Answer:
The equation of a parabola that has a curvature 6 at the origin is [tex]f(x) = 3\cdot x^{2}[/tex].
Step-by-step explanation:
All parabolas are represented by second-order polynomials, whose standard form is:
[tex]f(x) = a\cdot x^{2}+b\cdot x + c[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficient of the parabola, dimensionless.
From Vectorial Calculus we know that curvature ([tex]K[/tex]), dimensionless, is defined by the following expression:
[tex]K = \frac{\left|\frac{d^{2}y}{dx^{2}} \right|}{\left[1+\left(\frac{dy}{dx} \right)^{2}\right]^{\frac{3}{2} }}[/tex] (Eq. 2)
Where [tex]\frac{dy}{dx}[/tex] and [tex]\frac{d^{2}y}{dx^{2}}[/tex] are the first and second derivatives of the function, respectively. Each expression is described below:
[tex]\frac{dy}{dx} = 2\cdot a\cdot x + b[/tex]
[tex]\frac{d^{2}y}{dx^{2}} = 2\cdot a[/tex]
If we know that [tex]a > 0[/tex], [tex]b = c = 0[/tex], [tex]x = 0[/tex] and [tex]K = 6[/tex], then the equation of curvature and polynomial are, respectively:
[tex]\frac{2\cdot a}{1^{\frac{3}{2} }} = 6[/tex]
[tex]a = 3[/tex]
The equation of a parabola that has a curvature 6 at the origin is [tex]f(x) = 3\cdot x^{2}[/tex].
An equation of a parabola that has curvature 6 at the origin is [tex]\rm f(x) = 3x^2[/tex].
We have to determine
An equation of a parabola that has curvature 6 at the origin.
What is the equation of a parabola that has a curvature at the origin?The equation of a parabola that has a curvature a at the origin is;
[tex]\rm f(x) = ax^2[/tex]
The value of a is given by k(0) = 8;
[tex]\rm k(0) = 2a\\\\6 = 2a\\\\a = \dfrac{6}{2}\\\\a=3[/tex]
Therefore,
The equation of a parabola that has a curvature a at the origin is;
[tex]\rm f(x) = ax^2[/tex]
[tex]\rm f(x) = 3x^2[/tex]
Hence, an equation of a parabola that has curvature 6 at the origin is [tex]\rm f(x) = 3x^2[/tex].
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Use the information below to complete the steps of this Sample Work assignment by hand.
A high school club is conducting a cupcake sale at a local fair to raise money for a trip. The club members
are baking a total of 444 cupcakes. Each cupcake will sell for $3.00. The display tables cost $75.00 to rent.
Part A (2 points)
If n is the number of cupcakes sold and p is the profit earned, which is the independent variable and which is
the dependent variable? Explain.
Independent variable:
Dependent variable:
Explain:
Part B (2 points)
Write an algebraic equation that represents the profit.
is the relationship between n and p a function? Explain.
Answer:
cookie
Step-by-step explanation:
PLEASE HELP!!!!! WORTH 60 POINTS!!!
Answer:
graph a straight line through coordinates (0, 5) and (1, 3) then shade above that line
Step-by-step explanation:
(0, 5) is the y-intercept 5 and then from that point you go down 2 units and right 1 unit which would leave you at coordinate (1, 3) then you shade above that line since y is more than that line (-2x + 5)
Answer:
See in picture provided
What is the product of all the even integers from -6 to 8?
Use what you know about reflections of functions to match the graph to the function rule.
y = 3x
a
b
c
y = 3−x
a
b
c
y = −3x
a
b
c
On a coordinate plane, 3 exponential functions are on the graph. A goes through (negative 1, 3) and (0, 1) and approaches the x-axis in quadrant 1. B goes through (1, 1) and (1, 3) and approaches the x-axis in quadrant 2. C goes through (0, negative 1) and (1, negative 3) and approaches the x-axis in quadrant 3.
pick a,b or c for each answer choice.
need it by tomorrow
Answer:
B A C
Step-by-step explanation:
this website is the only reason im graduating LOL. love yall
The exponential functions are plotted on the graph and solved
1) y = 3ˣ = b)
2) y = 3⁻ˣ = a)
3) y = -3ˣ = c)
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
a)
y = 3ˣ
Now , the exponential function is plotted on the graph and is represented by the line b
b)
y = 3⁻ˣ
Now , the exponential function is plotted on the graph and is represented by the line a
c)
y = -3ˣ
Now , the exponential function is plotted on the graph and is represented by the line c
Hence , the exponential equations are solved
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The complete question is attached below :
Use what you know about reflections of functions to match the graph to the function rule.
1) y = 3ˣ
2) y = 3⁻ˣ
3) y = -3ˣ
6x-(2x-1) =9x+2(2-x) what does x equal?
