The potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.
The potential function can be used to find the maximum value of f by taking the partial derivatives with respect to x and y, setting them equal to zero, and solving for the x and y values that correspond to the maximum. This will give the x and y values that will produce the maximum value of f.
To prove this, we can start by taking the partial derivatives of f(x,y), which are given by:
f_x = 2x + 2y
f_y = 2y + 2x
Therefore, the potential function for f(x,y) is equal to the integral of the partial derivatives with respect to x and y:
∫f_xdx + ∫f_ydy = x^2 + y^2 + 2xy
This shows that the potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.
Learn more about partial derivatives here:
https://brainly.com/question/29652032
#SPJ4
Complete question: What is the potential function for the function f(x, y) = x + y + xy?
Describe and correct the error in writing the polynomial in standard form.
polynomial: 3m^(2)-5m^(5)+m^(4)
Standard form: -5m^(3)+3m^(2)+m^(4)
The error in writing the polynomial 3m²-5m⁵+m⁴ in standard form
as -5m³+3m²+m⁴ is, Power of -5m is 5 not 3 and powers should be in descending order
What are polynomials?The polynomials are the algebraic expressions, which have multiple powers. Polynomials are always written in a form of descending powers.
And based on powers of polynomials, we can categorize polynomials into following categories-
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The polynomial- 3m²-5m⁵+m⁴
The standard form- -5m³+3m²+m⁴
the errors are in standard form of given polynomial,
3m²-5m⁵+m⁴
For converting it into standard form,
So, it can be arranged in descending powers
-5m⁵+m⁴+ 3m²
By comparing it with given standard form
It can be seen that there are two errors in given form
1. Power of -5m is 5 not
2. Variables should be arranged in descending powers
Hence, the correction is power -5 and descending order of powers
To know more polynomials check:
https://brainly.com/question/11536910
#SPJ1
Type 540,000,000 as a floating-point literal using scientific notation with a single digit before and after the decimal point. Check Show answer 4) Type 0.000001 as a floating point literal using scientific notation with a single digit before and after the decimal point. Check Show answer 5) Type 623.596 as a floating point literal using scientific notation with a single digit before and five digits after the decimal point. Check Show answer
Type 540,000,000 as a floating-point literal using scientific notation with a single digit before and after the decimal point is 5.4e8
What is floating-point literal?Numbers with a decimal point or an exponential component are known as floating-point literals. Real literals are one way to describe them. binary literals for floating points. Hexadecimal literals for floating points (C only). An exponent, a decimal point, a fractional part, and an integer part are all components of a floating-point literal. Either decimal form or exponential form can be used to express floating point literals. A floating point number is a full number that has a decimal point and can be positive or negative. In contrast to 91 and 0, floating point numbers include anything like 5, 0, 25, and -103.342. Because the decimal point can "float" to any required position, floating point numbers receive their name.Type 540,000,000 as a floating-point literal using scientific notation with a single digit before and after the decimal point is 5.4e8.
To learn more about floating-point literal refer to:
https://brainly.com/question/28591429
#SPJ4
Please help anyone!!! Thanks so much!
The label of the triangles based on the center are;
A) Incenter
B) Orthocenter
C) Circumcenter
D) Centroid
How to find the center of a triangle?1) The centroid of a triangle is defined as the point in which the three medians of the triangle intersect.
2) The orthocenter of a triangle is defined as the point where all the three altitudes of the triangle cut or intersect each other.
3) The incenter of a triangle is defined as the intersection point of all the three interior angle bisectors of the triangle.
4) The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.
Looking at the given triangles, we can conclude that triangle A shows the incenter, triangle B shows the orthocenter, triangle C shows the circumcenter while triangle D shows the centroid,
Read more about center of triangle at; https://brainly.com/question/7644338
#SPJ1
An employee is reimbursed at a rate of 29 cents per mile. Travels at a 25 miles 3 days a week
The total reimbursement for the employee will be $21.75.
How to calculate the word problem?It is important to note that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this situation, the employee is reimbursed at a rate of 29 cents per mile and he ravels at a 25 miles 3 days a week.
The total reimbursement will be:
= 0.29 × 25 × 3
= $21.75
Learn more about word problem on:
brainly.com/question/21405634
#SPJ1
Complete question
An employee is reimbursed at a rate of 29 cents per mile. Travels at a 25 miles 3 days a week. Find the total reimbursement.
