the center of a circe is located at (1,3). The point (0,1) lies on the circle. Find the equation of the circle
Answers
Answer:
\((x-1)^{2}+(y-3)^{2} = 5\)
Step-by-step explanation:
Given the general equation of a circle represented as:
\((x-a)^{2}+(y-b)^{2} = r^{2}\) where:
(a, b) is the centre of the circle and r is the radius
Given the centre located a (1,3), to get the radius we will take the distance between the centre point of the circle the the point that lies on its circumference i.e (0,1).
Using the formula for calculating thee distance between 2 points, we have:
\(r = \sqrt{ (x2-x1)^{2}+(y2-y1)^{2}}\)
x1 = 1, y1 = 3, x2 = 0, y2 = 1
\(r = \sqrt{ (0-1)^{2}+(1-3)^{2}}\\r=\sqrt{1^{2} +(-2)^{2}}\\r=\sqrt{1+4}\\r=\sqrt{5}\)
Substituting this values of the centre and radius of the circle into the general equation of a circle we have:
\((x-1)^{2}+(y-3)^{2} = (\sqrt{5}) ^{2}\\(x-1)^{2}+(y-3)^{2} = 5\)
This gives the required equation of the circle.
Related Questions
When Lisa started at her current job, her employer gave her 2 days of paid
vacation time with a promise of 3 additional paid vacation days for each year
she remains with the company to a maximum of 4 workweeks of paid vacation
time. The equation y=3x+2 (where y represents numbers of vacation days and
x represents number of years) models this relationship.
a. It has been 5 years since Lisa began working for this employer. How many
paid vacation days has she earned?
b. When will she reach the maximum number of paid vacation days allowed?
Answers
a. The equation computed shows that the number of paid vacation days has she earned will be 17 days.
b. The time when she will reach the maximum number of paid vacation days allowed is 6 years.
How to compute the equation?a. The equation computed shows that the number of paid vacation days has she earned will be:
= 2 + 3x
x = 5
= 2 + 3(5)
= 2 + 15
= 17 days.
b. The maximum number of days for a pod vacation will be:
= 4 × 5
= 20 days.
The time when she will reach the maximum number of paid vacation days allowed will be:
20 = 3x + 2
3x = 20 - 2.
3x = 18
x = 18/3
x = 6 years
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What are the properties of the circumcenter of a triangle quizlet?
Answers
For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.
What do you mean by a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
What do you mean by circumcenter of triangle?The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.
Properties of circumcenter of triangle are:
In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle. Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.To learn more about circumcenter visit:
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Please solve the equation
\(5 {}^{2x + 1} - 26(5 {}^{x} ) \: + 5 = 0\)
Answers
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
The formula for log \(x^n\) = n log x
The value of x is 0.043
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
\(5^{2x + 1} - 26(5^x) + 5 = 0\)
\(5^{2x + 1} + 5 = 26(5^x)\)
The formula for log \(x^n\) = n log x
Taking logs on both sides.
log \((5^{2x + 1} + 5)\) = log \(26(5^x)\)
log \(5^{2x + 1}\) + log 5 = log 26 + log \(5^{x}\)
(2x + 1) log 5 + log 5 = 1.41 + x log 5
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
(2x + 1) x 0.69 + 0.69 = 1.41 + 0.69x
1.39x + 0.69 + 0.69 = 1.41 + 0.69x
0.70x = 1.41 - 1.38
x = 0.03 / 0.70
x = 0.043
Thus,
The value of x is 0.043
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Can someone please help me with this problem??
Answers
Answer:
no this is impossible friend
a team of soccer players spend an average of 15 minutes on weight weight training per practice session.how many minutes of weight trainingon an average would they have to complete in 116 practise?
Answers
Answer:
The answer to your problem is, 1,740 minutes
Step-by-step explanation:
The time period of 116 trainings solutions;
The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740
Thus the answer to your problem is, 1,740
Answer:1,740 minutes
Step-by-step:
I first saw that I need to take 15 minutes and x it be the 116 Practices.
So 15 x 116 is 1,740.
1,740 minutes is your answer.
