Answers
Answer: [tex]f^{-1}(x) = -\sqrt{36-x^2}[/tex]
====================================================
Here are the steps to find the inverse
[tex]f(x) = \sqrt{36-x^2}\\\\y = \sqrt{36-x^2}\\\\x = \sqrt{36-y^2} \ \text{ swap x and y; solve for y}\\\\x^2 = 36-y^2\\\\x^2+y^2 = 36\\\\y^2 = 36-x^2\\\\y = \sqrt{36-x^2}\\\\f^{-1}(x) = \sqrt{36-x^2}\\\\[/tex]
Now this would be the answer if our original domain was [tex]0 \le x \le 6[/tex]
However, that's not the case and instead our domain is [tex]-6 \le x \le 0[/tex]
Reflecting any (x,y) point in this domain restriction, over the the line y = x, will have us land on a point with a negative y value. This is because the inverse will swap the x and y values.
Therefore, the inverse function must ultimately be negative.
Currently [tex]f^{-1}(x) = \sqrt{36-x^2}[/tex] is positive since the result of any square root is never negative.
To fix this, we stick a negative out front to get the final answer being [tex]f^{-1}(x) = -\sqrt{36-x^2}[/tex]
Related Questions
Assume that y varies directly with x. If y = 2/5 when
x= 1/3, find y when x = 1/4. Enter in any fractions using
a/ (e.g. "1/2" is the same as ?).
Answers
Answer:
y = 3/10
Step-by-step explanation:
(1/3) / (2/5) = (1/4) / y
y = (1/4) (2/5) / (1/3) = (2/20) / (1/3) = 3/10
check: (1/3) / (1/4) = 4/3
(2/5) / (3/10) = 20/15 = 4/3
trigonometry and trigonometric functions
Answers
Answer:
The trigonometric functions include the following 6 functions: sine, cosine, tangent, cotangent, secant, and cosecant. For each of these functions, there is an inverse trigonometric function. The trigonometric functions can be defined using the unit circle.
Step-by-step explanation:
Find the volume of a right circular cone has a height of 5.6 m and a base with a radius of 16.6 m
Answers
Answer:
Step-by-step explanation:
V≈1615.97m³
Answer:
1615.968 m^3
Step-by-step explanation:
V = h/3 * π * r^2
V = 5.6/3 * π * 16.6^2
V = 1615.968 m^3
If you’re correct I’ll give u brainlist ‘
Answers
Answer:
Additive property of length
Step-by-step explanation:
Additive property of length
the question is on the sheet.
Answers
[tex]3x + 4x + 3x + 5x + 3x + 4x[/tex]
[tex]22x[/tex]
What is the answer to 2 + (c + 0) = ?
Answers
Solve. What is 9% of 56?
Answers
Answer:
it will be 5.04
Step-by-step explanation:
so we know 56=100%
so we want to get what 1% is so we divide both sides by 100 to get 0.56=1%
so know we multiply both sides of 9 to get 5.04=9%
34. Find the equation of the straight line which
.
passes through the point (3,1) and makes
intercepts on the axes the difference of
whose length is 4.
Answers
Answer:
The equation of the straight line passing through the point ( 3,1 )
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Step-by-step explanation:
Step(i):-
The equation of the straight line passing through the point ( 3,1 )
[tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]
[tex]\frac{3}{a} + \frac{1}{b} = 1[/tex]
3b + a = ab ...(i)
Given the difference of length is 4
a-b = 4
b = a - 4 ...(ii)
Step(ii):-
substitute b=a-4 in equation (i) , we get
3( a-4 ) + a = a (a-4)
3a - 12+ a = - 4 a + a²
a² - 8 a + 12 =0
Find the factors of 'a'
a² - 6a -2a +12 =0
a (a-6) -2(a-6) =0
a =2 and a=6
we know that a-b =4
put a = 2
2 - b =4
b = -2
The equation of the straight line whose intercepts on the axes
[tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
The equation of the straight line
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Verification:-
The equation of the straight line passing through the point (3,1)
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Put x =3 and y=1
[tex]\frac{3}{2} + \frac{1}{-2} = 1\\\frac{2}{2} =1\\[/tex]
1 = 1
∴ The point (3,1) is satisfies the equation
Is it a b c or d someone plz answer
Answers
Answer:
answer is c
Step-by-step explanation:
Mark my answer as brainliest
6x + 2 + 3x + 1 =
Please helpppp
Answers
Answer:
Factored is 3(3x+1)
Simplified is 9x+3
I'm not sure which one you need.
Literally struggle help pls (right answer only ) giving brainliest
Answers
Answer:
PR=21
Step-by-step explanation:
make x+1 and 5x-79 equal bec it is isosceles triangle. So x+1=5x-79. Then isolate x.
4x=80
x=20
Plug x in the PR equation or PQ equation
5(20)-79
Which equals 21
find the slope of the line passing through the points (-7,-7) and (4,-7)
Answers
Answer:
it it negative
Step-by-step explanation:
Which is 0
Please help me, I need an explanation as well please, not just the answer
Answers
Another name for 3/3 is
OA) 0
OB) 3
OC) 1
Answers
Given a polynomial f(x), if (x + 2) is a factor, what else must be true?
Оа
f(0) = 2
Ob
f(0) = -2
Oc
f(2)= 0
Od
f(-2) = 0
Answers
Given:
(x+2) is a factor of polynomial f(x).
To find:
The correct statement.
Solution:
If (x-c) is a factor of polynomial f(x), then c is a zero of the polynomial and f(c)=0.
