Answer:
[tex]f(x)= 2x[/tex]
Step-by-step explanation:
For which function is f(x) not equal to f^-1(x)
LEts check with each function, we find out inverse for each option
[tex]f(x)= 2-x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= 2-x[/tex]
[tex]x= 2-y[/tex], Add y on both sides
[tex]x+y= 2[/tex], Subtract x from both sides
[tex]y= 2-x[/tex], Inverse is equal to f(x)
[tex]-f(x)= \frac{2}{x}[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]-y= \frac{2}{x}[/tex]
[tex]-x= \frac{2}{y}[/tex], cross multiply it
[tex]-xy = 2[/tex], divide by x on both sides
[tex]-y= \frac{2}{x}[/tex], Inverse is equal to f(x)
[tex]f(x)= -x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= -x[/tex]
[tex]x=-y[/tex], Add y on both sides
[tex]x+y= 0[/tex], Subtract x from both sides
[tex]y=-x[/tex], Inverse is equal to f(x)
[tex]f(x)= 2x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= 2x[/tex]
[tex]x= 2y[/tex], divide by 2 on both sides
[tex]\frac{x}{2}=y[/tex], Inverse is not equal to f(x)
Simplify: 20 sin(2x) cos(2x)
To simplify 20 sin(2x) cos(2x), apply the double-angle trigonometric identities for sine and cosine.
The given expression: 20 sin(2x) cos(2x) can be simplified using the double-angle trigonometric identity for sine and cosine.
Apply the identities sin(2x) = 2sin(x)cos(x) and cos(2x) = cos²(x) - sin²(x).Substitute these identities into the expression and simplify to get the final result.Solve for "W"
-1 > 2W + 7
-1>2W+7
-8>2w
w = -8/2 = -4
w>-4
Traveling at 65 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San Diego to Malibu?
We can establish a proportion:
Since an hour = 60 minutes
If it takes 60 minutes to travel 65 miles (speed)
X minutes it will take to travel 125 miles
X = 125miles*60 minutes/65 miles = 115 minutes approximately
Answer : 115 minutes approximately
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
how much will the toll be after the increase
130% = 1.30
multiply 2.50 x 1.30
2.50 x 1.30 = 3.25
the new toll is 3.25
1)broccoli is 4lbs for $5 if she buys 3 pounds how much will it cost 2) if she buys 4.2 pounds of it what will be the cost
The distance between points
A survey conducted by a song rating service finds that the percentages of listeners familiar with poker face by lady gaga who would give the song ratings of 5, 4, 3, 2, and 1 are, respectively, 50 percent, 18 percent, 19 percent, 8 percent, and 5 percent. assign the numerical values 1, 2, 3, 4, and 5 to the (qualitative) ratings 1, 2, 3, 4, and 5 and find an estimate of the probability distribution of x = this song’s rating by a randomly selected listener who is familiar with the song.
The probability distribution of the song 'Poker Face' ratings by a randomly selected listener familiar with the song can be represented by assigning probabilities to each rating based on the survey percentages. The sum of these probabilities equals 1, confirming a valid distribution.
Explanation:The student is asking about how to find the probability distribution for the ratings given to the song 'Poker Face' by Lady Gaga. To solve this, we assign numerical values to the qualitative ratings: 1, 2, 3, 4, and 5 correspond to the ratings 1 through 5, respectively.
We can list out the probabilities for each rating based on the survey as such:
Rating 5: P(X=5) = 50% or 0.50Rating 4: P(X=4) = 18% or 0.18Rating 3: P(X=3) = 19% or 0.19Rating 2: P(X=2) = 8% or 0.08Rating 1: P(X=1) = 5% or 0.05This list represents the estimation of the probability distribution of a song's rating by a randomly selected listener familiar with the song. In other words, it tells us the likelihood that a listener would rate the song at a certain level.
To confirm this is a valid probability distribution, we must check that the sum of all probabilities adds up to 1:
0.50 + 0.18 + 0.19 + 0.08 + 0.05 = 1.00
Since the sum is equal to 1, we have a valid probability distribution.
Professor whata guy surveyed a random sample of 420 statistics students. one of the questions was, "will you take another mathematics class?" the results showed that 252 of the students said yes. what is the sample proportion, p, of students who saud they would take another math class?
