaller bag of seed.
Answers
A 33 pound bag of grass seed has = 2 pounds less than 5 smaller bags of seed
= 33 pounds = 2 pounds less than 5 smaller bags
Let the weight of smaller bag of seed be ' x ' . Then ,
= 33 = 5x - 2
= 5x -2 = 33
= 5x = 33 + 2 ( transposing -2 from LHS to RHS changes -2 into +2 )
= 5x = 35
= x = 35 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 )
= x = 7 = weight of smaller bag of seed
Then , the weight of smaller bag of seed will be 7 pounds . Let us check it by putting 7 in the place of x :
= ( 5 × 7 ) - 2 = 33
= 35 - 2 = 33
LHS = RHS
Therefore , the weight of of smaller bag of seed is 7 pounds .
What is 2.068 rounded to the nearest 0.1
Answers
Answer:
2.1
Step-by-step explanation:
Answer:
2.1
Step-by-step explanation:
A license plate is to have the following form: 4 letters followed by 4 numbers. How many different license plates can be made, assuming that letters and numbers can be reused?
Answers
If we assume your letters range from A to Z and your digits from 0 to 9, you have 26 possibilities per letter and 10 per digit. This gives you 26^4*10^4 which is roughly 4 billion and a half.
The number of different license plates that can be made will be 260⁴.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
A license plate is to have the following form: 4 letters followed by 4 numbers.
We know that the total number of letters will be 26 (A to Z) and the total basic numbers will be 10 (0, 1, ..., 9).
The number of different license plates that can be made will be
⇒ 26 x 26 x 26 x 26 x 10 x 10 x 10 x 10
⇒ 26⁴ x 10⁴
⇒ (26 x 10)⁴
⇒ 260⁴
The number of different license plates that can be made will be 260⁴.
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John and Amelia have a baby daughter Sonia John is 23 kg heavier than Amelia who is four times as heavy as Sonia their combined weight is 122. how heavy is each person
Answers
x+4x+4x+23
9x+23=122
122-23=99
9\99=11
J=67
A=44
S=11
11+44+67=122 kg
The weight of John, Amelia and Sonia are 67 kg, 44 kg and 11 kg respectively.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that
Let j , a and s be the weights of John, Amelia and Sonia respectively.
John is 23 kg heavier than Amelia.
j = a + 23
Amelia is four times as heavy as Sonia.
a = 4s ⇒ s = a/4
Their combined weight is 122.
j + a + s = 122
Substituting the above expressions of j and s in terms of a in the equation j + a + s = 122, we get,
(a + 23) + a + (a/4) = 122
2a + a/4 + 23 = 122
9a/4 = 122 - 23
2.25a = 99
a = 44
j = 44 + 23 = 67
s = 44/4 = 11
Hence the weight of each person is 67 kg, 44 kg and 11 kg.
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On a number line, which fraction would be to the right of 1/2?
A) 2/12
B) 1/3
C) 10/20
D) 16/25
Answers
Answer:
C. I hope this helps! Have a great day.