the answer is: f · dr = -30
To find f · dr for the line c from (3, 2, -2) to (6, 1, 7), we first need to parametrize the line in terms of a vector function r(t). We can do this as follows:
r(t) = <3, 2, -2> + t<3, -1, 9>
This gives us a vector function that describes all the points on the line c as t varies.
Next, we need to calculate f · dr for this line. We can use the formula:
f · dr = ∫c f · dr
where the integral is taken over the line c. We can evaluate this integral by substituting r(t) for dr and evaluating the dot product:
f · dr = ∫c f · dr = ∫[3,6] f(r(t)) · r'(t) dt
where [3,6] is the interval of values for t that correspond to the endpoints of the line c. We can evaluate the dot product f(r(t)) · r'(t) as follows:
f(r(t)) · r'(t) = <5y, 2, -1> · <3, -1, 9>
= 15y - 2 - 9
= 15y - 11
where we used the given expression for f and the derivative of r(t), which is r'(t) = <3, -1, 9>.
Plugging this dot product back into the integral, we get:
f · dr = ∫[3,6] f(r(t)) · r'(t) dt
= ∫[3,6] (15y - 11) dt
To evaluate this integral, we need to express y in terms of t. We can do this by using the equation for the y-component of r(t):
y = 2 - t/3
Substituting this into the integral, we get:
f · dr = ∫[3,6] (15(2 - t/3) - 11) dt
= ∫[3,6] (19 - 5t) dt
= [(19t - 5t^2/2)]|[3,6]
= (57/2 - 117/2)
= -30
Therefore, the answer is:
f · dr = -30
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Which of the following is zero of the polynomial x5-x3+2x-2? options 1,-1,2,-2
The zeroes of the polynomial x5-x3+2x-2 are 0.618033988749895 and -1.618033988749895.
The given polynomial is x5-x3+2x-2. To find the zeroes of the polynomial, it should be set equal to zero.
Thus, x5-x3+2x-2 = 0
To solve this equation, the quadratic formula can be used. The quadratic formula is x = [-b ± √(b2 - 4ac)]/2a.
In this equation, a = 1, b = -1 and c = -2.
Thus, x = [-(-1) ± √((-1)2 - 4(1)(-2))]/2(1)
x = [1 ± √5]/2
The zeroes of the equation are
x = 0.618033988749895 and x = -1.618033988749895
Therefore, the zeroes of the polynomial x5-x3+2x-2 are 0.618033988749895 and -1.618033988749895.
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f(x)= 2x^2+3x-5
f(f(2))
Answer:
[tex]f(f(2))=184[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+3x-5\\f(2)=2(2)^2+3(2)-5=2(4)+6-5=8+1=9\\f(f(2))=f(9)=2(9)^2+3(9)-5=2(81)+27-5=162+22=184[/tex]
Solve for d. You can choose to show your work below or solve on paper.
Answer:
-4/5
Step-by-step explanation:
Just simply use your knowledge to eliminate the d
Solve the system of equations by graphing
Because the first equation is already solved for y we can substitute 3x−5 for y in the second equation and solve for x:
y=x−3 becomes:
3x−5=x−3
3x−5+5−x=x−3+5−x
3x−x−5+5=x−x−3+5
3x−1x−0=0+2
2x=2
2x/2=2/2
2x/2=1
x=1
Substitute
1 for x in the first equation and calculate y:
y=3x−5 becomes:
y=(3×1)−5
y=3−5
y=−2
The solution is x=1 and y=−2 or (1, -2)
What is graphical representation?Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.To learn more about anomalies refer to:
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Implicit Differentiation Homework Date Period Problems 1 - 8, Find Dy/Dx By Implicit Differentiation. 1. 8x^2 + Y^2 = 10
The solution to the implicit differentiation problem is dy/dx = -16x/2y.
To solve this problem, we must use implicit differentiation. This means that we must differentiate both sides of the equation with respect to the independent variable, x. We can do this by taking the derivative of both sides of the equation.
The derivative of 8x^2 is 16x and the derivative of y^2 is 2y dy/dx.
Therefore, the equation becomes: 16x + 2y dy/dx = 0
We can then solve for dy/dx by dividing both sides by 2y, which gives us dy/dx = -16x/2y.
Therefore, the solution to the implicit differentiation problem is dy/dx = -16x/2y.
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it takes 10 identical pieces to form a circular track for a toy race car. if the width of the track is 3.5 inches then how much longer is the outside arc of each piece compared to the inside arc?