What is the value of the expression below if y=5
Answers
Answer:
27
Step-by-step explanation:
Its a long step by step but trust me
x² + y² +6y-67= 2y-6x; circumference
Answers
The circumference of the circle is approximately 60.27 units.
We have,
To determine the circumference of the circle represented by the equation x² + y² + 6y - 67 = 2y - 6x, we first need to rearrange the equation into the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
Starting with the given equation:
x² + y² + 6y - 67 = 2y - 6x
Rearranging and grouping like terms:
x² + 6x + y² - 6y - 2y = 67
Combining like terms:
x² + 6x + y² - 8y = 67
To complete the square for the x-terms, we need to add (6/2)² = 9 to both sides and to complete the square for the y-terms, we need to add (-8/2)² = 16 to both sides:
x² + 6x + 9 + y² - 8y + 16 = 67 + 9 + 16
Simplifying:
(x + 3)² + (y - 4)² = 92
Now we can see that the equation is in the standard form of a circle equation, where the center of the circle is at the point (-3, 4) and the radius squared is 92.
Thus, the radius is the square root of 92, which is approximately 9.59.
The circumference of a circle is given by the formula C = 2πr, where r is the radius. Substituting the radius value into the formula, we have:
C = 2π(9.59) ≈ 60.27
Therefore,
The circumference of the circle is approximately 60.27 units.
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Twice a number increased by 6 is at least 35.
Answers
The number will be represented by x
Twice a number = 2x
Increased by 6 = +6
2x+6
A tree grew from 4 ft. to 12 ft. in
3 years. What is the percent of
increase?
Answers
Answer:
Percent increase is a percent change that describes an increase in quantity
To determine percent increase we first find the amount of change
It is given:A tree grew from 4ft to 12ft in 3 years .
Amount of change =12-4=8 ft.
We use proportion to find percent increase.
Or ,
Cross multiplying we have:
4 ( percent Increase )= 800
Dividing by 4 we have Percent change = 200
Percent Increase = 200%.
On a map, the distance between two towns is 12 centimeters. If 3 centimeters represents 90 miles, what is the actual distance between the cities in miles?
Answers
Find the first and second derivatives of the function. (Factor your answer completely.)
g(u) = u(2u − 3)^3
g ' (u) = g'' (u) =
Answers
The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.
Given function: `g(u)
= u(2u - 3)^3`
To find the first derivative of the given function, we use the product rule of differentiation.`g(u)
= u(2u - 3)^3`
Differentiating both sides with respect to u, we get:
`g'(u)
= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`
Using the chain rule of differentiation, we have:
`g'(u)
= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`
Simplifying:
`g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`
To find the second derivative, we differentiate the obtained expression for
`g'(u)`:`g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`
Differentiating both sides with respect to u, we get:
`g''(u)
= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`
Using the product rule and chain rule of differentiation, we have:
`g''(u)
= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`
Simplifying:
`g''(u)
= 12(u - 1)(2u - 3)^2`.
The first derivative of the function `g(u)
= u(2u - 3)^3` is `g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)
= 12(u - 1)(2u - 3)^2`.
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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).
Using the product and chain ruleFirst, let's find the first derivative:
g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]
Using the chain rule, we can differentiate (2u - 3)³ and u as follows:
d(u)/du = 1
d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du
= 3(2u - 3)² * 2
Plugging these values back into the equation for g'(u), we have:
g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2
= (2u - 3)³ + 6u(2u - 3)²
Simplifying the expression, we have:
g'(u) = (2u - 3)³ + 6u(2u - 3)²
Now, let's find the second derivative:
g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]
Using the chain rule and product rule, we can differentiate each term:
d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du
= 3(2u - 3)² * 2
d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]
= 6(2u - 3)² + 6u * 2(2u - 3)
The Second derivativePlugging these values back into the equation for g''(u), we have:
g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)
= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)
= 12(2u - 3)² + 12u(2u - 3)
Simplifying the expression further, we have:
g''(u) = 12(2u - 3)² + 12u(2u - 3)
Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).
