The inequality c + 1/c ≥ 2 for c > 0 is proven by using the AM-GM inequality method. By applying this method, we find that the arithmetic mean of the variables is indeed greater or equal to 2, hence confirming the inequality.
Explanation:To solve the inequality c + 1/c ≥ 2 for c > 0, we can use the AM-GM (Arithmetic Mean - Geometric Mean) inequality method.
According to AM-GM inequality, for any positive numbers a, b, the arithmetic mean is always greater or equal to the geometric mean. In notation: (a + b)/2 ≥ sqrt(a * b). Applying this to our problem where a = c and b = 1/c, we get (c + 1/c) / 2 ≥ sqrt(c * 1/c). This simplifies to c + 1/c ≥ 2*1 = 2, therefore our inequality is confirmed.
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The inequality c + 1/c ≥ 2 for c > 0 is proven using the AM-GM inequality by setting a = c and b = 1/c, showing that their arithmetic mean is always greater or equal to their geometric mean.
To prove the inequality c + 1/c ≥ 2 for c > 0, we can apply the AM-GM inequality which stands for Arithmetic Mean - Geometric Mean inequality. The AM-GM inequality states that for any non-negative real numbers a and b, the arithmetic mean is always greater than or equal to the geometric mean. That is, (a + b)/2 ≥ √(ab).
In our case, we can let a = c and b = 1/c. Then, according to the AM-GM inequality, we get:
(c + 1/c)/2 ≥ √(c * 1/c)(c + 1/c)/2 ≥ √(1)(c + 1/c)/2 ≥ 1When we multiply both sides of the inequality by 2, we get:
c + 1/c ≥ 2This completes the proof for the inequality c + 1/c ≥ 2 when c > 0.
The current value of a baseball card is 60 times its original value v
(in dollars). The baseball card is worth $15. Write and solve an equation to find the original value of the baseball card.
I have no clue how to do this. Help.
Answer:
i think its x = -880
Step-by-step explanation:
so the triangle equals 180 degrees so you would put (x + 10) + (x + 20) + 50 = 180 and solve the equation. i might be wrong but i think thats how
The relation R is shown in the table below.
*
Y
-
35
-1 | 2
1
- 1
_
14
-1
Domain:
Range:
Answer:
(Insert table here)
Domain: {-3,-1,1}
Range: {-1,2,4,5}
The relation Q is described as a list of ordered pairs, shown below.
Q = { (-2, 4), (0, 2), (-1, 3), (4, -2) }
Domain: {-2,-1,0,4}
Range: {-2,2,3,4}
Step-by-step explanation:
Because its the answer
The Domain: {-3,-1,1} and Range: {-1,2,4,5}
What is domain and range?Domain – All of the values that go into a relation or a function are called the domain.
Range – All of the entities (output) which emerge from a relation or a function are called the range.
All input values that are used (independent values) forms the Domain set.
All output values that are used (dependent values) forms the Range set.
Example: Given Function:- f = 2x+1 , Find the domain, range if 1<=x<=5.
The values of x lies from 1 to 10.
So, domain is {1, 2, 3, 4, 5}.
The values of f obtained by putting domain elements in the function will be range.
So, if x=1 then f = 2(1)+1 = 3,if x=2 then f = 2(2)+1 = 5, if x=3 then f = 2(3)+1 =7, if x=4 then f = 2(4)+1 = 9, if x=5 then f = 2(5)+1 = 11.So, range is {3,5,7,9,11}.
We have relation Q as
Q = { (-2, 4), (0, 2), (-1, 3), (4, -2) }
so, we know domain are the input values
Domain: {-2,-1,0,4}
and range are the output values
Range: {-2,2,3,4}
Please answer this correctly
Answer: Steven
Step-by-step explanation: Steven lives further away from the park than anyone else.
Answer:
Steven
Step-by-step explanation:
I am going to use > and < signs to solve the problem.
From the first sentence,
Allie < Steven but Allie > Layla, so
Layla < Allie < Steven
From the second sentence,
Dave < Layla, so
Dave < Layla < Allie < Steven
Steven lives farther from the park
What is equal to 20/40?
Answer:
1/2 is equal to 20/40
that is the answer
20/40
divide the fraction by 20
20/20=1
40/20=2
Answer: 1/2
What is the absolute value of -|-7 3/5|
Answer:
7 3/5
Step-by-step explanation:
The absolute value is never a negative.
Ex: What is the absolute value of -37
A. 37
At 7:17AM this morning, it was 83˚F outside. What is 83˚F in Celsius? What is 83˚F in Kelvin?
Answer: 28.33 Celsius and 301.483 Kelvin
83°F − 32) × 5/9 = 28.333°C
(83°F − 32) × 5/9 + 273.15 = 301.483K
What is the LCM of 36 and 108?
Answer:
Answer is 108
Step-by-step explanation:
See answer in above picture or attachment
The least comm multiple for 36 and 108 is 108. This is because 36 is already a multiple of 108 so it will be the least common multiple between both numbers.
There are 15 pieces of fruit in a box . 4 are apples. There are 3 more pears than bananas. How many pears are in the box ?
a patio has an area of 9 square yards. What is its area in square inches
I need help with number 1
Answer:
1a. 0< -4 false
1b. -3> or = -7 true
1c. 4<= -1/2 false
the number 1 is it's own multiplicative inverse. name another number with this property.
The number -1 is its own multiplicative inverse, just like the number 1, because multiplying -1 by itself results in 1.
The number 1 is indeed its own multiplicative inverse because when you multiply it by itself, you get 1. The property of a number being its own multiplicative inverse means that the number multiplied by itself equals 1. There is another number with this property, which is -1. When you multiply -1 by itself (-1 x -1), the result is 1. Therefore, -1 is also its own inverse when it comes to multiplication.
This concept is rooted in the properties of identity elements and inverses within the mathematical field of abstract algebra. When considering the set of numbers 1 and -1, they form an abelian group under the operation of multiplication. In this group, every element is its own inverse, and the identity element for multiplication is 1, as any number multiplied by 1 yields the original number.
What's the difference between a rational number and an irrational number. Give one example of each.
Answer: A rational number is any value that can be expressed as a ratio of two integers. An irrational number is any value that cannot be expressed as a ratio of two integers.
Rational 4 and 1/4
Irrational π and √3
If a number can be written in the form of the fraction of p and q then that number is known as the rational number whereas a number is not written in the form of the fraction p and q then that number is known as the irrational number.
Rational Number - If a number can be written in the form of the fraction of p and q then that number is known as the rational number, that is:
[tex]\rm Rational \;Number = \dfrac{p}{q}[/tex]
Where q is the denominator and p is the numerator.
For example - [tex]\dfrac{4}{3}[/tex] , [tex]\dfrac{1}{4}[/tex] , etc
Irrational Number - If a number is not written in the form of the fraction p and q then that number is known as the irrational number, that is:
[tex]\rm Irrational \;Number \neq \dfrac{p}{q}[/tex]
Where p is the numerator and q is the denominator.
For example - [tex]\pi, \sqrt{3}[/tex], etc
For more information, refer to the link given below:
https://brainly.com/question/23017717
Can someone please do 1,2 and 3 please
Answer:
1. x= -1, -5
2. x= 9, -15
3. x= 3. -3
Step-by-step explanation:
A bowling ball is traveling at 15 mi/h when it hits the
pins. How fast is the bowling ball traveling in feet per
second?
Express each decimal as a fraction in lowest terms.
0.64
Answer:
16/25
Step-by-step explanation:
16/25 is equel to 0.64
Have a beatiful day!
find the area of of the rectangle with the given base and height.
2ft 4in
ANSWER IN INCHES
Answer:8in
Step-by-step explanation:
You will multiply 2in•4in=8in
What is the rate of 28/22
How much is 22 out of 28 written as a percentage? Convert fraction (ratio) 22 / 28 Answer: 78.571428571429%
Hope this helped! Enjoy! :)
Simplify the expression. Write your answer as a complex number.
please help
7. Write the number 0.21212121... as a fraction.
Let x =
100x =
100x - x =
99x =
x=
So 0.2121... is equal to
Answer:
21 / 99
Step-by-step explanation:
You want to get rid of the decimals so
Let x = 0.21212121
then 100x = 21.21212121
then 100x - x = 21
99x = 21
x = 21 / 99
So 0.2121... is equal to 21 / 99
To write the repeating decimal 0.21212121... as a fraction, we can use the method of infinite geometric series. The fraction equivalent of the decimal is 21/99.
Explanation:To write the repeating decimal 0.21212121... as a fraction, we can use the method of infinite geometric series. Let x = 0.21212121... . Multiplying both sides of the equation by 100 gives 100x = 21.21212121... . Subtracting the original equation from this, we get 99x = 21, which means x = 21/99. Therefore, the decimal 0.21212121... is equal to the fraction 21/99.
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Solve for y 3(2y+5)=33 what do y=
Answer:
y = 3
Step-by-step explanation:
Given
3(2y + 5) = 33 ( divide both sides by the multiplier 3 )
2y + 5 = 11 ( subtract 5 from both sides )
2y = 6 ( divide both sides by 2 )
y = 3
Blanca eamed $3999.60 after working for 18.5 hours. How much did she earn for
one hour?
Answer: $216.19
Step-by-step explanation:
3999.60/18.5 = 216.19
Hey!
------------------------------------------------
[tex]\large\boxed{214.1945...~or~roughly~214~dollars~an~hour!}[/tex]
------------------------------------------------
Steps To Solve:
~Divide
3999.60 / 18.5 = 214.1945945...
~Round
214.1945945... ≈ 214
------------------------------------------------
Hope This Helped! Good Luck!
so what is the square root of 81
Answer:
The 2nd root of 81, or 81 radical 2, or the square root of 81 is 9.
HOPE THIS HELPED!!!!!!!!!!!!! XDDDDDDDDD
Matthew built 30 toys airplanes in 5 hours. What was Matthew’s unit rate for building the airplanes?
What is the solution
y = 1/2y-6
X=-4
Neeeed help pleaseeeee????
Answer:
Leonard did make an error. He should have multiplied -7 by -5
Step-by-step explanation:
When you multiple a negative by a negative, it is a positive.
the blueprint of a conference room is made using a scale of 2 centimeters to 1 meter. if the drawing shows the room is 12 centimeters long,how long is the actual room
Answer:
6meters
Step-by-step explanation:
Use simple proportion
2cm = 1m
12cm = ?
(12x1)/2 = 6m
Answer: 6m
Step-by-step explanation:
which of the following is equivalent to the equation 4x+7y=z?
The equivalent expression is: B. y = ((z + 4x)) / 7
To find an equation equivalent to 4x + 7y = z, we want to isolate one of the variables (either x or y on one side of the equation.
Let's isolate x in terms of y and z:
Starting with 4x + 7y = z, subtract 7y from both sides:
4x = z - 7y
Now, divide both sides by 4 to solve for x:
[tex]\[x = \frac{z - 7y}{4}\][/tex]
Therefore, the correct choice is option B: [tex]\(x = \frac{z - 7y}{4}\)[/tex].
Complete question:
Which of the following is equivalent to the equation 4x+7y=z ?
A. x=4z-28y
B. x= ((z-7y))/4
C. y=7z+28x
D. y= ((z+4x))/7
b) Mr. Wonderful has called on these students in class:
boy, boy, girl, boy, girl, boy, girl, girl, boy, boy
Based on this data, what is the probability that the next student called on
x+y=-9. 5x-2y=32. elimination using manipulation
Answer:
x=2, y=11.
Step-by-step explanation:
x + y = -9.
5x - 2y = 32 Multiply the first equation by 2:
2x + 2y = -18 Adding the last 2 equations to eliminate y:
7x = 14
x = 2,
Substitute x = 2 in the first equation:
2 + y = -9
y = -9 - 2
y = -11.