Answer:
The inverse of g(x) is [tex]g^{-1}(x)=\frac{2x}{1-x}[/tex]
The domain of g(x) is (-∞,-2)U(-2,∞)
The domain of f(x) is (-∞,-1)U(-1,1)U(1,∞)
Step-by-step explanation:
Find the inverse of g(x).
[tex]y=\frac{x}{x+2}[/tex]
Solve for x
[tex]x=y(x+2)[/tex]
[tex]x=xy+2y[/tex]
[tex]x(1-y)=2y[/tex]
[tex]x=\frac{2y}{1-y}[/tex]
[tex]g^{-1}(x)=\frac{2x}{1-x}[/tex]
Find the domain of g(x)
[tex]g(x)=\frac{x}{x+2}[/tex]
Numerator and denominator have domain
(-∞,∞).
However, g(x) is undefined if the denominator is 0. Hence, x=-2 must be taken out of the domain. So, the domain of g(x) is
(-∞,-2)U(-2,∞).
Find the domain of f(x)
[tex]f(x)=\frac{1}{x^{2} -1}[/tex]
The numerator and denominator have the domain
(-∞,∞)
However, f(x) is undefined if the denominator is 0. This rules out +1 and -1. So, the domain of f(x) is
(-∞,-1)U(-1,1)U(1,∞)
I am not sure what you mean for (ii).
∠xangle, x and \angle y∠yangle, y are supplementary angles. \angle y∠yangle, y measures 142^\circ142 ∘
Answer:
Angle x = 38°
Step-by-step explanation:
It is important to note that:
Two angles are called supplementary when their measures add up to 180 degrees.
Angle x and y are supplementary
Angle y = 142°
Hence,
Angle x = 180° - 142°
Angle x = 38°
PLEASE HELP!!!!!!!!!!!! VOLUME OF A CONE!!!!!!
Hi! Your answer is 125/3 π
Please see an explanation for a clear understanding to the problem.
Any questions about the answer/explanation can be asked through comments! :)
Step-by-step explanation:
For this problem, I'll be demonstrating two methods to solve your problem which are Integration method and Formula method. Let's start with Formula method first!
Formula Method
Volume of Cone Formula
[tex]V=\huge{\frac{1}{3}\pi r^2h}[/tex]
r is a radius. Therefore, r² is a diameter.
h is height of cone.
Our r is 5. Therefore, 5² = 25.
Our h is 5.
Substitute these values in the equation.
[tex]V=\huge{\frac{1}{3}\pi (5)^2(5)}\\V=\huge{\frac{1}{3}\pi (25)(5)} \\V=\huge{\frac{1}{3}\pi (125)}\\V=\huge{\frac{125}{3}\pi}[/tex]
Hence, the volume of a cone is 125/3 pi. If you want in Mixed Number form then It'd be 41 and 2/3 pi [ 41 2/3 pi]
Integration Method - Proof
Let r':r = x:h
Therefore,
[tex]\huge{\frac{r'}{r}=\frac{x}{h}}\\\huge{r'=\frac{x}{h}r[/tex]
r and h both are same (r is still radius while h is still height)
[tex]\huge{S(x)=\pi(r')^2[/tex]
The reason why we add pi because the surface is a circle. If the surface is not a circle, we don't add pi.
[tex]\huge{S(x)=\pi(\frac{x}{h}r)^2}\\\huge{S(x)=\pi(\frac{x^2r^2}{h^2})}\\\huge{S(x)=\frac{\pi r^2}{h^2}x^2}\\[/tex]
The range starts from 0 ≤ x ≤ h
[tex]\huge{V=\int\limits^h_0 {S(x)} \, dx[/tex]
Substitute S(x) in.
[tex]\huge{V=\int\limits^h_0 {\frac{\pi r^2}{h^2}x^2 } \, dx[/tex]
Integrate, separate everything in the integrand out except for x^2
[tex]\huge{V=\frac{\pi r^2}{h^2} \int\limits^h_0 {x^2} \, dx}\\\huge{V=\frac{\pi r^2}{h^2}[\frac{1}{3}x^3]^h__0}}\\\huge{V=\frac{\pi r^2}{h^2}[\frac{1}{3}h^3]}\\\huge{V=\pi r^2[\frac{1}{3}h]}\\\huge{V=\frac{1}{3}\pi r^2h}[/tex]
As you notice, Integration method is pretty useful, but it's mostly for an advanced volume lesson only.
Integration Method - Problem Solving
Let r':r = x:h
r is given as 5
h is given as 5 as well.