Use inductive reasoning to predict the most probable next number in the list.
4, 7, 1, 4, -2, 1, -5, -2, -8, ?
The next number in the list would be -11.
What is Inductive reasoning?
Inductive reasoning is a form of reasoning that derives a general principle from a set of observations. It entails drawing broad conclusions from specific observations. Deductive reasoning differs from inductive reasoning.
Based on the pattern in the list, the next number in the sequence using inductive reasoning would likely be -11.
The pattern appears to be that each number is the previous number minus 3.
Hence, By using inductive reasoning the next number in the list would be -11.
To know more about Inductive reasoning visit,
https://brainly.com/question/1490615
#SPJ1
There are twenty-four 4 digit whole numbers that use each ofth four digits, 2, 4, 5, and 7 exactly once. Listed in numbericalorder from smallest to largest, the number in the 17th position inthe list is;
a. 4527 b. 5724 c. 5742 d. 7245 e. 7524
A straight concrete sidewalk is to be 3 feet wide, 60 feetlong and 3 inches thick. How many cubic yards of concretemust a contractor order for the sidewalk if concrete must beordered in a whole number of cublic yards?
a. 2 b. 5 c. 12 d.20 e. more than 20
The number in the 17th position in the list is 7425
We start by eliminating some of the options. The smallest possibility for the larger number is if the larger number were twice the smaller number. [tex]$2457\times2=4914$[/tex], since [tex]$2457$[/tex] the least value in the group. In order for the largest possibility to be less than or equal to 7542, the largest number in the set, when multiplied by 2, it must be twice as large as the largest number in the set.This happens to be [tex]$2754\times2=5508$[/tex]. As a result, the number would need to be even and between 4914 and 5508. 5472 and 5274 are the only even numbers in the set and in this range. Both of these numbers are not twice a number in the set, according to a cursory check. The number cannot be four times or higher than any other number in the set because [tex]$2457\times4=9828$[/tex], well past the range of the set. Therefore, the number must be triple another number in the set. The least possibility is [tex]$2457\times3=7371$[/tex]and the greatest is [tex]$2475\times3=7425$[/tex], since any higher number in the set multiplied by 3 would be out of the range of the set. Reviewing, we find that the upper bound does in fact work, so the multiple is [tex]$2475\times3=7425[/tex].
To learn more about the upper bound click here:
brainly.com/question/22965427
#SPJ4
please help me, im nose sure how to do this work
The measure of angle C is 149°.
What is Angle?In mathematics, an angle is a figure made up of two rays that share a terminal and are referred to as the sides of the angle and the vertices of the angle, respectively.
Angles, which are frequently expressed in terms of degrees or radians, are used to quantify the size of turns.
The law of cosines, the law of sines, and the Pythagorean theorem are only a few examples of mathematical equations that use angles, which are a key component of geometry.
When understanding shapes, angles are equally crucial.
The angles within a triangle, a quadrilateral, and a polygon can provide information on the number of sides a shape has in addition to whether or not it is regular.
Angles are also used to calculate the arcs and circles of an object.
From the given figure,
It is a pentagon, sum of sides of a pentagon is 540°
It is clear that,
90 + 90 + 90 + 6x + 1 + (8x - 11) = 540°
⇒ 260 + 14x = 540°
⇒ 14x = 540 - 260
⇒ 14x = 280
⇒ x = 20
∠ C = 8 × 20 - 11 = 160 - 11 = 149°
To Learn more about Angles from the given link
https://brainly.com/question/21865427
#SPJ1
let the random variable xx be the sum of three independent rolls of a fair die. find e[x]e[x] and var(x)var(x).
The expected value of a random variable is the sum of the probabilities of all possible outcomes which is 10.083
In this case, since the random variable is the sum of the three independent rolls of a fair die, the expected value, E[X], is the sum of all the possible outcomes of three die rolls, each multiplied by the probability of 1/6 that each outcome will occur:
E[X] = (1 + 2 + 3 + 4 + 5 + 6) × (1/6)³
= 3.5
The variance of a random variable is the expected value of the squared deviation from the mean. In this case, the variance for X is:
Var(X) = E[X^2] - (E[X])^2
= (1² + 2² + 3² + 4²+ 5² + 6²) × (1/6)³ - (3.5)²
= 10.0833
Learn more about probability:
https://brainly.com/question/24756209
#SPJ4
Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) 3x^2 − y^2 = C.
The orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.
To find this, we can take the derivative of the original equation 3x^2 − y^2 = C with respect to x, which will give us 6x. Then, we can take the negative reciprocal of this derivative, which is -1/6x. This is the slope of the orthogonal trajectories.
We then can use the point-slope form of a line to get y - y1 = -1/6x (x - x1). Since the slope of the orthogonal trajectories is always -1/6x, we can just set the equation y - y1 = -1/6x (x - x1) equal to 0 and solve for x to get x1 = -y1/6.
We can then plug this value back into the point-slope equation to get y - y1 = -1/6(-y1/6) (x - (-y1/6)), which simplifies to y - y1 = y1/6 + x. Now, if we let y1 = -C/3, then we get y - (-C/3) = C/6 + x, which can be rewritten as x^2 + y^2 = C/3.
Therefore, the orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.
Learn more about orthogonal trajectories here:
https://brainly.com/question/28164318
#SPJ4
Can Someone help Me, what is the correct box i have to pick?
After two hours, Cesar and Camden are both 48 kilometers from their homes as per the coordinates.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
given, Cesar and Camden are brothers and live in the same house. Cesar is 80 kilometers away from home and bikes toward home at a rate of 16 kilometers per hour. Camden is 20 kilometers away from home and keeps walking away from home at a rate of 14 kilometers per hour.
Linear Equation for Cesar:
y = 80- 16x
Linear equation for Camden:
Y = 14x + 20
The coordinates (2, 48) is showing the position of both brothers after 2 hours.
(2, 48) this graph represents that both brothers will be met at 48 kilometers if they are walking the same road.
therefore, As per the given coordinates Cesar and Camden are both 48 kilometers away from home after 2 hours.
Learn more about coordinates here:
https://brainly.com/question/20282507
#SPJ1
Please help asap due soon!!
The domain and the range of the composite function are given as follows:
a) Domain: {3, 5, 6, 7}.
b) Range: {0, 9}.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The points on the composite function are given as follows:
g(f(1)) = g(0) = undefined.g(f(3)) = g(7) = 9.g(f(5)) = g(3) = 9.g(f(6)) = g(3) = 9.g(f(7)) = g(2) = 0.The domain is the set of input values, hence it is given by:
{3, 5, 6, 7}.
The range is the set of output values, hence it is given by:
{0, 9}.
More can be learned about the domain and the range of a function at https://brainly.com/question/30248800
#SPJ1
please help due TONIGHT!! GRADED /35
The amount in the bank after 2.5 years will be $241.875.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. Mathematically -
[tex]$A = P (1 + rt)[/tex]
{A} = final amount
{P} = initial principal balance
{r} = annual interest rate
{t} = time (in years)
Given is the amount deposited by Velvet in a bank for 2.5 years at a rate of 3%.
The amount in the bank after 2.5 years will be -
A = 225(1 + 0.03 x 2.5)
A = 225(1 + 0.075)
A = 225 x 1.075
A = 241.875
Therefore, the amount in the bank after 2.5 years will be $241.875.
To solve more questions on simple interest, visit the link below -
https://brainly.com/question/25845758
#SPJ1
Consider the solid S whose base is the triangular region with vertices (0, 0), (1,0), and (0, 1). Cross-sections perpendicular to the x-axis are equilateral triangles.
The solid S is a triangular prism whose base is a triangle with vertices (0, 0), (1,0), and (0, 1). The cross-sections perpendicular to the x-axis are equilateral triangles of the same height.
The solid S is a three-dimensional shape with a triangular base. The base is a triangle with vertices (0, 0), (1,0), and (0, 1). This triangle has sides of length 1, and the angles at each vertex are equal. The equilateral triangles are the cross-sections of the solid perpendicular to the x-axis. This means that each side of each triangle is the same length, and all the angles are equal. Each cross-section has the same height, determined by the height of the solid. The shape of the solid is a triangular prism, with triangular sides that connect the three vertices. This shape has a three-dimensional volume, and the volume can be calculated by multiplying the area of the base by the height of the solid.