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(1 pt) Olaf's Ski Rental rents skis, boots, and poles for $ 24 per day. The daily cost per set of skiis is $ 6. It includes maintenance, storage, and overhead. Daily profits depend on daily demand for skis and the number of sets available. Olaf knows that on a typical weekend the daily demand for skis is given in the table.Probability 0.10.0750.6750.0750.075Number of Customers 60 61 62 63 64a) Find the expected number of customers:b) If 60 sets of skis are available, compute Olaf's expected profit:c) If 61 sets of skis are available, compute Olaf's expected profit.d) If 62 sets of skis are available, compute Olaf's expected profite) If 63 sets of skis are available, compute Olaf's expected profitf) If 64 sets of skis are available, compute Olaf's expected profitg) How many sets of skis should Olaf have ready for rental to maximize expected profit?
Answers
a) The expected number of customers is 61.5.
b) Olaf's expected profit for 60 sets of skis is 369.
c) Olaf's expected profit for 61 sets of skis is 378.45.
d) Olaf's expected profit for 62 sets of skis is 387.9.
e) Olaf's expected profit for 63 sets of skis is 397.35.
f) Olaf's expected profit for 64 sets of skis is 406.8.
g) The optimal number of sets of skis Olaf should have ready for rental to maximize expected profit is 62.
a) Find the expected number of customers:
This can be calculated by multiplying the probability of each customer group by the number of customers, and then adding the results together.
For example, 0.10 × 60 = 6, 0.075 × 61 = 4.575, 0.675 × 62 = 41.25, 0.075 × 63 = 4.725, and 0.075 × 64 = 4.8,
which added together results in 61.5.
b) If 60 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 369).
c) If 61 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 378.45).
d) If 62 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 387.9).
e) If 63 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 397.35).
f) If 64 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 406.8).
g) How many sets of skis should Olaf have ready for rental to maximize expected profit?
This is because the highest expected profit (387.9) occurs when 62 sets of skis are available.
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what is $20.00 take away $4.60
Answers
The wheels on Jackson’s dirtbike measures 19 inches in diameter how many revolutions will the wheel make when Jackson rides for 500 feet use 3.14 for pie
Answers
To solve this problem, we need to use the formula:
Number of revolutions = Distance traveled / Circumference of wheel
First, we need to find the circumference of the wheel using the formula: Circumference = diameter x pi
To calculate the number of wheel revolutions for Jackson's dirtbike, we'll need to use the diameter of the wheel and the distance he rides. Here's a step-by-step explanation:
1. Convert the diameter of the wheel (19 inches) to feet: 19 inches × (1 foot / 12 inches) = 1.583 feet
2. Calculate the circumference of the wheel using the diameter and the value of pi (3.14): Circumference = Diameter × pi = 1.583 feet × 3.14 = 4.97062 feet
3. Now, divide the total distance ridden (500 feet) by the circumference of the wheel to find the number of revolutions: Revolutions = Distance / Circumference = 500 feet / 4.97062 feet ≈ 100.59 revolutions
The wheel on Jackson's dirtbike will make approximately 100.59 revolutions when he rides for 500 feet.
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PLEASE HELP!!! <3 I'LL MARK BRAINLEST :)))
Answers
What function is a vertical shift of f(x) = x?
A) g(x) = 3f(x)
B) g(x) = f(x - 3)
C) g(x) = f(x) + 4
D) g(x) = 1/2 f(x)
Answers
Answer:
C) g(x) = f(x) + 4
Step-by-step explanation:
A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A
-anumber would slide the function DOWN instead.
As for the other answers:
A) the 3multiplied in front is a vertical STRETCH.
D) the 1/2 multiplied in front is a vertical shrink (smash)
B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.
Chen subtracted two polynomials as shown. Explain Chen’s error.
P^2+7mp+4-(-2p^2-mp+1)
P^2+2p^2+7mp-mp+4+1
3p^2+6m+5
Answers
The correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
What is a polynomial?
In mathematics, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which involves only the operations of addition, subtraction, and multiplication. Polynomials can have one or more terms, and each term can have one or more variables with non-negative integer exponents.