Therefore, r':5 = x:5
[tex]\huge{\frac{r'}{5}=\frac{x}{5}}\\\huge{r'=\frac{x}{5}(5)}\\r'=x[/tex]
[tex]\huge{S(x)=\pi(r')^2}\\\huge{S(x)=\pi(x^2)}\\\huge{S(x)=\pi x^2}[/tex]
The range of volume starts from surface to height. Therefore the range is 0 ≤ x ≤ 5
[tex]\huge{V=\int\limits^5_0 {S(x)} \, dx }\\\huge{V=\int\limits^5_0 {\pi x^2} \, dx }\\\huge{V=\pi\int\limits^5_0 {x^2} \, dx }\\\huge{V=\pi[\frac{1}{3}x^3]^5__0}}\\\huge{V=\pi[(\frac{1}{3}(5)^3-\frac{1}{3}(0)^3]}\\\huge{V=\pi[(\frac{1}{3}(125)-0)]}\\ \huge{V=\pi[(\frac{1}{3}(125)]}\\\huge{V=\pi(\frac{125}{3})}\\\huge{V=\frac{125}{3}\pi}[/tex]
Notice that both methods have same answer. Hence, we can conclude that the volume of a cone is 125/3 pi units²
can someone pls help it’s rate of change and i only need to do all of the evens. it’s due in an hour
Answer: I wasn't sure if number 18 was 350.00 but that's what I put down to do the problem hope I'm not too late.
9. $72.45
10. $15.52
11. $30.69
12. $48.95
13. $6.39
14. $67.6
15. $18.02
16. $51.6
17. $11.25
18. $175.00
19. $3.20
20. $10.00
21. $31.25
22. $45.90
Step-by-step explanation:
through (-5.-2) with a slope = 4/5
The Chromebook has 25% battery at the beginning of getting
charged. An additional 1 percent is gained every 4 minutes.
IPhone
Answer this questions
1)which is charging faster
2)how much faster?
3)which device started with more charge
4)how much more
5) which device will be charged first
Answer:
Chromebook: 0.25 percent per minute
iPhone: 0.5 percent per minute
1) The phone
2) Faster by 0.25 percent per minute, or 1 percent every four minutes
3) The phone
4) 25 percent more
5) The phone
A person invests 8000 dollars in a bank. The bank pays 5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14100 dollars?
Answer:
3 years
Step-by-step explanation:
To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14100 dollars is: 11.6.
TimeUsing this formula
A=P(1+r/n)^nt
Let plug in the formula
14,100=8000(1+0.05)^t
(1+0.05)^t=14,100/8000
(1+0.05)^t=1.7625
1.05^t=1.7625
t=log(1.7625)/log(21/20)
t=0.246/0.021189
t=11.6
Therefore how long must the person leave the money in the bank until it reaches 14100 dollars is: 11.6.
Learn more about time here:https://brainly.com/question/4931057
#SPJ2
p divided by 2 written as an algebraic expression
Answer:
p/2
Step-by-step explanation:
Written as a fraction, p/2 is the same as p divided by 2.
How many perpendicular bisectors are required to be constructed to devide a line segment into four equal parts?
Answer:
Three perpendicular bisectors are required
Step-by-step explanation:
A perpendicular bisector of a line segment is a line that cuts the line segment at a 90° angle, dividing it into two equal halves.
In this example, one bisector produces two equal parts of the segment
two bisectors produce three segments and three bisectors, four segments as shown in the diagram.
Perpendicular bisectors are constructed using a compass and a pencil, you can check out how to construct one, it is pretty interesting.
In \triangle VWX,△VWX, \overline{XV}\cong \overline{WX}
XV
≅
WX
and \text{m}\angle W = 27^{\circ}.m∠W=27
∘
. Find \text{m}\angle X.m∠X.
Answer:
m<X = 27 degrees
Step-by-step explanation:
From △VWX, since WX = XV, this mean that the triangle is isosceles
The base angle of an isosceles triangle are equal hence <W = <X
Since <W = 27 degrees, hence m<X = 27 degrees
What is the area of the trapezoid shown below?
units2
Answer and Step-by-step explanation:
Use the Pythagorean Theorem to solve for the height.
[tex]a^{2}+ b^{2}= c^{2} \\\\\\4^{2} + b^{2} = 5^{2}\\\\\\16 + b^{2} = 25\\\\\\b^{2} = 9\\\\\\b = 3[/tex]
The height of the triangle is 3.
Now we can solve the shapes in the trapezoid.
4 times 3 = 12 (Rectangle)
[tex]\frac{4 * 3}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6 (Triangle)
12 + 6 = 18 (Trapezoid)
The area of the trapezoid is 18 [tex]units^{2}[/tex].
#teamtrees #PAW (Plant And Water)
What is the equation of the line that passes through the point (-4, 7) and has an
undefined slope?
Answer:
x = -4
Step-by-step explanation:
Since the slope is undefined, the line is a vertical line. All vertical lines have an equation x = k. In your problem k = -4, so the equation of the line is x = -4
8/3 = 3 (c + 5/3) how to solve step by step
Answer:
Step-by-step explanation:
8/3=3(c+5/3)
multiply both sides by 3
8=9(c+5/3)
divide both sides by 9
8/9=c+5/3
subtract 5/3 from both sides
c=8/9-5/3
change 5/3 to 15/9
c=8/9-15/9
c=-7/9
A painter paints rooms in a house. The painter purchases 12 gallons of paint and uses 4 gallons on the first day of work.
