Answer: x=0 is a counterexample to Kelvin's conjecture.
Explanation:-
Given that x is a number that is not negative, Kelvin conjectured that [tex]x^2>x+1[/tex]
A counter example is an example that contradicts or opposes the conjecture.
Thus -12 and -2 cannot be the value of x for the counter example as they are negative
The positive numbers in options are 0 and 5,such that
[tex]0^2>0+1\\\Rightarrow0>1...\text{which is not true.}[/tex]
[tex]5^2>5+1\\\Rightarrow25>6...\text{which is true.}[/tex]
Thus the value of x=0 contradicts the conjecture made by Kevin.
⇒x=0 is a counterexample to Kelvin's conjecture.
If you work 52 weeks out of the year and 40 hours a week how many hours would you work in one year
Find the limit of the function algebraically. limit as x approaches zero of quantity negative six plus x divided by x to the fourth power.
The limit as x approaches zero of the function (-6 + x)/x^4 is 0. This is arrived at using L'Hopital's Rule, which instructs us to take the limits of the derivatives of the numerator and denominator when the initial function limit causes an indeterminate form (0/0, infinity/infinity).
Explanation:The limit of the function negative six plus x divided by x to the fourth power as x approaches zero cannot be solved using traditional limit computations as it creates indeterminate form. However, the L'Hôpital's rule
Rule can be used to determine this limit.
Under L'Hôpital's rule
rule, to solve for the limit of a function that results in an indeterminate form 0/0 or infinity/infinity, you take the derivative of the numerator and the derivative of the denominator independently, and then find the limit of that quotient as x approaches the given value.
In this case, the function is (-6+x)/x4. The derivative of -6+x is 1 and the derivative of x4 is 4x3. Therefore, after the first iteration of L'Hopital's rule, you are finding the limit as x approaches zero of 1/(4x3). Running the rule again we get 0/(12x2). Clearly there, the numerator is 0 and since x2 will be a non-negative number the limit would be 0. Hence, the limit of the function as x approaches zero is 0.
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Relationship a has a greater rate than relationship
b. this table represents relationship
b. hours worked 2 4 5 8 amount paid 30.40 60.80 76 121.60 which equation could represent relationship a? select each correct answer. y = 14.9x y = 16.4x y = 15.4x y = 15.2x
The required equation is y = 15.2x which could represent relationship A.
which is the correct answer would be an option (B).
What is a Linear Function?A linear function is defined as a function in the form of f(x) = mx + c where 'm' and 'c' are real numbers.
We have been given that relationship A has a greater rate than relationship B.
Hours Worked Amount Paid
2 30.4
4 60.8
5 76
8 121.60
Let the number of hours worked x and the total amount paid y.
As per the given functions
⇒ y = 15.4x ...(i)
⇒ y = 15.2x ...(ii)
⇒ y = 16.4x ...(iii)
⇒ y = 14.9x ...(iv)
As per the linear function (ii),
⇒ y = 15.2×2
⇒ y = 30.4
The above is satisfy the point, therefore, it represents relationship A
Hence, the required equation is y = 15.2x which could represent relationship A.
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The coordinates of point t are (0,4). the midpoint of st is (3,−2). find the coordinates of point s.
Find the standard form of the equation of the circle with endpoints of a diameter at the points
Mark has a container in the shape of a cube. He uses 64 cubes with side lengths of 1 inch to completely fill the container. What is the edge length of the container?
Answer:
4 inches is the edge length of the container.
Step-by-step explanation:
Length of the small cubes = a = 1 inch
Volume occupied each small cube = v = [tex]a^3=(1 inch )^3= 1 inches^3[/tex]
Length of the big cube = A
Volume of the big cube = V
[tex]V=A^3[/tex]
He uses 64 cubes with side lengths of 1 inch to completely fill the container.
[tex]V=64\times v=64\times 1 inches^3[/tex]
[tex]A^3=64\times 1 inch^3[/tex]
A = 4 inch
4 inches is the edge length of the container.
Sari has 3 times as many pencil erasers asSam. Together they have 28 erasers. How many erasers does Sari have?
3x +x = 28
4x = 28
x = 28/4 = 7
7x3 = 21
Sari has 21 erasers
Question 2 options:
All questions are about this system of equations:
{5x +18y =23
x +3y = 2
When you multiply the second equation by this number, what does it become?
Cube root of 0.000064
A fair coin is tossed 10000 times the odds of getting exactly 5000 heads is closest to
Answer:
5000 tails there are only two sides on coin
Step-by-step explanation:
What is the next term in the sequence? 44, 22, 11, 5.5...
PLEASE HELP!
Solve for x.
x/3≤−6
A) x≤−18
B) x≤−2
C) x≥−2
D) x≥−18
Plz help with my gasoline question that I just put its due tomorrow!!?? it's number 7
Which is the correct label of the parallel lines? parallel lines a and b are shown. points a and b lie on line a while points c and d lie on line
b?
The parallel lines mentioned in the question are correctly labeled as 'AB' for Line a (which involves points A and B) and 'CD' for Line b (which refers to points C and D).
Explanation:In geometry, parallel lines are often labeled with the same letter. In your case, the parallel lines are described as Line a and Line b. Points A and B lie on Line a, and Points C and D lie on Line b. Therefore, to correctly label the lines, 'Line a' is written as 'AB' since points A and B are on this line. Meanwhile, 'Line b' is labeled as 'CD' since points C and D are on that line.
So, in conclusion, the correct labels for the mentioned parallel lines are AB for 'Line a' and CD for 'Line b'.
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What is the simplified answer for -2/3+4/3
-2 + 4 = 2
so:
-2/3 + 4/3 = 2/3
if y =6.6 when x=9.9, find y when x=6.6
The sum of a number times 5 and 28 is less than 29
Use the variable b for the missing number
What is the measure of angle x, In degrees?
Helps please!!
Answer:
40° is the right answer for apex learners
A games console costs £100
The cost is increased by 20%
The new cost is decreased by 20%
Which of the following is true?
[1 mark]
- The final cost of the console is less than the original cost
- The final cost of the console is the same as the original cost
- The final cost of the console is more than the original cost
The township of Brock is growing at a rate of 6.5% per annum. How many people are there in Brock township now, if there will be 15000 in 4.5 years?
A friend eats eats one-fifth of a pizza; you decide to eat half of what was left. How much is left after you eat the pizza?
it would be 2/5 since 1/5 is subtracted from your friend, and you are eating half which would be 2/5 since you have 4/5 now and 2/5 = half of 4/5. (Fun Fact: I cant even eat half a pizza).
Eight plus the quotient of a number and 3 is -2
Find the value of x or y so that the line through the points has the given slope of (x, -8) and (-7,5); slope: -13/7
The required value of x is 112/13 which line through the points has the given slope of (x, -8) and (-7,5).
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Assume two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We have been given two points :(x, -8) and (-7,5)
As per the line of slope,
m = (y₂ - y₁)/(x₂ -x₁ )
Here
x₁ = x, y₁ = 8
x₂ = -7, y₂ = 5
Substitute values in the above formula
-13/7 = (5 - 8)/(-7 - x )
-13/7 = -3/(-7 - x )
-13(-7 - x ) = -21
91 + 13x = -21
13x = -21 - 91
13x = 112
x = 112/13
Therefore, the required value of x is 112/13.
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Which of the following products represents 6 1/2% tax, in dollars, on a price of $14.29? a. (0.00675)(14.29) b. (0.0675)(14.29) c. (0.675)(14.29) d. (6.75)(14.29)
Answer:
B
Step-by-step explanation:
6 3/4% tax
write the equation of a line that is perpendicular to y=3z-2 and that passes through the point (-9,5)
plz help me with number 9
and show work so i can understand thx
I think the answer is C, since it is measured to 2 decimal places
A forest owned by the Jumbo Lumber Corporation contains 7,054 trees. If Jumbo Lumber cuts down 37 trees every day, which function can be used to find the number of trees, n, left in the forest after t days?
Answer:
n(t)= 7,054 - 37t
Step-by-step explanation:
what is the measure of
Esin started a T-shirt-printing business. She spent $2500 to purchase supplies to get started and she uses about $4.50 worth of supplies per T-shirt printed. Esin charges $25 for each T-shirt. Let s represent the number of T-shirts.
What is the minimum number of T-shirts Esin will need to sell to make a profit?
4.5s≥2500+25s
4.5s>2500+25s
25s<2500+4.5s
25s>2500+4.5s
Which equation is NOT an example of a linear function? A) y = 9 - 2x B) y = 6/x C) y = x/2 + 9 D) y = 5/6 x - 8