The equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that,
f(x) = 6x/(2 + x²)
f'(x)=(6x)(2+x²)-6x(2+x²)/(2+x²)²
f'(2)=(6×2)(2+2²)-6x(2+2²)/(2+2²)²
f'(2)=1/3
The value of functions gives the slope of the equation passes through the point (2, 2).
y-y₀=m(x-x₀)
y-2=(1/3)x-2
Thus, the equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.
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Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8 $8.26 $9 $9.26
Answer:
I think A
Step-by-step explanation:
Given the following functions: f(u)=u9/2 and g(x)=x10+1. Find:
f(g(x)=
f′(u)=
f′(g(x)=)
g′(x)=
(f∘g)′(x)=
The function f(g(x)) is ((x^10+1)^(9/2), the derivative f'(u) is (9/2)u^(7/2), the derivative f'(g(x)) is (9/2)(x^10+1)^(7/2), the derivative g'(x) is 10x^9, and the derivative (f ∘ g)'(x) is the product of g'(x) and f'(g(x)) which equals to 10x^9 * (9/2)(x^10+1)^(7/2).
Explanation:The functions are defined as f(u)=u9/2 whereas g(x)=x10+1.
To find f(g(x)), input g(x) into the f function. Thus, f(g(x))=((x10+1)9/2.
Next, the derivative of f(u) would be: f'(u)= (9/2)u7/2.
For f'(g(x)), replace u with g(x) in f'(u): f'(g(x))=(9/2)(x10+1)7/2.
The derivative of g(x) is: g'(x)=10x9.
Lastly, to find (f ∘ g)'(x), use the chain rule which states that (f ∘ g)'(x) = g'(x) * f'(g(x) : (f ∘ g)'(x) = 10x9 * (9/2)(x10+1)7/2.
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A factory produces 7,482 widgets per day. It ships these widgets in 2 crates. Each widget sells for $7. How much money does one crate earn?
The rise and span for a roof are shown. The pitch of a roof is the ratio of the rise to the half-span . If the rise is 8 feet and the span is 30 feet, what is the pitch in simplest form?
A person plans to invest a total of $140,000 in a CD at 7% annual interest and in a mutual fund that has a three-year average annual interest of 10% by X and Y represent the money in dollars invested in the CD and the mutual fund respectively how much money should be invested in each account to earn a total of $12,200 in one year
Final answer:
The student should invest $60,000 in the CD at 7% annual interest and $80,000 in the mutual fund at 10% to earn a total interest of $12,200 in one year. This is determined by setting up and solving a system of linear equations.
Explanation:
The student asked how much money should be invested in a CD at 7% annual interest and a mutual fund with a three-year average annual interest of 10%, given a total investment of $140,000, to earn a total of $12,200 in one year. We can set up a system of equations to solve for X (the amount invested in the CD) and Y (the amount invested in the mutual fund).
Let X be the amount invested in the CD and Y be the amount invested in the mutual fund. We then have the following system of equations:
X + Y = $140,000 (the total investment)0.07X + 0.10Y = $12,200 (the total interest earned in one year)Solving this system, we subtract the first equation from the second equation multiplied by 0.07:
0.07X + 0.10Y = $12,2000.07X + 0.07Y = $9,800Subtract the second equation from the first we get:
0.03Y = $2,400
Dividing both sides by 0.03 gives:
Y = $80,000
Substitute Y in the first equation:
X + $80,000 = $140,000
X = $140,000 - $80,000 = $60,000
Therefore, $60,000 should be invested in the CD and $80,000 in the mutual fund to obtain a total interest of $12,200 in one year.
Complete the patterns 9430, 94.3, 9.43
What does academic integrity mean?
Academic integrity is essential for a fair and genuine educational experience, emphasizing honesty and accountability in all academic endeavors. It is crucial for building trust, equity, and facilitating real learning outcomes, necessitating a collective effort from the academic community to maintain these values. The widespread issue of academic dishonesty further highlights the need for strict adherence to integrity principles.
Explanation:Academic integrity is the cornerstone of a meaningful educational experience, emphasizing the value of honesty and fairness within the academic community. It involves the commitment to avoid cheating, plagiarism, and any form of deception or fraud in academic work, ensuring that all academic activities, from research to examination, are conducted in a manner that is fair, respectful, and accountable. The importance of academic integrity lies not only in the cultivation of a fair and trustworthy academic environment but also in fostering genuine learning and understanding, thereby empowering students to achieve authentic success that extends well beyond their academic careers.
Despite the challenges posed by technological advancements and digital resources, which have made cheating more accessible and harder to detect, maintaining academic integrity is crucial. It builds trust, understanding, equity, and facilitates real, meaningful learning outcomes. Faculty, administrators, and students alike bear the responsibility of upholding these principles to ensure that the academic community remains a space where fairness prevails and genuine knowledge acquisition is celebrated.