Which equation could be used to find how many gallons of paint are left, g?
g+4=12
g÷12=4
4×g=12
12+g=4
Answer:
g+4=12
Step-by-step explanation:
Since the painter used 4 of the 12 gallons, the painter now has 8 gallons, so g=8.
The equation g+4=12 represents this because if we solve it by isolating g then we get that g=8.
PLEASE HELP ME SOLVE THIS PROBLEM ASAP
Answer:
r = 1
Step-by-step explanation:
how many terms are in the following?
5x-7+8k+2x+k
Answer: 5
Step-by-step explanation:
Terms are single numbers, variables, or the product of a number and variable.
Find the value of x. Round to the nearest tenth
PLEASE HELP
Answer:
x = 38.2°
Step-by-step explanation:
sin 27° = x°
11 15
15 · (sin 27°) = 11 · x°
cross-multiply:
6.81 = 11x
6.81 / 11 = x
x = 0.619
sin^-1 (0.619) = 38.2°
Which is true? Plssss
Answer:
the very first one 8.62<8.623
Omg I’m begging you please help me quick please help
my baby brother needs help 7z+4-9z=8
what is z=
A cannonball is shot from the ground, reaching the height of 50 meters before landing on a target 500 meters away.
Assuming the cannonball is fired from the origin and its trajectory can be modeled by a quadratic function, where is the maximum point of the trajectory?
(500, 50)
(250, 25)
(250,50)
(0, 50)
Answer: (250,50) i hope this helps lol
Answer:
250,50
Step-by-step explanation:
Just did the Quick check, np
Today only, a table is being sold at a 32% discount. The sale price is $357.
What was the price yesterday?
Answer:
Step-by-step explanation:
(1-0.32)p=357
0.68p=357
p=$525
Answer:
471.24
Step-by-step explanation:
First you want to find 32% of 357, which is 114.24. Then you want to add that onto 357. Hope this helps!
While in Manchester, England, Jaslene bought a sweater for £28(GBP). When she returned,
she saw the same sweater for $38CAD. Which sweater cost more? By how much in Canadian
dollars?
Answer:
The Manchester, England sweater is more expensive.
27 GBP is equal to 49.52 CAD, which is more than the 38 CAD from the afterwards.
Step-by-step explanation:
The volume of a cone-shaped tunnel is 424 cubic centimeters. The height of the funnel is 5 centimeters. Find the radius of the funnel. Round your answer to the
nearest whole number.
Answer:
volume of cone=424cm³
height(h)=5cm
radius (r)=?
Step-by-step explanation:
we have
volume of cone=1/3(πr²h)
424=1/3(22/7×r²×5)
424×3=15.71r²
r²=1272/15.71
r=√80.9=8.9=9cm
Someone please help me ASAP
Answer:
[tex]-\frac{3}{4\\}[/tex]
Step-by-step explanation:
A snowman dumped 18 inches of snow in a 12 hour period. how many inches were falling per hour?
Answer:
1.5 inch/hr
Step-by-step explanation:
Amount of snow falling = 18 inch
Time = 12
Rate = 18/12 = 1.5 inch/hr
I hope Im right!!!
MP1 18. Allen has 13 carrots. He wants to put an equal amount of carrots into
5 sandwich sized bags. How much should Allen put into each bag?
Show your work.
Answer:
Put 2.6 carrots in each bag.
Step-by-step explanation:
Just divide the carrots with 5.
13 carrots / 5 sandwhich bags
This then makes 2.6 carrots which is a perfect fit for each bag.
4. A worker uses 450 inches of steel wire to make 300 springs of the same size. At this rate how many inches of steel wire are needed to make 1 spring?
Answer:
1.5 inches. you take 450 and divide it by 300
Which shows the simplified expressions ordered from least to greatest by the value of the exponent?
Answer:
Step-by-step explanation:
theres no information
Answer:
none because there are no numbers there I'll help you when you add the numbers
Step-by-step explanation:
but have a good rest of your day :) ❤
Please help quickly!!!
Answer:
I might be wrong but Karl misplaced the (5). Karl puth the 5 in the (x) area instead of the y.it had to be (3-5)^2
Which of the following represents the area of the shaded region in the figure above?
∫dcf(y)dy
the integral from c to d of f y d y
A
∫ba(d−f(x))dx
the integral from A to b of open paren d minus f of x close paren, dx
B
f′(b)−f′(a)
f prime times b minus f prime times A
C
(b−a)[f(b)−f(a)]
open paren b minus A close paren times open bracket f of b minus f of A close bracket
D
(d−c)[f(b)−f(a)]
It's B isn't it? If this is the question I'm thinking of. No image here so I'm just guessing.