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
(Essential Question) How do you create equations and use them to solve problems?
Answers
Answer:
Step-by-step explanation:
equations are created to solve for a certain variable. you can use the data given in the word problem to formulate a valid equation that incorporates all important components of the word problem. the variable can be represented as any letter (most commonly x or y) to find a value that is inconsistent or unknown. this is helpful to find a certain thing in the problem, such as the amount of hours needed to earn a certain amount of money.
Answer:
Equations are created to solve for a certain variable. you can use the data given in the word problem to formulate a valid equation that incorporates all important components of the word problem. the variable can be represented as any letter (most commonly x or y) to find a value that is inconsistent or unknown. this is helpful to find a certain thing in the problem, such as the number of hours needed to earn a certain amount of money.
Rearrange the equation A = xy to solve for x.
x equals y over A
x equals A times y over x
x equals A times x over y
x equals A over y
Answers
You divide the y from both sides
The y on the right cancels
On the left you have A/y = x
Answer:
X=A/Y
Step-by-step explanation:
just did it
How much is a $20 shirt if it is 5% off?
Answers
you save $1.00
Answer:
$19.00
Step-by-step explanation:
This is the answer because:
1) In order to know what 5% of 20 is, you have to do 20 x 5/100 = 100/100
2) Next, 100/100 = 1
3) Finally, we have to do 20-1 which is 19
Therefore, the answer is $19.00
Hope this helps! :D
A high-performance composite flywheel rotor can spin anywhere between 30,000 and 100,000 revolutions per minute. What
is the range of degrees through which the composite flywheel can travel in a minute? Write your answer in scientific
notation.
Answers
Answer:
Step-by-step explanation:
1 revolution will equal 360 degrees
Because of that 30,000 revolution would be 10,800,000 degrees
100,000 rev would equal 36,000,000 degrees
The range through which the composite flywheel rotates in one minute be denoted by ' F ' . (1.08 x 107)° F (3.6 x 107)°
The range of degrees the composite flywheel can travel in a minute is 2.52 × 10⁷ degrees/minute.
What is the Scientific Notation?Scientific Notation is a way of writing down in the easy form of very large or very small numbers.
The range of revolutions per minute for the rotor is from 30,000 to 100,000, which means that the rotor can spin a total of 70,000 revolutions per minute (100,000 - 30,000 = 70,000).
To find the range of degrees through which the composite flywheel can travel in a minute, we need to multiply the range of revolutions by the number of degrees in one revolution.
A full revolution is 360 degrees, so the composite flywheel can travel in a minute :
70,000 revolutions/minute × 360 degrees/revolution = 25,200,000 degrees/minute
This can be written as 2.52 × 10⁷ in scientific notation.
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Help me please math is a pain...
Answers
Answer:
D
Step-by-step explanation:
The degree of 10 moves the decimal. As we are multiplying, move the decimal 5 places to right.
Pls mark me brainliest
Answer:
Answer is D (750,000)
Step-by-step explanation:
Basically you do 10^5 = 10 x 10 x 10 x 10 x 10 to get 100,000 then you multiply by 7.25 lol
Carlos is having a big party. He invited 5 times as many children as adults. He invited 15 adults. Which equation shows how to find the number of children invited to the party?
Answers
Answer:
75 children.
Step-by-step explanation:
If the amount of children is 5 times as many adults, you just need to multiply 15x5.
15x5=75 The number of children invited to the party is 75.
If you wanted this in an algebraic equation, it would look similar to this...
15(5)=x To solve for x, multiply 15 by 5.
75=x
Hope this helps! Have a great day ^^
(x² + 4x – 22) + (x + 6)
Answers
Answer:
12
Step-by-step explanation:
What is the inequality solution for y+2<4
Answers
Answer:
y<2
Step-by-step explanation:
Subtract 2 on both sides
Answer:
y<2
Step-by-step explanation:
what is 40% of 80 please hellppppppppp
Answers
Answer:
32
Step-by-step explanation:
(a) It takes 37 pounds of seed to completely plant a 6-acre field.
How many acres can be planted per pound of seed?