The sample proportion, p, of students who said they would take another math class, p = 0.6 or 60%.
To determine the sample proportion, p, you can use the following formula:
p = x/nwhere:
x is the number of students who said yes (successes).n is the total number of students surveyed.From the question,
x = 252n = 420Substituting these values into the formula gives:
p = 252 / 420 = 0.6
Therefore, the sample proportion of students who said they would take another math class is 0.6 or 60%.
For football tryouts at a local school, 12 coaches and 42 players will split into groups. Each group have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?
There are 6 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2 students are possible?
Which of theses numbers is the smallest 0.02, 0.24, 0.11, 0, 2
The mean incubation time for a type of fertilized egg kept at 100.7100.7â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 22 daysdays. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 1919 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?
Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?
Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
Final answer:
The question asks for the original vector function given its derivative and an initial condition. Through integration and applying the initial condition, the vector function is found to be r(t) = t⁵i + t⁶j + (t²/2 + 1/2)k.
Explanation:
The question involves finding the vector function r(t) given its derivative r'(t) = 5t⁴i + 6t⁵j + t k and an initial condition r(1) = i + j. To find r(t), integrate each component of r'(t) with respect to t. The integration results in:
The i component: ∫5t4 dt = t⁵/1 + C₁The j component: ∫6t5 dt = t⁶/1 + C₂The k component: ∫t dt = t²/2 + C₃Therefore, r(t) = (t⁵/1 + C₁)i + (t⁶/1 + C₂)j + (t²/2 + C₃)k. Substituting t = 1 and using the initial condition r(1) = i + j to find the constants C₁, C₂, and C₃, we get:
C₁ = 0C₂ = 0C₃ = 1/2Finally, r(t) = t⁵i + t⁶j + (t²/2 +1/2) k.
The function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
To find [tex]\( r(t) \) given \( r'(t) \) and \( r(1) \)[/tex], we need to integrate[tex]\( r'(t) \)[/tex]with respect to ( t ) and then use the given initial condition ( r(1) ) to determine the constant of integration.
Given:
[tex]\[ r'(t) = 5t^4i + 6t^5j + tk \][/tex]
[tex]\[ r(1) = i + j \][/tex]
First, let's integrate [tex]\( r'(t) \)[/tex] with respect to [tex]\( t \)[/tex] to find [tex]\( r(t) \)[/tex]:
[tex]\[ r(t) = \int 5t^4i \, dt + \int 6t^5j \, dt + \int tk \, dt \][/tex]
[tex]\[ r(t) = \frac{5}{5}t^5i + \frac{6}{6}t^6j + \frac{1}{2}t^2k + C \][/tex]
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k + C \][/tex]
Now, we apply the initial condition [tex]\( r(1) = i + j \)[/tex]:
[tex]\[ r(1) = (1)^5i + (1)^6j + \frac{1}{2}(1)^2k + C = i + j \][/tex]
[tex]\[ i + j + \frac{1}{2}k + C = i + j \][/tex]
Comparing the coefficients of [tex]\( i \), \( j \), and \( k \)[/tex], we get:
Coefficient of [tex]\( i \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( j \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( k \): \( \frac{1}{2} = 0 \)[/tex] (doesn't match)
So, to make the coefficients match, [tex]\( C = -\frac{1}{2} \)[/tex].
Therefore, the function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
Write the given system without the use of matrices. d/dt (x y z) =( 1 −1 6 3 −8 1 −2 7 5) (x y z) + (1 2 2)
URGENT!!!
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation
y = -16t^2 + 400, where t represents the seconds after the camera is dropped. How long will it take (in seconds) before Kay sees the splash from the camera hitting the water.
The given equation in this case is:
y = -16 t^2 + 400
We can see that the slope of the equation is negative (-16) which means that the position of Kay is on the positive y-axis , while the bottom of the river is in the origin. This is supported by taking t = 0, the initial y becomes y = 400. Therefore the position of Kay now is at (0, 400).
So to find for the time when the camera hits the water, then y must be zero (t, 0) so we have to find for t in this case.