Answer:
x = -5/3
Step-by-step explanation:
6x-(2x-1) =9x+2(2-x)
6x - 2x - 1 = 9x + 4 - 2x
4x - 1 = 7x + 4
collect like terms
4x - 7x = 4 + 1
-3x = 5
x = -5/3
Answer:
x= -1
Step-by-step explanation:
Trust
plzzzz help giving 30 points
Answer:
why is there only 5 points?
Step-by-step explanation:
61. The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02
Answer: Required minimum sample size = 2017
Step-by-step explanation:
Formula : Sample size(n) for population proportion(p):
[tex]n= p(1-p)(\frac{Z^c}{E})^2[/tex] , where E = Margin of error
If p = proportion of smokers
Given: p =0.30 and E=0.02
[tex]z^c[/tex] for 95% confidence level = 1.96
So,
[tex]n=0.30(1-0.30)(\dfrac{1.96}{0.02})^2\\\=0.30(0.70)(98)^2\\\\=2016.84\approx2017[/tex]
Hence, required minimum sample size = 2017
what is the difference of the fractions? Use the number line and equivalent fractions to help find the answer. -2 1/2 - ( -1 3/4)
A: -4 1/4
B: -4
C: -3/4
D: -1/2
ANSWER ASAP PLEASE
Зу + 5 < 10
Solve the inequality
Answer:
y<5/3
Step-by-step explanation:
3y+5<10
subtract 5 on both sides
3y<5
divide both sides with 3
y<5/3
Answer:
Step-by-step explanation:
You take the plus 5 and subtract it from 10
So then you have 3y<5
So then you divide both sides by 3
So you get y<5/3
Richard only has $50 to spend for some new video games. The sign in the store window says “5 games for $68,” and all games cost the same amount. Can Richard buy 4 games at this rate?
Answer:
No he will pass his 50$ budget
Step-by-step explanation: 68 divided by 5 is 13.6
13.6 multiplied by 4 is 54.4
Evaluate. 7m + 2n - 8p divided by n for m= -4, n= 2 and p = 1.5
A. –30
B.–10
C. –19
D. –22
Answer:
7*-4= -28 +4-12/2
-24-6
=-30
Step-by-step explanation:
Tickets to a dance recital cost $27 each. The auditorium for the recital has 902 seats. If the show sells out, how much money is brought in from the ticket sales?
Answer:
24354
Step-by-step explanation:
Alejandro bought $3.50 worth of pencils and erasers at the school store. Pencils cost $0.50 apiece, and erasers cost
$0.75 apiece. Which equation written in standard form represents the number of pencils, p, and the number of erasers,
e, that Alejandro bought?
O 0.75e = 3.50 -0.50p
O 0.50p + 0.75e = 3.50
O 3e = 14 -2p
O 2p + 3e = 14
I need help with this question
Answer:
answer: C, 24 photos per day
Step-by-step explanation:
Answer:
it's either the first one or the third one.
I'm so sorry if they are both wrong.
what is the slope of this graph Algebra 1b
please help me fill in both boxes
Answer:
1st box: -1/2
2nd box: 2/1 or just 2
Step-by-step explanation:
1st box: parallel slopes have the EXACT same slope as the original
2nd box: perpendicular slopes are the negative reciprocal of the original
I dont understand this
80 total students 6/2 are girls how many are girls
Answer:
60
Step-by-step explanation:
Can someone help me please
Answer:
-50
Step-by-step explanation:
Since the rate is -2 degrees per minute and you need to know what the temperature will be after 25 minutes, simply multiply the two numbers:
= -2 x 25
= -50
It will reach a temperature of -50 degrees after 25 minutes.
What is the probability that six consecutive integers will be chosen as the winning numbers in a lottery where each number chosen is an integer between 1 and 40 (inclusive)?
Answer:
0.00000911843
Step-by-step explanation:
Since the number chosen is an integer between 1 and 40 (inclusive), it means that the number of terms is 40.
Thus; n = 40
Probability that 6 integers (r = 6) which is number of possible outcomes will be gotten without repetition is gotten by the combination formula which is;
C(n, r) = n!/(r!(n - r)!)
C(40, 6) = 40!/(6!(40 - 6)!)
C(40,6) = 3838380
Now, to select 6 consecutive integers, it can be done in different combinations such as;
(1 - 6, 2 - 7, 8 - 13,...e.t.c)
Total number of favorable outcomes will be 35.
Now,probability that six consecutive integers will be chosen as the winning numbers is;
P(that six consecutive integers will be chosen as the winning numbers) = number of favorable outcomes/number of possible outcomes = 35/3838380 = 0.00000911843
[tex] \frac{ \frac{1}{ x} - \frac{1}{12} }{x - 12} [/tex]
how do i solve when looking for the limit as x approches 12?