Can y’all answer both
Answers
Answer:
This answer is 67 because I think its the answer and I'm really just trying to get points on early sorry but you are
Solve for x. 25 + 15x = 0
Answers
Answer:
x=−
3
5
=−1.667
Step-by-step explanation:
Answer:
[tex]\sf x=-\frac{5}{3}[/tex]Step-by-step explanation:
[tex]\sf 25 + 15x = 0[/tex]
[tex]\sf 25+15x-25=0-25[/tex]
[tex]\sf 15x=-25[/tex]
[tex]\sf \frac{15x}{15}=\frac{-25}{15}[/tex]
[tex]\sf x=-\frac{5}{3}[/tex]
Solve 6y + 2x = 14 for x.
Answers
Answer:
x = 7 - 3y
Step-by-step explanation:
6y + 2x = 14 (divide all by two)
3y + x = 7 (move 3y to the right to isolate x)
x = 7 - 3y
Answer:
7-3y=x
Step-by-step explanation:
6y+2x=14
2x=14-6y >>> isolate x variable
x=7-3y >>> simplify because everything is divisible by 2
(SAT Prep) Rays
OM
,
ON
, and
OP
coincide at time t=0. At the same instant in time,
OM
and
OP
begin to rotate in the plane about point O, but in opposite directions. Ray
ON
remains fixed. Ray
OM
rotates at a constant rate of 3° per second with respect to
ON
, while
OP
rotates at a constant rate of 6° per second. What is the smallest positive value of t, in seconds, in which rays
OM
and
OP
will coincide again? When t=30 min, how many more revolutions has ray
OP
completed than ray
OM
?
Answers
Answer:
T=40 sec. OP does 15 revolutions more than OM.
Step-by-step explanation:
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know the answer! This is my first answer!!! I hope its correct, i trple checked it! :)
HOPE YOU ENJOYYYYYY!!
1/8 as a decimal show how to do it
Answers
Answer:
0.125
Step-by-step explanation:
1/8 is the same as 1 ÷ 8
1 ÷ 8 = 0.125
I hope this helped!
Answer:
0.125
Step-by-step explanation:
how i do it it to multiply 125 by 8 that equals 1000. now, every 125 is 1/8 so there is your answer
Consider the following table that describes the mass of a kitten as weeks go by. If you know the kitten grows by 10% each week for the first 5 weeks, fill in the table for the values each week. Week Mass (grams) (start) 80
Answers
Answer:
Week Mass (gram)
(start) 80
1 88
2 96.8
3 106.48
4 117.128
Step-by-step explanation:
From the question we are told that
The mass of the kitten at the start week is m = 80 g
The rate at which the kitten grows is r = 0.10
Generally the mass of the kitten at the first week is mathematically represented as
[tex]m_1 = ( r * m) + m[/tex]
=>[tex]m_1 = ( 0.10 * 80 ) + 80 [/tex]
=>[tex]m_1 = 88 \ g [/tex]
Generally the mass of the kitten at the second week is mathematically represented as
[tex]m_2 = ( r * m_1) + m_1[/tex]
=>[tex]m_2 = ( 0.10 * 88 ) + 88 [/tex]
=>[tex]m_2 = 96.8 \ g [/tex]
Generally the mass of the kitten at the third week is mathematically represented as
[tex]m_3 = ( r * m_2) + m_2[/tex]
=>[tex]m_3 = ( 0.10 * 96.8) + 96.8 [/tex]
=>[tex]m_3 = 106.48 \ g [/tex]
Generally the mass of the kitten at the fourth week is mathematically represented as
[tex]m_4 = ( r * m_3) + m_2[/tex]
=>[tex]m_4 = ( 0.10 * 106.48) + 106.48 [/tex]
=>[tex]m_4 = 117.128 \ g [/tex]
Week Mass (gram)
(start) 80
1 88
2 96.8
3 106.48
4 117.128
Express as a trinomial.
(3x + 3)(3x + 8)
PLEASE HELPPP:)
Answers
Answer:
9x^2+33x+24
Step-by-step explanation:
The factors (3x + 3)(3x + 8) can be expressed as a trinomial 9x² + 33x + 24.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
To express (3x + 3)(3x + 8) as a trinomial, we can use the distributive property and FOIL (First, Outer, Inner, Last) method.