Learn more about height here
https://brainly.com/question/10726356
#SPJ4
A certain forest covers an area of 3400 km2. Suppose that each year this area decreases by 5.5% . What will the area be after 7 years? Use the calculator provided and round your answer to the nearest square kilometer.
The area that the forest would occupy after 7 years is 2288 km²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let y represent area of the forest after x years.
y = abˣ
a is the initial value and b is the multiplication factor.
A certain forest covers an area of 3400 km², hence a = 3400 km². The area decreases by 5.5%, hence b = 100% - 5.5% = 94.5%. Hence:
y = 3400(0.945)ˣ
After 7 years:
y = 3400(0.945)⁷ = 2288 km²
The area of the forest after 7 years is 2288 km²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
If a persons eye level is 8 m above sea level and she can see de kilometers to the horizon the D equals 3.6 radical H suppose the person can see 13.5 km to the horizon what is the height of her eye level above the sea
The height of her eye level above the sea is 45.6 km
How to determine the height?Height talks about how high the persons eye is above te sea level.
The equation so formed is
3.6√h = 13.5 Kilometers
Making √h the subject of the relation we have
√h = 3.75 Kilometers
Making h the subject by squaring both sides of the equation we have
h = √3.75 Kilometers above sea level
h = 1.9 Kilometers above sea level rounded
Taking these various steps, the height of the eye is 1.9 kilometers above sea level.
Learn more about distance on https://brainly.com/question/15172156
#SPJ1
Correct question:
If a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d = 3.6√h . Suppose the person can see 13..5 kilometers to the horizon
Use the x-cube tool to graph the x-cube function
The graph of the y = x³ function is given by the image given at the end of the answer.
How to graph the function?The function for this problem is defined as follows:
y = x³.
The domain and the range of the function are given as follows:
Domain: all real values, as the function has no restrictions regarding the input.Output: all real values.Some points on the graph of the function are given as follows:
(-3, -27), as when x = 3, y = (-3)³ = -27.(-2,-8).(-1,-1).(0,0).(1,1).(2,8).(3,27).More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
A rancher has 260 meters of fence with which to endose three sides of a rectangular meadow (the fourth side is a river and will not require fencing). Find the dimensions of the meadow with the largest possible area (For the purpose of thls problem , the width will be the smaller dimenslon (needing two sides); the length with be the longer dimension (needing one side) ) length ..... meters width ...... meters What is the largest area possible for this meadow? area meters-squared Enter your answers as numbers. If necessary; round to the nearest hundredths
The maximum area of rectangle is 8450 m².
Given that there is fence only on 3 sides and one length side have river flowing trough it
so the perimeter of the plot is given by:
l + w + w
=> 2w+l
where w is width and l is length of the plot
given , perimeter = 260
=> 2w+l = 260 ---- (i)
area of the plot is = l*w
putting the value of w from equation (i) we get
(260-2w)*w
=> 260w-2w²
so A = 260w-2w²
To maximise A we have dA/dw=0
=> d(260w-2w²)/dw
=> 260-4w
so 260 - 4w=0
=> 4w = 260
=> w = 65
l = 260 -2 w
=> 260 -2 *65
=> 260-130
=> 130
so Maximum area of the rectangle = 130*65 = 8450
To know more about area of the rectangle click on below link:
https://brainly.com/question/20693059#
#SPJ4
distinguishing between linear growth and exponential growth identify the type of function graphed to the right. linear exponential other graph
To distinguish between linear growth and exponential growth, you need to look at the equation of the function and the shape of the graph.
Linear functions have a constant rate of change, meaning that the slope of the line is always the same. The equation for a linear function is y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
Exponential functions, on the other hand, have a variable rate of change, meaning that the slope of the line changes as the x-value increases. The equation for an exponential function is y = ab^x, where a and b are constants. The graph of an exponential function is a curve that increases or decreases rapidly.
If the graph is a straight line it is linear, if it is curved and increases or decreases rapidly then it is exponential, otherwise, it would be considered as other.
You can learn more about linear functions at
https://brainly.com/question/2248255
#SPJ4
solve x to the power of 2 divided by 3 end exponent minus 5 x to the power of 1 divided by 3 end exponent minus 6 equals 0?