The length of the outside arc of each piece compared to the inside arc is 5.57 inches
How to calculate the circumference of a circleLength of outer track = sum of length of 10 pieces = circumference of the outer circle
if R is the Radius of outer circle then...
Circumference of the outer track = 2pi*R
Similarly the circumference of the inner track (with radius r) = 2pi*r
length of each outer piece is 3.5 inch more than length of inner piece
So total outer length is 10*3.5 =35 inches more than the inner length.
=> Outer Circumference - Inner Circumference = 35 inches
=> 2pi*R - 2pi*r = 35
=> 2pi(R -r) = 35
=> R-r = 35/2pi = 5.57 inches
=> R-r = Width of the track = 5.57 inches
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15% of $9 is… can someone please help with the solution
Answer:
$1.35
Step-by-step explanation:
15% of $9
= [tex]\frac{15}{100}[/tex] × $9
= 0.15 × $9
= $1.35
In 2006, the U.S. Population (or persons) per square mile of land area was 85. In 2014, the persons per square mile was 89.48.
a. Write an equation describing the relationship between year and persons per square mile. Use ordered pairs of the form (years past 2006, persons per square mile)
b. Use equation on question 7 to predict the persons per square mile in 2023. Round to the nearest whole person.
In 2006 we have 93.3 people per sq mile .
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
In order to determine the equation for this relationship, we need to first find the slope between these two values. There are two ways to do this:
1. Create a graph
*Create a graph with the x-axis representing the years past 2000 (so 2000 would be 0 and 2003 would be 3 and so on)
*Use the fact that slope=rise/run to get slope=2.7/3 (because we rise 87-84.3=2.7 and run 3 (from 2000 to 2003), and 2.7/3=27/30=9/10
*Plug this and the point (0, 84.3) into the formula y=mx+b to find the y-intercept of your equation
--> 84.3=(9/10)(0)+b --> b=84.3
So, your equation can be written now as y=(9/10)x+84.3
[Note: To check, if you plug in 3 you should get 87, and you do, so it works!]
2. Use the slope formula
Alternatively, you could have did slope=(y2-y1)/(x2-x1)=(87-84.3)/(3-0)=2.7/3=9/10
The process here would be the same as above
b) Here, just plug 10 into the equation above (since 10 is the number of years 2010 is after 2000, or 2010-2000=10). Doing this we get:
y=(9/10)(10)+84.3=9+84.3=93.3
So, in 2006 we have 93.3 people per sq mile
Therefore, In 2006 we have 93.3 people per sq mile .
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A touchdown in football count for 6 point. If n tand for the number of touchdown, which equation repreent how many point n touchdown are worth
A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]
Given that,
A touchdown in football count for 6 point.
If n and for the number of touchdown,
We are given that a touchdown in football counts for 6 points.
We have to find an equation which represents number of points in n touchdown.
In order to find the number of points in n touchdown we will multiply 6 with n.
Number of points in one touchdown y = 6
Number of points in n touchdown y = [tex]6*n[/tex]
Number of points in n touchdown y = [tex]6n[/tex]
Therefore,
A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]
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Which equation has infinitely many solutions?
• A 3x - 2 - 2 - 3х
B. x+3x+6=6+4x
C 2x+7x-5=-9x+5
D 4x-5x+3= -5x + 4x -3
Answer: i think its A
Answer:
B. x+3x+6=6+4xStep-by-step explanation:
B)
x+3x+6=6+4xx+3x+6-6=6+4x-6x+3x=4x4x=4xSince both sides are equal, there are infinitely many solutions.
-Hope this helps!
Select the correct answer. The product of two numbers, x and x + 3 , is 550. Which equation could be solved to find the value of the smaller number, x? A. x 2 + 3 = 550 B. 3 x + 3 = 550 C. x 2 + 3 x = 550 D.
The product of two numbers, x and x + 3 , is 550, then x²+3x = 550: Option C
What is a quadratic equation?You should be aware that a quadratic equation is an equation whose highest power of its variable is two. A quadratic equation in the form x can be written as ax²+bx+c = 0 where a, b and c are positive or negative integers
The given expression is
The product of two numbers, x and x + 3 , is 550
this implies x(x+3) = 550
Opening the brackets to get
x²+3x = 550
This in conclusion means that the best option is x²+3x = 550
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Use the function f(x) = 4x2 − 7x − 15 to answer the questions.
Part A: Completely factor f(x).
Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Part C: Describe the end behavior of the graph of f(x). Explain.