We have, (x+2) is a factor of polynomial f(x).
On comparing (x-c) and (x+2), we get
[tex]c=-2[/tex]
It means, -2 is a zero of the polynomial f(x) and the value the polynomial at x=-2 is 0, i.e.,
[tex]f(-2)=0[/tex]
Therefore, the correct option is d.
55.57
What is the equation of the line that is parallel to the
given line and passes through the point (12, -2)?
Oy=-x +10
Oy=-x + 12
Oy=-x- 10
Oy=x - 12
Answers
Answer:10
Step-by-step explanation:and a slope 2/12 roof slope means your roof has 2 inches of vertical drop for every 12 inches of horizontal distance.Aug
The equation of the line that is parallel to the given line and passes through the point (12, -2) is y = 5/6(x)-12
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line passing through the points (12, 6) and (0, -4)
Slope = -4-6/0-12
=-10/-12
=5/6
Now let us find y intercept passing through (12, -2)
-2=5/6(12)+b
-2=10+b
-12=b
Hence, the equation of the line that is parallel to the given line and passes through the point (12, -2) is y = 5/6(x)-12
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ7
HELPPPP ITS AN EMERGENCY!!!!!!
Answers
AB = 17
CD = 25
x = 17
hope this helps!!
Answer:
17
Step-by-step explanation:
The correct answer would be 17!
what is the value of x/y when x = -15 and y = -3
A 5
B -5
C 12
D -12
Answers
Answer:
x= -15
y= -3
x/y
=-15/-3
=5
option A is correct
as dividing 15 by 3 it’ll be 5
and the negative signs when divided are canceled
1st Equation
2nd Equation
3rd Equation
2+ 3 = 5
9 + (-1) = 8
11 to x = 7
3 + 2 = 5
8+1=9
5-3 = 2
1-(-8)=9
5- 2 + 3
8-9=1
Answers
Answer:2nd
Step-by-step explanation:
what is the value of 2.57 - 1.75
Answers
Answer:
0.82
Step-by-step explanation:
35/54 in simplest form ?
Answers
Answer:
it can't go to simplest form it has no common numbers
Step-by-step explanation:
Answer:
35/54 is already in the simplest form. It can be written as 0.648148 in decimal form (rounded to 6 decimal places).
Which of the following is a solution to this inequality?
y greater than one half times x plus 2
Answers
Answer:
(1, 4)
Step-by-step explanation:
It costs Seth's socks $1.25 to produce each pair of socks. Seth's sells its socks for $4.00 per pair. What is the percent markup on the socks?
A- 31.25%
B- 68.75%
C- 220%
D- 320%
Answers
Answer:
4.00 - 1.25/1.25= 2.2 x 100 = 220
Which shows how to find the value of this expression when x=-2 and Y = 5? (3x^3y^-2)^2
3^2(-2)^6/5^4
3(-2)^6/5^4
3^2(5)^6/(-2)^4
3/(2)^65^4
plz answer I'll give Brainliest to first (as long as it's right lol)
Answers
use a calculator and work out the following and write all the figures from your work display. a) (6.2 - 3.51) x (11.7 x 0.3)
Answers
Answer:
Solving the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex] we get 9.4419
Step-by-step explanation:
We need to solve the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex]
According to DMAS rules first we solve brackets and then we will multiply the results found after solving brackets
So,
[tex](6.2 - 3.51) \times (11.7 \times 0.3)\\=2.69 \times 3.51\\=9.4419[/tex]
First we solved the terms (6.2-3.51) and get 2.69 and by solving (11.7 x 0.3) we get 3.51
Now, we will multiply 2.69 with 3.51 to get the final result.
The final result is 9.4419
So, solving the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex] we get 9.4419
help !! help !! help !!
Answers
Answer:
A: The cube of a number less than the square root of the number.
Step-by-step explanation:
None
It takes 3 hours 15 minutes to fly from ato b at constant speed.Find howlong the journdy takes if(a) the speed is3÷2 times that of the original speed (b) if the speed is three_quarters of the original speed.
Answers
Answer:
For 3/2 of the speed = 292.5 minutes
For 3/4 of the speed = 146.25 minutes
Step-by-step explanation:
It takes 3hrs 15 minutes to fly from A to B
From A to B = 180minutes + 15 minutes
= 195 minutes (At constant speed)
At constant speed,
If the speed is 3/2 of the original speed,
It will be,
3/2 X (195 minutes) = 585 / 2 = 292.5 minutes
On the other-hand,
If the speed is 3/4 of the original speed,
3/4 X (195 minutes) = 585 / 4 = 146.25 minutes
Kai saved all she earned each month and put it into a savings account. The amount she had in her savings account is recorded below. What equation best represents this data?y = 230x + 230
y = 230
y = 230x + 100
y = 230x
Answers
since she didn't have any money in there when she first started, and she puts it in every month, the correct answer is
y = 230x
hope this helps!!
Could someone help me with this one? I'm a tad stuck. I'll give brainliest to the correct answer!
Answers
Answer: 130 or a
Step-by-step explanation: 360-230=130
Answer:
130°
Step-by-step explanation:
First step you need draw a line from X to O and line Z to O. Both of them are radius.
as we know, radius and tangent line are always perpendicular. so the degree is 90° each.
shape of XYZO is kite with total of 360°
so the arc XZ have
360 - 50 - 90 - 90 = 130°
PLEASE PLEASE HELP!!! WILL GIVE BRAINLIEST
Answers
Answer:
a. this b>9 B. the first one C. the second one
Step-by-step explanation:
D is the first one