When y = 0
0 = -16 t^2 + 400
16 t^2 = 400
t^2 = 25
t = 5 s
Therefore it takes 5 seconds for the camera to hit the water and for Kay to see a splash.
Answer:
5 seconds
Step-by-step explanation:
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation
y = -16t^2 + 400, where t represents the seconds after the camera is dropped.
When splash from the hits the water then the height becomes 0
height is y so we replace y with 0 and solve for t
0 = -16t^2 + 400
Subtract 400 on both sides
-400 = -16t^2
Divide by 16 on both sides
25= t^2
take square root on both sides
t= 5
It takes 5 seconds
You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the volume of the tent? Round your answer to the nearest hundredth.
23.33 cubic feet
46.67 cubic feet
93.33 cubic feet
140 cubic feet
V=(l*w*h)/3
need to find length = square root(35) 5.916
(5.916 *5.916*4)/3 =46.665
round to 46.67 cubic feet
Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.2 (16 – π) in.2 (64 – 16π) in.2 (64 – 4π) in.2vvvv
Answer: [tex]64-16\pi[/tex] unit square.
Step-by-step explanation:
Here, four circle are removing from a square from the square of edge 8.
Since, The area of the square= [tex]8^2=64[/tex] square unit ( because, area of square=side×side)
The area of a circle with radius 2 = [tex]\pi(2)^2=4\pi[/tex] square unit.
The area of four circle of radius 2= [tex]4\times4\pi=16\pi[/tex] square unit.
According to the question, these four circle are removed by the above square.
Therefore remaining area of the square after removing these four circle=area of the square- area of four circle of radius 2= [tex]64-16\pi[/tex] square unit.
The remaining area of the square is 64 - 16π.
What is a circle?A circle is a bounded figure in which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius
Area of one circle = 2²π = 4π
Area of four circles = 4 x 4π = 16π
What is a square?A square is a quadrilateral with four equal sides.
Characteristics of a square includes:
Area of a square = length²
= (2x4)²
= 64
The remaining area of the square = 64 - 16π
To learn more about the area of a circle, please check: https://brainly.com/question/14351152
A cylinder storage tank is to contain V=16,000pi cubic feet (about 400,00 gallons). the cost of the tank is proportional to its area, so the minimal-cost tank will be the one with minimum area. The volume (V) of a cylinder of radius r and height h is (pi)(r^2)(h). its surface area is the area of top and bottom, 2(pi)(r^2), plus the side area 2(pi)(r^2)(h). find the dimensions, r and h, of the minimal-area tank
A minor league baseball team plays 72 games in a season. If the team won 15 more than twice as many games as they lost, how many wins and losses did the team have?
the length of a rectangular floor is 5 feet less than twice it's width. the area of the floor is 150 square feet. what is the width of the room?
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.
Here, number of hours represents input value and minutes represents the output value,
Now, By the given table,
The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),
Also,
[tex]\frac{120-60}{2-1}=\frac{180-120}{3-2}=\frac{240-180}{4-3}=\frac{300-240}{5-4}=60[/tex]
⇒ The rate of change output value with respect to input value remains constant,
Hence, It represents a linear function because there is a constant rate of change.
Martina made 35 hats. Martina made 7 times as many hats as shen. Let h be the number of hats that shen made
Which property of polynomial addition says that the sum of two polynomials is always a polynomial
Answer:
Closure
Step-by-step explanation:
How to find two fractions between 1/2 and 1/3
What's the best five terms to the list?
the letters are going backwards and they use each letter twice
so next 5 should be vt, ut, us, ts, tr
Which factor do 64x^2+48x+9 and 64x^2 - 9 have in common?
Can someone please answer this?
A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.
It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:
25 + 0.2 * X = 200 ---> 1
25 + 0.2 * X = 800 ---> 2
Where X represents the original bill.
Calculating for X in equation 1:
25 + 0.2 * X = 200
0.2 * X = 175
X = 875
Calculating for X in equation 2:
25 + 0.2 * X = 800
0.2 * X = 775
X = 3875
Therefore the original bill ranges from $875 to $3875. The equality equation would be:
$875 ≥ X ≥ $3875
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight? If muscle weight is 90 pounds, how much does the person weigh?