According to the International Center for Academic Integrity, a significant number of students have admitted to engaging in dishonest behaviors, which underscores the ongoing battle against academic dishonesty. Highlighting the importance of maintaining integrity, these statistics serve as a reminder of the collective effort needed to nurture an academic culture that values honesty above all.
a car recently sold for $32,345. if there is a 6% sales tax on automobile sales, how much tax will be added to the price of the car? I got $194.70. is this right?
What must be true of two rational expressions before they can be added?
A They must have common numerators.
B They must be of the same degree.
C They must have the same variables.
D The must have common denominators.
Answer:
D They must have common denominators.
Step-by-step explanation:
Rational expressions are fractions formed by two polynomials, one in the numerator and other in the denominator.
The numerator is the polynomial that is at the top of the fraction and denominator is the polynomial that is at the bottom of the fraction.
To add any fractions it is necessary that they have the same denominator, this applies to rational expressions, to add them it is required that they have the same polynomial in the denominator.
How do I solve 3x+5x+10x=16x-6
Multiply using partial products Estimate then record the product 149*5
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
Answer:
[tex]7ab^3[/tex]
Step-by-step explanation:
the greatest common factor of [tex]42a^5b^3[/tex], [tex]35a^3b^4[/tex], and [tex]42ab^4[/tex]
LEts write the factors for each expression
[tex]42a^5b^3=6*7*a*a*a*a*a*b*b*b[/tex]
[tex]35a^3b^4=5*7*a*a*a*b*b*b*b[/tex]
[tex]42ab^4=6*7*a*b*b*b*b[/tex]
From all the terms we have common factors
7, 'a' and b^3
So GCF is [tex]7ab^3[/tex]
help me! need to show work!
The sum of two numbers is x. If one of the numbers is 12, what is the other ?
The length of a rectangle is 4 ft longer than it’s width. If the perimeter of the rectangle is 28 ft, find it’s area.
The Area of the rectangle is 45 square feet.
What is Perimeter?The perimeter of a form is the space surrounding its edge. To Find the perimeter of various forms by summing the lengths of their sides.
Given, The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 28 ft.
Let "l" be the length of the perimeter
Thus, width = l - 4
From the general formula of perimeter:
perimeter = 2*(length + width)
In our case
Perimeter = 2* (l + l -4)
Perimeter = 4l - 8
Since the perimeter is given 28 ft
thus,
4l - 8 = 28
4l = 36
l = 9 ft
thus width = 9 - 4 = 5 ft
Since,
Area = Length * width
Area = 9 * 5
Area of rectangle = 45 square feet.
therefore, The Area of the rectangle is 45 square feet.
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Which set of data has the same mode and median?
3, 4, 6, 7, 8
3, 3, 4, 5, 5
6, 7, 7, 8, 9
2, 2, 3, 4, 6
Answer:
6,7,7,8,9 both have 7 for mode and median
Step-by-step explanation:
Write a real world situation that can be modeled by the inequality
834 + 14s > 978 - 10s. Then solve the inequality.
The inequality 834 + 14s > 978 - 10s can represent a situation involving saving and spending money over time. To solve it, you perform a series of operations to isolate variable 's', which in this case results in s > 6, indicating more than six weeks required for savings to exceed spending.
Explanation:A real world situation that can be modelled by this inequality 834 + 14s > 978 - 10s could be a scenario involving saving and spending money. Say you start with $834 and each week you save $14 (s represents the number of weeks). On the other hand, you have $978 and you spend $10 each week. You want to figure out how many weeks it will take for the amount you have from saving to be more than the amount left from spending.
Now, to solve the inequality: subtract 834 from both sides which gives 14s > 144 - 10s, then combine like terms to get 24s > 144. Finally, divide both sides by 24 to solve for s: s > 6. Therefore, it will take more than six weeks for the money you save to exceed what remains from your starting amount of $978 after spending $10 each week.
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3 pounds fruit salad = how many ounces
Answer: 48 ounces
Step-by-step explanation: To convert 3 pounds into ounces, we first need to identify the conversion factor for pounds and ounces, which is shown below.
16 ounces = 1 pound
We are going from a larger unit, pounds, to a smaller unit, ounces.
When we go from a larger unit to a smaller unit, we multiply.
So here, we multiply 3 lb x 16 which gives us 48 ounces.
Note that I multiplied by the conversion factor.
This means that the fruit salad is 48 ounces.
wrong answer its the right one above you
Carys is checking her tax bill for the last year. The tax rates were as follows: No tax of the first £11 000 of earnings. Earnings in excess of of £11 000 and up to £43 000 taxed at a rate of 20%. Earnings in excess of £43 000 and up to £150 000 taxed at a rate of 40%. Earnings over £150 000 taxed at a rate of 45%. Last year Carys, earned £45 600 before tax. How much tax did she pay in total. Show your working.