The roots of the given quadratic equation [tex]\frac{x^{2} }{3} - \frac{5x}{3} - 6= 0[/tex] after solving are [tex]\alpha = \frac{5 + 47i }{2}[/tex] and [tex]\beta = \frac{5 - 47i }{2}[/tex] .
Given,
Quadratic Equation is [tex]\frac{x^{2} }{3} - \frac{5x}{3} - 6= 0[/tex]
Multiply L.H.S. and R.H.S. by 3, and we get:
[tex]x^{2} -5x - 18 = 0[/tex]
Here, [tex]a= 1, b= -5 ,c= -18[/tex]
Let's find out the determinant,
[tex]D = b^{2} - 4ac[/tex]
[tex]D= (-5)^{2} - 4(1)(-18)\\D = 25 - 72\\D = -47\\[/tex]
Therefore, the roots of the quadratic equation will be :
[tex]\alpha = \frac{-b + \sqrt{D} }{2a}[/tex] and [tex]\beta= \frac{-b - \sqrt{D} }{2a}[/tex]
Now, Substitute the value of [tex]a,b,c[/tex]
[tex]\alpha = \frac{5 + 47i }{2}[/tex] and [tex]\beta = \frac{5 - 47i }{2}[/tex]
Learn more about Quadratic Equation:
https://brainly.com/question/17177510
#SPJ4
write the simplest polynomial function with the given zeros (use the math equation editor) and write out your answer in box below.
simplest polynomial function with zeroes -2 and 3 is expanded form is f(x) = [tex]x^2 - x - 6[/tex].
To write a polynomial function with given zeros, we can use the factorization method. The zeros of a polynomial function are the solutions of the equation f(x) = 0. So, if we know the zeros of a polynomial function, we can use them to write the function in factored form.
For example, if the zeros of the polynomial function are -2 and 3, we can write the function as:
f(x) = (x + 2)(x - 3)
This function can be expanded into:
f(x) = [tex]x^2 - x - 6[/tex]
It's important to notice that the degree of the polynomial function is determined by the highest exponent of the variable in the equation, in this case 2.
It's also important to notice that the zeroes of the function are -2 and 3, as when you substitute them in the equation, the result is zero.
Learn more about polynomial function:
https://brainly.com/question/17333460
#SPJ4
The complete question is:
What is the simplest polynomial function with zeroes -2 and 3? Write the equation in the expanded form.
Class members that should be public are:I. ConstructorsII. Instance VariablesIII. Accessors/ MutatorsIV. Methods the class uses for itself, but the user does not needV. Methods the user needs to manipulate the objects of the classa. I, II, IVb. I, II, IIIc. I, III, Vd. I, II, III, V
Constructors, instance variables, accessors/mutators, and methods the user needs to manipulate the number of objects of the class should all be public.
Public members of a class are those that are visible and accessible to users of the class. These include constructors, instance variables, accessors/mutators, and methods that the user needs to manipulate the objects of the class. These members should be designed and implemented carefully, since they form the interface between the class and its users. Properly designed public members can ensure that the class is easy to use and understand. Making the wrong members public can lead to confusion, bugs, and difficult-to-maintain code.
Constructors, instance variables, accessors/mutators, and methods the user needs to manipulate the number of objects of the class should all be public.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
The figure below is a net for a triangular prism. Side a = 46inches, side b = 12 inches, side c = 32inches, and altitude d = 22inches. What is the surface area of this figure?
A. 1,948square inches
B. 2,668square inches
C. 2,884 square inches
D. 2,332 square inches
This figure's surface measures 2332 square inches.
What is Surface area?The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.
Given, The figure below is a net for a triangular prism. Side a = 46inches, side b = 12 inches, side c = 32inches, and altitude d = 22inches
From the figure,
The surface area of triangle = 1/2* d * a + 1/2* d * a
The surface area of the rectangle = b *a +2 * c * b
Thus the complete surface area of Shape = The surface area of the rectangle + The surface area of a triangle
Total surface area =d*a + b*a + 2*c*b
Total surface area = 22 * 46 + 12 * 46 + 2 * 32 * 12
Total surface area = 2332
Therefore, The surface area of this figure is 2332 square inches.
