We're asked to find inverse of the function,
[tex]\longrightarrow\rm{f(x)=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}[/tex]
Take [tex]\rm{y=f(x).}[/tex]
[tex]\longrightarrow\rm{y=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}[/tex]
Subtract 2.
[tex]\longrightarrow\rm{y-2=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}[/tex]
We apply componendo - dividendo rule.
[tex]\rm{\dfrac{a}{b}=\dfrac{c}{d}\quad\iff\quad\dfrac{b+a}{b-a}=\dfrac{d+c}{d-c}}[/tex]
Thus,
[tex]\longrightarrow\rm{\dfrac{y-2}{1}=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}[/tex]
[tex]\Longrightarrow\rm{\dfrac{1+(y-2)}{1-(y-2)}=\dfrac{(e^x+e^{-x})+(e^x-e^{-x})}{(e^x+e^{-x})-(e^x-e^{-x})}}[/tex]
[tex]\longrightarrow\rm{\dfrac{y-1}{3-y}=\dfrac{2e^x}{2e^{-x}}}[/tex]
[tex]\longrightarrow\rm{\dfrac{e^x}{e^{-x}}=\dfrac{y-1}{3-y}}[/tex]
[tex]\longrightarrow\rm{e^{2x}=\dfrac{y-1}{3-y}}[/tex]
[tex]\longrightarrow\rm{(e^x)^2=\dfrac{y-1}{3-y}}[/tex]
Take square root.
[tex]\longrightarrow\rm{e^x=\sqrt{\dfrac{y-1}{3-y}}}[/tex]
Take natural logarithm.
[tex]\longrightarrow\rm{x=\log_e\sqrt{\dfrac{y-1}{3-y}}}[/tex]
[tex]\longrightarrow\rm{x=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}[/tex]
Now take [tex]\rm{x=f^{-1}(y).}[/tex]
[tex]\longrightarrow\rm{f^{-1}(y)=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}[/tex]
Replace y by x and finally we get,
[tex]\longrightarrow\rm{\underline{\underline{f^{-1}(x)=\dfrac{1}{2}\log_e\left(\dfrac{x-1}{3-x}\right)}}}[/tex]
This is the inverse of the given function.
Ms. Sanchez has $200 to spend on parking and admission to a museum. The parking will cost $10 and admission tickets cost $15.50 per person, including tax. Write and solve an equation that can be used to determine the number of people that she can bring to the museum, including herself.
Answer:
12 people including herself
Step-by-step explanation:
x = number of people
($200 - $10)/$15.50 = x
x = 12.26
someone help me with math homework
I hope this helps you
8/4=8/4=18/9=2
Side - Side - Side
Answer:
SSS~Explanation:
All corresponding sides have the same ratio
4) If there was a coupon for 40% off, what is the final deconstructed
percent written as a DECIMAL? *. A.1.4
B.0.6
C.0.4
D.60%
Answer:
c
Step-by-step explanation:
Think of it like this. When you convert a percent to a decimal, just put a decimal point before the number. For example, 40%. You would put . before 40, making it 0.40, and you don't need the zero, so it becomes 0.4. For something like 8%, you would first put a zero before the 8, and then put a period before the zero, like so: 8%= 08%=0.08
Simon bought a 10-pound bag of cat food. He gives his cat 0.3 pound of food per day. Which equation with two variables to describe how the amount of cat food in the bag changes over time.
Answer:
y = 10 - 0.3t
Step-by-step explanation:
Amount of cat food purchased= 10 pounds
Daily pounds fed to dog = 0.3 pounds
How the amount of cat food in bag changes over time ;
Let y = amount of cat food left in bag
t = number of days since cat food was purchased
Amount of cat food left in bag = amount of cat food purchased - (daily pounds fed to dog * Number of days since cat food was purchased)
y = 10 - 0.3t
Please Help!!
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answer:
15.57
Step-by-step explanation:
I think it is this but I am not sure
Rewrite y= 7/16x+14 in standard form
Answer:
7x - 16y = -224
Step-by-step explanation:
Standard Form:
Ax + By = C
y= 7/16x+14
-7/16x + y = 14
(Multiply everything by 16)
-7x + 16y = 224
(Multiply everything by -1)
7x - 16y = -224
How do u make 4.5 m to *what* cm?
Answer:
To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100. So, 4.5 meters times 100 is equal to 450 centimeters.
Esh deposits $3500 in an account that
earns 3.75% interest each year. After the
first year, Esh has $3631.25 in the account.
After the second year, Esh has $3767.42 in
the account, and after the third year Esh has
$3908.70 in the account.
Answer:
Compound interest
Step-by-step explanation:
The question requires us to determine if the interest earned is a simple or compound interest
Simple interest = amount deposited x time x interest rate
Future value with compounding = A( 1 + r)^n
A = amount deposited
r = interest rate
n = time
We would calculate the simple interest and the future value in year 2
Simple interest in year 2 = $3500 x 0.0375 x 2 = 262.50
Future value in 2 years with a simple interest = 262.50 + 3500 = $3762.50
Future value in year 2 with compounding = 3500 x (1.0375)^2 = $3767.42
The value provided in year 2 with compounding matches that provided in the question. Thus, it is compounding of interest that is done
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer:
Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.
This section is worth 20 points. See the scoring rubric for more details on how you
will be graded
Use the evidence you gathered to tell the story of a hypothetical indigenous
community in the Americas and its experience involving the Columbian Exchange.
Come up with a community whose circumstances are typical of many in Central
America, the West Indies, or another part of the Americas that had direct contact with
Europeans. Tell the story in chronological order, but feel free to skip whole years or
decades so that you can cover each of the important topics related to the activity: the
availability of goods, the effects of disease, and the impact of European culture
(language and religion, for example), at the very least.
Think of your story as more of a summary than a work of fiction; you must cover a
large span of time in few words. Base the details of the story on factual evidence and
cite your sources, but keep in mind that the text should be written as a story, not as
an essay with a conventional introduction, body, and conclusion. Aim for about 700
to 1,200 words.
free body diagram can be used to help work out the net force acting on an object. True or, false?Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.
This section is worth 20 points. See the scoring rubric for more details on how you
will be graded
Use the evidence you gathered to tell the story of a hypothetical indigenous
community in the Americas and its experience involving the Columbian Exchange.
Come up with a community whose circumstances are typical of many in Central
America, the West Indies, or another part of the Americas that had direct contact with
Europeans. Tell the story in chronological order, but feel free to skip whole years or
decades so that you can cover each of the important topics related to the activity: the
availability of goods, the effects of disease, and the impact of European culture
(language and religion, for example), at the very least.
Think of your story as more of a summary than a work of fiction; you must cover a
large span of time in few words. Base the details of the story on factual evidence and
cite your sources, but keep in mind that the text should be written as a story, not as
an essay with a conventional introduction, body, and conclusion. Aim for about 700
to 1,200 words.
free body diagram can be used to help work out the net force acting on an object. True or, false?
Step-by-step explanation:
where my brainlest
Increase 280g in the ratio 5:2
Answer:
700
Step-by-step explanation:
Therefore, the increase in 280 in the ratio 5:2 is 700
.................................................6y=8x
Answer: look at the picture
Step-by-step explanation: Hope this help :D
What is BD?
C
X + 5
B
х
12
27
А
BD =
This Question Can't be anwsered, Because there is nothing on the right hand side of the equation.
3(x-5)=9 i don't know what to do
Answer:
x=8
Step-by-step explanation:
3(x-5)=9
3x-15=9
3x-15+15=9+15
3x=24
x=8
Answer:
x=8
Step-by-step explanation:
3(x-5) = 9
(3(x-5))/3 = 9/3
x-5 = 3
x-5+5 = 3+5
x=8
Describe how to find the square of -12
BRAINLY TO WHOEVER HELPS
Answer:
9: D 10: A
Step-by-step explanation:
Answer:
9 is a
Step-by-step explanation:
Use a net to find the surface area of the cone to the nearest
square centimeter. Use 3.14 for it.
23 cm
(The figure is not drawn to scale.)
The surface area of the cone is about cm2.
(Round to the nearest whole number as needed.)
Answer:
[tex]V=497.16\ cm^3[/tex]
Step-by-step explanation:
The attached figure shows a cone of radius 5 cm and height 19 cm. The formula for the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Substitute all the values,
[tex]V=\dfrac{1}{3}\times 3.14\times 5^2\times 19\\\\V=497.16\ cm^3[/tex]
So, the volume of the cone is equal to [tex]497.16\ cm^3[/tex].
What is the solution to the equation: 3x + 5 = 3x − 5
Answer:
no solution
Step-by-step explanation:
Answer:
the answer is no solution
Step-by-step explanation:
Can someone help me? The question is on the image.
Answer:
top one is 16
bottom one is 9
Step-by-step explanation:
Answer:
the to side length would be 16 and the bottom would be 9
Step-by-step explanation:
Hope this helps :)
Help please man please
Answer: 7
Step-by-step explanation:
40 POINTS!!!! can you guys please answer these? and make sure they are right!! please hurry im taking this test at the moment!!
Answer:
1) ?
2) B
3) x = 2*
4) x = 0
5) B
6) y = -5x + 4
7)?
Step-by-step explanation:
1) 5(4x + 2y) - y = 20x + 10y + y = 20x + 9y = 20x + 9y
2)* Any value of x makes the equation true. All real numbers. (You may say x = 2 or anything else).
Interval Notation:
(−∞,∞)
CAN SOMEONE HELP ME PLS TELL ME THE LETTER ANSWER CHOICE!!!!!!!!!!!!!!!!!!!1;))))))))))))))))))))))
Answer:
C
Step-by-step explanation:
27÷12=2.25
Each gallon costed 2.25$
If you deposited $10,000 in to a bank savings account on your 18th birthday....Said account yielded 3% compounded a nnually, how much money would be in your account on your 58th birthday?
Answer:
$32600
Step-by-step explanation:
Given data
Principal= $10000
Rate= 3%
Time= 58-18= 40 years
The compound interest expression is
A=P(1+r)^t
Substitute
A=10000(1+0.03)^40
A=10000(1.03)^40
A=10000*3.26
A=$32600
Hence the amount at the 58th birthda is $32600
Help please!! Will mark brainstest!!
Scatter Plot is in the picture.
It says write an equation for the trend line.
A) y=-12.5x+250
B) y=12.5x+250
C) y=6.25x+225
D) y=-6.25+225
giving brainliest pls answer
Answer:
8π cubic units
Step-by-step explanation:
V = (4πx 6)/3 = 8π cubic units
Kaitlin has been given a list of bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Complete question :
Kaitlin has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Answer:
20 different votes
Step-by-step explanation:
Total number of bands = 5
To select her favorite ; she chooses 1 from the five ;
Number of bands left = 4
From. The 4 she chooses one ; which is her second favorite
Number of different votes possible :
Favorite selection * second favorite selection
(5 * 4) = 20 different votes.
Can someone help me please
Answer:
B!
Step-by-step explanation:
Hope this helps :))
Answer:
B) 60 square inches
Step-by-step explanation:
They are asking for the area of the triangle. The formula for area is (length × width) ÷ by 2 = area
so, (8 × 15) ÷ 2 = 60 square inches
9. State Bank pays 5.5 percent interest compounded semiannually on regular
savings accounts. Iva Howe deposited $2,800 in a regular savings account for
2 years. She made no other deposits or withdrawals during the period. How
much interest did her money carn?
Here is part of a shopping bill for clothing.
Work out the cost of the jacket before the discount.
Answer:
how are we supposed to answer this
Answer:
Hewo ❤
Step-by-step explanation:
❤ how are you? ❤
Help please ASAP
Give brainiest if correct.
What do I have to do?
The points in the table lie on a line. What is the slope?
The slope is 1/2, I explain in the other question
HELPPP ASAP!! 10TH GRADE GEO
Answer:
[tex]\huge\purple {\boxed {m\angle FEG =23\degree}} [/tex]
[tex] \huge \orange {\boxed {m\angle FEH=113\degree}} [/tex]
Step-by-step explanation:
In the given circle, [tex] \overline{EG} [/tex] is diameter and [tex] \overline{EH} [/tex] is tangent at point E.
[tex]\therefore \widehat {EFG} [/tex] is a semicircular arc.
Since, measure of semicircular arc is 180°
[tex]\therefore m(\widehat {EFG})=180\degree... (1)[/tex]
[tex]\because m( \widehat {EF}) +m(\widehat {FG}) = m(\widehat {EFG}) [/tex] .... (2)
From equations (1) & (2)
[tex]\therefore 134\degree +m(\widehat {FG}) = 180\degree[/tex]
[tex]\therefore m(\widehat {FG}) = 180\degree-134\degree [/tex]
[tex]\therefore m(\widehat {FG}) = 46\degree [/tex]
By inscribed angle theorem:
[tex] m\angle FEG =\frac{1}{2} m(\widehat {FG} ) [/tex]
[tex] m\angle FEG =\frac{1}{2} \times 46\degree [/tex]
[tex]\huge\purple {\boxed {m\angle FEG =23\degree}} [/tex]
By tangent secant theorem:
[tex] m\angle FEH=\frac{1}{2} (46\degree +180\degree) [/tex]
[tex] m\angle FEH=\frac{1}{2} (226\degree) [/tex]
[tex] \huge \orange {\boxed {m\angle FEH=113\degree}} [/tex]