It isn't £18240 it says its wrong
Answer:
total tax is = 14685 pound
Step-by-step explanation:
Given data:
For first year -
earning is 11000 pound
for second year
income is = 43000 - 11000 = 32000 pound
tax rate = 20%
for third year
income is = 150000 - 43000 = 107000 pound
tax rate = 40%
for fourth year
income is = 158900 - 150000 = 8900 pound
tax rate = 45%
As it is given there is no tax on first year
Tax in 2nd year = 0.20 × 32000 = 6400 pound
Tax in 3rd year = 0.40 × 107000 = 42800 pound
Tax in 4th year = 0.45 × 8900 = 4005 pound
What is this when you subtract 4
In January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year before what is the percent of decrease in price
The percentage decrease in a price is 37 percent.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, in January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year.
Cost of gas per gallon = 2.05+1.20
= $3.25
Now, Percentage decrease = (Original Price - New Price)/Original Price ×100
= (3.25-2.05)/3.25 ×100
= 1.20/3.25 ×100
= 0.3692×100
= 0.37×100
= 37%
Therefore, the percentage decrease in a price is 37 percent.
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.
A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.
–12,540 ft
12,940 ft
10,740 ft
12,540 ft
As an advertising campaign, a chocolate factory places golden tickets in some of its candy bars, with the promise that a golden ticket is worth a trip through the chocolate factory, and all the chocolate you can eat for life. if the probability of finding a golden ticket is p, find the mean and the variance of the number of candy bars you need to eat to find a ticket
The mean number of candy bars needed to find a golden ticket is 1/p, and the variance is (1-p)/p^2.
Explanation:To find the mean and variance of the number of candy bars you need to eat to find a golden ticket, we need to use the concept of a geometric distribution. The geometric distribution models the number of trials it takes to achieve a success, where each trial has the same probability of success.
The mean of a geometric distribution is given by μ = 1/p, where p is the probability of success. In this case, p represents the probability of finding a golden ticket. Therefore, the mean number of candy bars needed to find a golden ticket is 1/p.
The variance of a geometric distribution is given by σ^2 = (1-p)/p^2. This represents the spread or variability in the distribution. Using the given value of p, you can calculate the variance of the number of candy bars needed to find a golden ticket.
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Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
Answer:
A. [tex](-1,-2)[/tex]
D. [tex](-6,0)[/tex]
E. [tex](-5,-1)[/tex]
Step-by-step explanation:
We have been given an inequality [tex]x+3y\geq -8[/tex]. We are asked to find the ordered pairs that are solution to the given inequality.
Let us check each ordered pair by substituting in the given inequality.
A. [tex](-1,-2)[/tex]
[tex]-1+3(-2)\geq -8[/tex]
[tex]-1-6\geq -8[/tex]
[tex]-7\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-1,-2)[/tex] is a solution for the inequality.
B. [tex](-16,2)[/tex]
[tex]-16+3(2)\geq -8[/tex]
[tex]-16+6\geq -8[/tex]
[tex]-10\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](-16,2)[/tex] is not solution for the inequality.
C. [tex](0,-3)[/tex]
[tex]0+3(-3)\geq -8[/tex]
[tex]0-9\geq -8[/tex]
[tex]-9\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](0,-3)[/tex] is not solution for the inequality.
D. [tex](-6,0)[/tex]
[tex]-6+3(0)\geq -8[/tex]
[tex]-6+0\geq -8[/tex]
[tex]-6\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-6,0)[/tex] is a solution for the inequality.
E. [tex](-5,-1)[/tex]
[tex]-5+3(-1)\geq -8[/tex]
[tex]-5-3\geq -8[/tex]
[tex]-8\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-5,-1)[/tex] is a solution for the inequality.
S the square footage of a housesquare footage of a house discrete or continuous?
The perimeter of a triangle is 105. the lengths of all three sides are represented by three consecutive odd integers. Find the length of the longest side
Determine all values of the constant α for which {1 + αx2, 2 + x + x2, 3 + x} is a basis for p2. (enter your answers as a comma-separated list.)
Sides that match up between two similar figures are called corresponding sides.
Use the diagram of two similar triangles to complete the statements below.
The person's shadow in the smaller triangle corresponds to the _________ in the larger triangle.
A. Height of the Flag Pole
B. Shadow of the Flag Pole
C. Longest side
The longest side of the large triangle corresponds to the ________ side of the small triangle.
A. Shortest
B. Vertical
C. Longest
Corresponding sides in similar figures match up. The person's shadow in the small triangle corresponds to the shadow of the Flag Pole in the large triangle. The longest side of the large triangle corresponds to the Longest side of the small triangle.
Explanation:Corresponding sides in similar figures are the sides that match up.
In the given diagram of two similar triangles, the person's shadow in the smaller triangle corresponds to the shadow of the Flag Pole in the larger triangle.
The longest side of the large triangle corresponds to the Longest side of the small triangle.
Approximately 1 million people immigrated to the U.S. from 1850 to 1900.
True
False