Learn more about the Surface area here:
https://brainly.com/question/29298005
#SPJ1
Complete question:
6
5
Compared to Jenny, Sally is as tall and May is
6
7
How many times taller is Sally than May?
as tall.
0-
[3]
Mark it
locating a number's component. Doing percentage and decimal calculations proportional relationships.So, 7/6 times taller is Sally than May.
Why is it important to use fractions?
Identifying the portion of a number is one application for fractions. figuring out percentages and decimals. Verhältnis und Proportion.
Learning more complex mathematical concepts requires a strong foundation in fractions. The greatest way to introduce algebra is through fractions because they are a student's initial exposure to mathematical abstraction.
Let's call Jenny's height H. Next, we have this:
Sally's height is equal to 7/8*H.
May's height is equal to 6/8"H.
We only need to divide Sally's height by May's height to compare their heights:
Sally's height divided by May's height equals (7/8)*H / (6/8)*H.
= (7/8) / (6/8) = (7/8) * (8/6) = 7/6
Sally therefore outranks May by 7/6.
Therefore, the answer is 7/6.
To learn more about fractions refer to:
brainly.com/question/78672
#SPJ1
Calculate and record the net income or net loss. Label the amount in the Account Title column. Total the Income Statement and Balance Sheet columns.
Net income is the amount of accounting profit a business has left over after covering all of its expenses. Sales revenue is multiplied by COGS, SG&A, depreciation and amortisation, interest expenditure, taxes, and any other expenses to arrive at net income.
What is meant by net income?Net income is the amount that may still be left over from your paycheck after taxes and other withholdings. Net income for a company is the money that is still available after covering all operational costs, administrative expenses, cost of products sold, taxes, insurance, and other business charges. The COGS of a company in the manufacturing sector, for instance, would probably be listed, whereas the COGS of a company in the service sector might be listed under operational expenses. Net Income = Total Revenue – Total Expenses is the general formula for calculating net income. Employees' gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.To learn more about net income, refer to:
https://brainly.com/question/15530787
#SPJ4
find the legth of the radius of a circle where the endpoints of the diameter are located at b(4,-3) and at d(-2,5)
The length of a circle's radius where the diameter's endpoints are at (2,4) and (-3,-1) is 5/2.
What is meant by radius?The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulas involving circles. A circle's radius can also be used to calculate its surface area and circumference. Circle circumference equals 2π (Radius). A radius is a segment of a line having one terminus in the centre and the other on the circle. Radius = Circular Diameter: The diameter of a circle is defined as the length of a line segment with its endpoints on the circle and passing through its centre. Radius 2 = diameter.Then,
[tex]$D=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
As a result, the diameter's end points are (2,4) and (-3,-1)
[tex]d=\sqrt{(-3-2)^2+(-1-4)^2}[/tex]
[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]
[tex]\mathrm{d}=\sqrt{25+25}=\sqrt{50}=5 \sqrt{2}[/tex]
[tex]$\text { We know Radius } & =\frac{\text { Diameter }}{2} \\[/tex]
[tex]$& =\frac{5 \sqrt{2}}{2}=\frac{5}{\sqrt{2}}[/tex]
Hence, the radius of given circle is [tex]$} \Rightarrow \frac{5}{\sqrt{2}}[/tex]
To learn more about radius, refer to:
https://brainly.com/question/26215003
#SPJ4
At a run festival 7/12 of the runners are women. If there are 1440 runners, how many are women
According to the given expression There will be 910 women among the 1,560 runners.
What does "expression" mean in mathematics?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.
How does a number convey itself?Using mathematical operations like addition, subtraction, multiplication, and division, a combination of numbers and integers can be expressed numerically in mathematics.
According to the given information:I'm looking for 7/12 of 1560. I really do mean, "Divide 1560 among 12 groups and count how many there are in each category overall."
1560 divided into 12 groups.
1560/12
=130.
There are 130 people in each group. We multiply to determine how many there are in the seven groupings.
130/7
=910
Among the 1,560 runners, 910 of them will be female.
To know more about expression visit:
https://brainly.com/question/16804733
#SPJ1
Find the derivative of f(x) = 8sqrt(10x^4+x^2-1) ⁹
Derivative of f(x) = 8√(10x⁴+x²-1)⁹ is (1440x³ + 72x)(10x⁴ + x² - [tex]1)^{(7/2)}[/tex].