First, we multiply the first term of each binomial (3x) with the first term of the other binomial (3x), which gives us (3x)(3x) = 9x².
Next, we multiply the first term of one binomial (3x) with the second term of the other binomial (8), which gives us (3x)(8) = 24x.
Then we multiply the second term of one binomial (3) with the first term of the other binomial (3x) , which gives us (3)(3x) = 9x
Finally, we multiply the second term of each binomial (3) with the second term of the other binomial (8) , which gives us (3)(8) = 24
Now we add all the products to get the trinomial
9x² + 24x + 9x + 24 = 9x² + 33x + 24
Therefore, (3x + 3)(3x + 8) can be expressed as a trinomial 9x² + 33x + 24.
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What is the first step to solve this equation:
11 - 3x = 44
Answers
Answer:
Subtract 11 from both sides
Step-by-step explanation:
X has to be alone
Answer:
Subtract 11 from sides
Step-by-step explanation:
You have to get the x by itself first
there were 3,905 more hits on the schools website in january than february. february had 9,854 hits, how many hits did the schools website have during both months
Answers
Answer:
If im not wrong the answer is 23,613.
Step-by-step explanation:
9,854+3,905=13,759+9,854=23,613.
Find the inverse of this function
g(x)=2(x-3)^5
Answers
A rectangle or plot of land has an area of 8/3 square miles and a length of 3/5 of a male What is the width of the plot of land in Miles?
Answers
The area of a square sports arena is 10,000 m² what are the dimensions of the sports arena on the map.
Answers
Answer:
Step-by-step explanation:10,000square you have to multiply them my all squares to get the answer
Match each retirement plan to its description.
Offered by a company to employees. ______?
Opened and managed by an individual._______?
Offered by a nonprofit organization to employees.______?
401(k)
IRA
403(b)
Answers
Answer:
401(k)IRA403(b)Step-by-step explanation:
The matches are Offered by a company to employees= 401(K).
Opened and managed by an individual = IRA.
Offered by a nonprofit organization to employees is 403(b)
What are the 3 types of retirement?Three types of retirement and how to plan for each
Traditional Retirement.
Semi-Retirement.
Temporary Retirement
By the given data we have to match
Offered by a company to employees= 401(K)
A 401(k) plan is a company-sponsored retirement account to which employees can contribute income.
Opened and managed by an individual is IRA.
An individual retirement account (IRA) allows you to save money for retirement in a tax-advantaged way.
Offered by a nonprofit organization to employees is 403(b)
A 403(b) plan allows employees to contribute some of their salary to the plan.
Therefore the matches are 401(K), IRA and 403(b).
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I think I know the answer but I just want to double check.
Answers
Answer:
D
Step-by-step explanation:
I think it's same with what ur thinking
write a decimal number
ral for 3/5
Answers
Answer:
0.6 or 0.60
Step-by-step explanation:
3/5 mulitply denominator to see how much it goes to 100 which is 20 so 5x20 which is 100 and u go to other number u get 60 so 60/100 or you can just divide 3 by 5 which is also 0.6
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
Answers
Answer:
it needs 234 grass seeds for the acre
Which of the following represents the expression (-3) (-3) (-3) (-3). 7.7.7.7.7. 7 using exponents
Answers
The late fee at the library is based on the number of days a book is late. Carter paid $1.08 for a book that was 9 days late. If his sister Sydney had a fee of $1.92 for a late book, how many days late was the book?
Answers
Answer:
16 days
Step-by-step explanation:
1.08 $:9 days
1.92 $: x
1.08 x: 17.28
x = 16
What is the slope of this line?
Enter your answer as a fraction in the simplest term in the box.
Answers
Answer:
1/4
Step-by-step explanation:
.12 times .096 im having trouble with this i know ou all might be like wow he is dumb but idk why im stuck on here :(
Answers
Answer:
Its Ok! I'm here to help! The answer would be 0.01152 If I'm correct!
Step-by-step explanation:
I really hope this help!
Solve equation:7t-48=113
Answers
Answer:
The answer is 23
Answer:
t = 23
Step-by-step explanation: