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For the following exercises, use the graph of
to sketch the graph of its inverse function.
For the following exercises, use composition to determine which pairs of functions are inverses.
For the following exercises, evaluate the functions. Give the exact value.
The function
converts degrees Fahrenheit to degrees Celsius.
- Find the inverse function
- What is the inverse function used for?
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[T] The velocity
V (in centimeters per second) of blood in an artery at a distance
x cm from the center of the artery can be modeled by the function
for
- Find
- Interpret what the inverse function is used for.
- Find the distance from the center of an artery with a velocity of 15 cm/sec, 10 cm/sec, and 5 cm/sec.
a.
b. The inverse function determines the distance from the center of the artery at which blood is flowing with velocity
V . c. 0.1 cm; 0.14 cm; 0.17 cm
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A function that converts dress sizes in the United States to those in Europe is given by
- Find the European dress sizes that correspond to sizes 6, 8, 10, and 12 in the United States.
- Find the function that converts European dress sizes to U.S. dress sizes.
- Use part b. to find the dress sizes in the United States that correspond to 46, 52, 62, and 70.
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[T] The cost to remove a toxin from a lake is modeled by the function
where
is the cost (in thousands of dollars) and
is the amount of toxin in a small lake (measured in parts per billion [ppb]). This model is valid only when the amount of toxin is less than 85 ppb.
- Find the cost to remove 25 ppb, 40 ppb, and 50 ppb of the toxin from the lake.
- Find the inverse function. c. Use part b. to determine how much of the toxin is removed for $50,000.
a. $31,250, $66,667, $107,143 b.
c. 34 ppb
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[T] A race car is accelerating at a velocity given by
where
v is the velocity (in feet per second) at time
t .
- Find the velocity of the car at 10 sec.
- Find the inverse function.
- Use part b. to determine how long it takes for the car to reach a speed of 150 ft/sec.
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[T] An airplane’s Mach number
M is the ratio of its speed to the speed of sound. When a plane is flying at a constant altitude, then its Mach angle is given by
Find the Mach angle (to the nearest degree) for the following Mach numbers.
-
-
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a.
b.
c.
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[T] The temperature (in degrees Celsius) of a city in the northern United States can be modeled by the function
where
is time in months and
corresponds to January 1. Determine the month and day when the temperature is
so, the temperature occurs on June 21 and August 15
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[T] The depth (in feet) of water at a dock changes with the rise and fall of tides. It is modeled by the function
where
is the number of hours after midnight. Determine the first time after midnight when the depth is 11.75 ft.
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[T] An object moving in simple harmonic motion is modeled by the function
where
is measured in inches and
is measured in seconds. Determine the first time when the distance moved is 4.5 ft.
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[T] A local art gallery has a portrait 3 ft in height that is hung 2.5 ft above the eye level of an average person. The viewing angle
can be modeled by the function
where
is the distance (in feet) from the portrait. Find the viewing angle when a person is 4 ft from the portrait.
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[T] Use a calculator to evaluate
and
Explain the results of each.
the expression does not equal 2.1 since
—in other words, it is not in the restricted domain of
since 2.1 is in the restricted domain of
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Questions & Answers
f(x) = x-2
g(x) = 3x + 5
fog(x)?
f(x)/g(x)
fog(x)= f(g(x))
= x-2
= 3x+5-2
= 3x+3
f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
find the bounded area of the parabola y^2=4x and y=16x
what is absolute value means?
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |.
The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
y=(x^2 + 3x).(eipix)
Claudia
A Function F(X)=Sinx+cosx is odd or even?
determine the area of the region enclosed by x²+y=1,2x-y+4=0
hello
please anyone with calculus PDF should share
Adegoke
Which kind of pdf do you want bro?
Aftab
can I get calculus in pdf
Abdul
okay I have such documents
Fitzgerald
How to use it to slove fraction
Hello please can someone tell me the meaning of this group all about, yes I know is calculus group but yet nothing is showing up
Shodipo
You have downloaded the aplication Calculus Volume 1, tackling about lessons for (mostly) college freshmen, Calculus 1: Differential, and this group I think aims to let concerns and questions from students who want to clarify something about the subject.
Well, this is what I guess so.
Jean
Im not in college but this will still help
nothing
how en where can u apply it
Migos
how can we scatch a parabola graph
how can I solve differentiation?
with the help of different formulas and Rules. we use formulas according to given condition or according to questions
CALCULUS
For example any questions...
CALCULUS
v=(x,y) وu=(x,y )
∂u/∂x* ∂x/∂u +∂v/∂x*∂x/∂v=1
what is the procedures in solving number 1?
Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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