What is Derivative?The derivative is what calculus is all about. The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.
Calculus defines a derivative as the rate at which one quantity, y, changes in relation to another, x. The differential coefficient of y with respect to x is another name for it. Finding a function's derivative is the process of differentiation.
The typical representation of a function's derivative is d/dx (f(x)) (or) df/dx (or) Df(x) (or) f' (x). Let's examine the technical definition of a derivative. Two points on a function f(x) curve are (x, f(x)) and ((x + h), f(x + h)), respectively. If so, [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h] will be the slope of the secant line across these locations. The second point overlaps the first point in the image below when the distance between two points is almost equal to 0 (i.e., when h approaches 0), and the secant line turns into the tangent line.
Given that;
f(x) = 8√(10x⁴+x²-1)⁹
So, First derivatives is ;
[tex]\begin{aligned}& \frac{d}{d x}[f(x)]=f^{\prime}(x) \\& \frac{d}{d x}\left[8\left(10 x^4+x^2-1\right)^{\frac{9}{2}}\right] \\& =8 \cdot \frac{d}{d x}\left[\left(10 x^4+x^2-1\right)^{\frac{9}{2}}\right] \\& \left.=8 \cdot \frac{9}{2}\left(10 x^4+x^2-1\right)^{\left(\frac{9}{2}\right.}-1\right) \cdot \frac{d}{d x}\left[10 x^4+x^2-1\right] \\\end{aligned}[/tex]
[tex]\begin{aligned} & =36\left(10 \cdot \frac{d}{d x}\left[x^4\right]+\frac{d}{d x}\left[x^2\right]+\frac{d}{d x}[-1]\right)\left(10 x^4+x^2-1\right)^{\frac{7}{2}} \\& =36\left(10 \cdot 4 x^3+2 x+0\right)\left(10 x^4+x^2-1\right)^{\frac{7}{2}} \\& \left.=36\left(40 x^3+2 x\right)\left(10 x^4\right)+x^2-1\right)^{\frac{7}{2}} \\& =\left(1440 x^3+72 x\right)\left(10 x^4+x^2-1\right)^{\frac{7}{2}}\\\end{aligned}[/tex]
So, the Derivative of f(x) = 8√(10x⁴+x²-1)⁹ is (1440x³ + 72x)(10x⁴ + x² - [tex]1)^{(7/2)}[/tex].
Learn more about Derivatives click here:
brainly.com/question/28376218
#SPJ1
What is the quotient of 88and -9
A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold? please show the steps to solve THANK YOU!!!!
Answer:
5 oranges and 10 apples were sold
Step-by-step explanation:
Let x be the number of oranges sold and y be the number of apples sold
Since 15 fruits were sold in all we get the following equation
x + y = 15 ....................[1]
Each orange costs $1 so if x oranges were sold that would fetch x dollars in sales = x dollars in sales
Each apple costs $2 so if y apples were sold, that would result in 2y dollars in sales
Total sales in $ = x + 2y and we know this is $25 so we get the second equation as
x + 2y = 25 ..................[2]
Look at the two equations. The coefficient of the x term is the same. We can eliminate the x term by subtracting equation [1] from equation [2] as follows:
x + 2y = 25
-
x + y = 15
-----------------
y = 10
(2y - y = y and 25-15 = 10)
Now that we know y = 10, we can use equation [1] to find x
x + 10 = 15
which makes x = 5
ANSWER
5 oranges and 10 apples were sold
Consider an election with 521 votes
a) If there are 5 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method?
The smallest number of first-place votes a candidate could win with under the Plurality method is 105.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, an election with 521 votes.
considering an election with 521 votes and 5 candidates up for the election
Dividing the votes amongst 5 candidates
= 521/5 = 104.2
So, the least number of first-place votes needed by a candidate using the plurality method would be = 105 votes
104.2+ 104.2 + 104.2 + 104.2 + 104.2 = 521 (Dividing the votes equally)
104+104+104+104+104= 520
Thus, the remaining vote = 521 - 520 = 1
Least first-place vote = 104+1= 105 votes
Therefore, the smallest number of first-place votes a candidate could win with under the Plurality method is 105.
To learn more about the division visit:
https://brainly.com/question/1575906.
#SPJ1