Answer:
[tex]\lim_{x \to 12} \frac{\frac{1}{x}-\frac{1}{12} }{x-12} =\frac{-1}{144}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\lim_{x \to 12} \frac{\frac{1}{x}-\frac{1}{12} }{x-12}[/tex]
Step 2: Solve
Numerator; Common denominator: [tex]\lim_{x \to 12} \frac{\frac{12}{12x}-\frac{x}{12x} }{x-12}[/tex]Numerator; Combine like terms: [tex]\lim_{x \to 12} \frac{\frac{12-x}{12x} }{x-12}[/tex]Rewrite entire fraction: [tex]\lim_{x \to 12} \frac{12-x}{12x} \div x-12[/tex]Rewrite operation: [tex]\lim_{x \to 12} \frac{12-x}{12x} \cdot \frac{1}{x-12}[/tex]Multiply: [tex]\lim_{x \to 12} \frac{12-x}{12x(x-12)}[/tex]Factor numerator: [tex]\lim_{x \to 12} \frac{-(x - 12)}{12x(x-12)}[/tex]Simplify: [tex]\lim_{x \to 12} \frac{-1}{12x}[/tex]Evaluate limit: [tex]\frac{-1}{12(12)} =\frac{-1}{144}[/tex]The LCM (12, 15, 20, k) = 420. What is the least possible value of k?
The least possible value of k is 7.
The given numbers;
12, 15, 20, k
LCM of 12, 15, 20, k = 420
The prime factor of each of the given is calculated as;
12 = 2² x 3
15 = 3 x 5
20 = 2² x 5
The LCM = 2² x 3 x 5 = 60
The least possible value of k is calculated as;
60k = 420
[tex]k = \frac{420}{60} \\\\k = 7[/tex]
Thus, the least possible value of k is 7.
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Zachary purchased a computer for $1,500 on a payment plan. Six months after he purchased the computer, his balance was $600. Eight months after he purchased
the computer, his balance was $300. What is an equation that models the balance y after x months?
The equation models the balance y after x months
9514 1404 393
Answer:
y = 1500 -150x
Step-by-step explanation:
Apparently, we're to assume that the balance is linear function of the number of months. We are given 3 points:
(0, 1500), (6, 600), (8, 300)
Any two of these can be used to write the equation of the line using the 2-point form:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (600 -1500)/(6 -0)(x -0) +1500
y = -900/6x +1500
y = 1500 -150x . . . models the balance after x months
What is 3 over 3 over 8?
Answer:
1/8
Step-by-step explanation:
What's 20% of 30% of 10% of 500?
Answer:
the answer is 3
Step-by-step explanation:
20% of 30% of 10% of 500 is 3
Step-by-step explanation:
A company places a seven-digit serial number on each part that is made. Each digit of the serial number can be any number from 0 through 9. Digits can be repeated in the serial number. How many different serial numbers are possible?
Answer: 10,000,000 different numbers are possible.
Step-by-step explanation:
Given: Serial number is of 7 digits.
Choices for digits = 10 (0 to 9)
If digits can be repeated, then by Fundamental principle of counting,
The different serial numbers are possible = [tex]10^7[/tex]
= 10,000,000
Hence, the different serial numbers are possible = 10,000,000
1. How much would the following items cost if they were 50% off?
TV: $349.95
shoes: $55.00
boat: $9,499.99
A rocket is fired vertically into the air at 40 m/s. The expression
--5+2 + 40t + 20 gives the rocket's height after t seconds. Factor this
expression.
Answer:
-5(t² - 8t - 4)
Step-by-step explanation:
Step 1: Define
-5t² + 40t + 20
Step 2: Simplify
Factor - GCF: -5(t² - 8t - 4)Here, we cannot factor the quadratic and to solve for the roots we will need to use the Quadratic Formula.
Please help I need 6 answers
can you please explain the question a bit
The Education Foundation hosted an annual fundraising dinner. There were 24 dinner tables with 8 chairs at each table. Each dinner ticket cost $12.50. If of the dinner tables were full, how much money was raised from the dinner ticket sales?
$225
⊝
$1,800
⊝
$2,400
⊝
$3,200
Answer:
2,400
Step-by-step explanation:
24 times 8 equals 192, 192 times 12.50 equals 2,400. If this does not help, sorry.
The amount raised is $2400.
Option C is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
There were 24 tables with 8 chairs at each table.
Total chairs.
= 24 x 8
= 192 chairs
Each dinner ticket cost $12.50.
And all the dinner tables were full.
So,
Total amount raised.
= 96 x 12.50
= 2400
Therefore,
The amount raised is $2400.
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