Chen's error is in the second line where they added the terms -(-2p²-mp+1) without distributing the negative sign to each term inside the bracket. The correct way to subtract a polynomial is to change the sign of each term inside the bracket and then add them to the other polynomial. So, the correct simplification would be:
P²+7mp+4-(-2p²-mp+1)
= P²+7mp+4+2p²+mp-1 (Distributing the negative sign)
= 3p²+8mp+3
Therefore, the correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
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What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
Answers
Answer:
Cumulative Frequency:
The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.
The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.
Step-by-step explanation:
4x-8=12 x= How do I find x? And what is it?
Answers
Answer:
x=-1
Step-by-step explanation:
4x-8=12x
4x=12+8
4x-12=8
-8x=8
-8x/-8= 8/-8
x=-1
Please help! I will mark as brainliest. <3
Answers
8m = w +2
m = (w/8) + 1/4
hope this helps :) (please mark brainliest!)
A social media website had 700,000 followers in 2014. The number y of followers increases by 6% each year.
a. Write an exponential growth function that represents the number of followers t years after 2014.
b. How many people will be following the website in 2019. Round your answer to the nearest thousand.
Answers
b. 2 years later which means t=2, hence, y=700,000*(1+6%)^2=786520
round to the nearest thousand: y=78700
Is 82 inches grater than 5feet and 10 inches
Answers
Answer:
False, 82 inches is not greater than 5 feet and 10 inches
Step-by-step explanation:
1 feet = 12 inches
5x12=60+10=70
82 is greater than 70.
A restaurant sells cheeseburgers to chicken sandwiches in a ratio of 7:2. If the restaurant sells 12 chicken sandwiches one day, how many cheeseburgers does it sell
Answers
Answer:
Food problems are fun :D
Step-by-step explanation:
\(\frac{7}{2}\) = \(\frac{cheeseburgers}{chicken}\)
chicken =12 sooo..
\(\frac{7}{2}\) = \(\frac{x}{12}\)
and solve for x.... that is... get x by itself... "isolate x"
12 * \(\frac{7}{2}\) = x
6 * 7 = x
42 = x
the restaurant sold 42 cheeseburgers :P
1. Consider a consumer with utility function
u(x1, x2) = min ( 4 x1 + x2, x1 + 2 x2)
(a) Draw indifference curves passing through points (2; 2), (1; 2) and (4; 2) (Note:
these points may lie on different indifference curves). Make sure you correctly
determine kink points.
(b) Determine all properties of the preferences that you can deduce from the shape of
indifference curves or utility function. For each claimed property, provide either
a formal proof or a graphical visualization that will clearly indicate that the
claimed property holds.
(c) When X -> R2+, does UMP have a solution when Pk = 0? What property of the
preference relation did you use to get your answer?
(d) Assume that prices are positive. Derive the Walrasian demand of each good. Is the
Walrasian demand always single valued? [Hint: graphically depicting the UMP
can pin down the maximizing bundles. If p1=p2 > 4 what can you say about the
location of the utility-maximizing consumption bundle? What is the location if
4 < p1=p2 < 1=2? What about prices such that p1=p2 < 1=2?]
(e) Let p1 = p2 = 1 and w = $60. Suppose that the consumer receives a $10 voucher
from the government that he can spend only on good 1. Draw the new budget
set of the consumer and calculate the quantity of each good demanded by the
consumer. Does receiving the voucher make consumer better-off?
(f) Suppose instead that the government allows the consumer to choose between a
cash payment of $10 that can be spent on both goods and a $10 voucher that
can be spent on good 1 only. Which one would the consumer choose and why?
Would your answer change if the government's assistance were $30? Explain your
answer.
Answers
(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).
(b) The shape of the indifference curves shows convexity.
(c) The property used to determine this is the non-satiation property of preferences.
(d) The Walrasian demand may not always be single-valued.
(e) Receiving the voucher makes the consumer better-off .
(f) The cash payment allows the consumer to maximize utility by making trade-offs
For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.
For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.
By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.
(b) Properties of the preferences deduced from the shape of indifference curves and utility function:
Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.
Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.
Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.
(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.
(d) Walrasian demand depends on relative prices:
If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.
If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.
If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.
Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.
(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.
(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.
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Help and please explain I don't get khan academy
Answers
Answer:
same y intercept
Step-by-step explanation:
The y intercept is when r = 0
Function 1
p = -3/2 r - 5
Let r = 0
p = 0-5
p = -5
Function 2
When r = 0 p = -5
They both equal -5, so they both have the same y intercept
The perimeter of a rectangle is 72 inches. The ratio of the width to the length is 4:5. What is the width of the rectangle?
Answers
9514 1404 393
Answer:
16 inches
Step-by-step explanation:
The sum of length and width is half the perimeter, so is 36 inches.
The width is 4/(4+5) = 4/9 of the total of length and width, so is ...
(4/9)(36 inches) = 16 inches
The width of the rectangle is 16 inches.
Which real-world scenario involves a right triangle? a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet
Answers
Answer:
The bike path
Step-by-step explanation:
A right triangle has a hypotenuse that can be found using the formula
a^2 + b^2 = c^2 where c is the hypotenuse
The street sign is obviously not correct because a hypotenuse is longer than the sides. The bathroom tile isn't correct either because 6^2 + 8^2 = 100, or 10 after you take the square root. That leaves the bike path.
Checking to make sure:
5^2 + 12^2 = c^2
25 + 144 = √169
√169 = 13
The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
When do three given line segments form a right triangle?Any three line segments can form a right triangle only when they satisfy the Pythagoras Theorem, according to which, the square of the largest side in a right triangle is equal to the sum of the squares of the other two sides, that is, a² = b² + c², where a is the largest side, and b and c are the two other sides.
How to solve the given question?In the question, we are asked to identify from the given scenarios, the case that involves a right triangle.
We know that for three segments to be a right triangle, they need to satisfy the Pythagoras Theorem. So we check every scenario with the theorem:
A triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (12² = 144) ≠ (6² + 8² = 36 + 64 = 100).A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles: This is a right triangle as it satisfies the Pythagoras theorem as (13² = 169) ≠ (12² + 5² = 144 + 25 = 169).A triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (15² = 225) ≠ (10² + 10² = 100 + 100 = 200).A triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as all the sides are equal, so it is an equilateral triangle.∴ The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
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Use Newton's method to find an approximate solution of ln(x)=9−x. Start with x0=10 and find x2. x2 =____ (Do not round until the final answer. Then round to six decimal places as needed.)
Answers
x2 ≈ 17.969712 is the approximate solution of ln(x) = 9 - x using Newton's method with x0 = 10.
To obtain an approximate solution of ln(x) = 9 - x using Newton's method, we start with an initial guess x0 = 10 and iterate until convergence.
The formula for Newton's method is:
x_(n+1) = x_n - f(x_n) / f'(x_n)
First, let's obtain the derivative of f(x) = ln(x) - 9 + x.
The derivative of ln(x) is 1/x, so:
f'(x) = 1/x - 1
Now, we can plug the values into the Newton's method formula to obtain x2:
x1 = x0 - (f(x0) / f'(x0))
= 10 - ((ln(10) - 9 + 10) / (1/10 - 1))
= 10 - ((ln(10) + 1) / (-9/10))
≈ 10 - (2.30259 + 1) / (-0.9)
≈ 10 - 3.30259 / (-0.9)
≈ 10 + 3.669544 / 0.9
≈ 10 + 4.077271
≈ 14.077271
Now, using x1 as the new approximation, we repeat the process:
x2 = x1 - (f(x1) / f'(x1))
= 14.077271 - ((ln(14.077271) - 9 + 14.077271) / (1/14.077271 - 1))
≈ 14.077271 - ((2.64748 + 1) / (-0.93644))
≈ 14.077271 - (3.64748 / -0.93644)
≈ 14.077271 + 3.892441
≈ 17.969712
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x^(2)-8x+15=0
that is x squared -8x+15=0
this is a algebra 2 problem
Answers
x = 5
x = 3
Write a recursive formula for the sequence 8, 10, 12, 14, 16, ... Then find the next term.
Answers
Answer:
answer is b
Step-by-step explanation:
The next term is : an=an-1+2= a1 8; 18
Based on the information given 2 is added ton each sequence
Sequence:
8+2=10
10+2=12
12+2=14
14+2=16
The next term will be:
16+2=8
Inconclusion The next term is an=an-1+2= a1 8; 18
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