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
a) The factored function is given as follows: f(x) = 4(x + 1.25)(x - 3).
b) The x-intercepts are given as follows: x = -1.25 and x = 3.
c) The end behavior is given as follows: Due to the positive leading coefficient, the function increases to left and right.
d) The graph of the function is given by the image presented at the end of the answer.
How to graph the function?The quadratic function for this problem is defined as follows:
f(x) = 4x² - 7x - 15.
The coefficients are given as follows:
a = 4, b = -7, c = -15.
Inserting these coefficients into a quadratic function calculator, the roots, which are the x-intercepts, are given as follows:
x = -1.25 and x = 3.
Considering the leading coefficient of 4 and the linear factors of the function, the factored function is given as follows:
f(x) = 4(x + 1.25)(x - 3).
The x-coordinate of the vertex is given as follows:
x = -b/2a = 7/8.
Hence the coordinates of the vertex are:
(7/8, f(7/8)).
Then the graph is made considering:
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What is a 30% residual?
A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.
What is residual?In statistical or machine learning models, the differences between actual and expected data values are referred to as residuals.
They act as a diagnostic instrument for assessing the caliber of a model. They are also known as errors.
The primary column, Inflation, of the table below provides details on US inflation for each month of 2017. Forecasts from a model that seeks to predict the rate of inflation are shown in the Predicted column.
Following are the calculations for the residuals: Residual is equal to predicted inflation.
The Residual column contains them.
The model predicted 1.8% for the data for January 2017, while the actual inflation rate was only 0.5%, leaving a residual of -1.3%.
Hence, A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.
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Question 6 of 25
Which system of inequalities is shown?
A. y> x
y> 2
OB. y> x
y<2
OC. y
y<2
OD. y
y> 2
5
9
5
Click here for long description
Answer:
Step-by-step explanation:
It is not possible to determine which system of inequalities is shown without a graph or more information about the inequalities. Without a graph, it is not possible to determine the region that is being represented by the system of inequalities. Additionally, without more information about the inequalities, it is not possible to determine which inequality is the upper bound and which is the lower bound. Therefore, the answer is "not enough information."
The solution of the system of inequalities is,
y > x and y > 2
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The graph of inequality is shown.
Now, We get;
The first graph is, y > x
And, The second graph is, y > 2
Thus, The solution of the system of inequalities is,
y > x and y > 2
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How do you dilate a linear equation?
Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation. How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r. Every time, k will have a value larger than 0.
What is the rule to dilate?A transformation in geometry is an action that shifts, rotates, or modifies an existing shape to produce a brand-new shape.
Increasing or decreasing the size of a figure (referred to as the preimage) to produce a new figure is a type of transformation termed dilation.
How much the dilation image will enlarge or reduce in size relative to the preimage is determined by the scale factor, r.
A two-scale factor dilation has been applied to Image A in relation to its origin. It is important to note that every coordinate point in the dilation picture is twofold that of the preimage.
The notation shown below can be used to represent a dilation with a scale factor close to the origin:
Dk (x , y ) = (kx, ky)
there will always be a number greater than 0 in the equation.
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4/5*A=920 aswer please
Taking the subject A and solving the equation, the resultant value of A will be 1,150.
What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, we have the equation:
4/5*A=920
Now, calculate the equation taking A as the subject:
4/5 * A = 920
4A = 920 * 5
4A = 4,600
A = 4,600/4
A = 1,150
Therefore, taking the subject A and solving the equation, the resultant value of A will be 1,150.
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6x - 12y + 24=0
(Turning it into slop- intercept form)
In slope-intercept form, the equation of a line is represented as y = mx + b. So the equation in slope-intercept form is y = (1/2)x + 2
What is slope?Slope is a measure of the steepness of a line or a linear function. It is often represented by the letter "m" and is calculated as the ratio of the change in the y-coordinates of two points divided by the change in the x-coordinates of those same two points. In other words, it is the ratio of the "rise" to the "run" of the line. The slope of a line can be positive, negative, zero, or undefined.
What is slope intercept form?The slope-intercept form of a linear equation is a way to represent the equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, and it is represented by the value of b. This form of the equation is useful because it allows us to easily identify the slope and y-intercept of a line, as well as to graph the line using these values.
The first step is to add 12y to both sides:
6x - 12y + 12y + 24 = 12y
6x + 24 = 12y
The next step is to divide both sides by 12 to get y by itself on one side:
y = (6/12)x + (24/12)
y = (1/2)x + 2
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Probability of being a senior or white
The probability of being a senior citizen and white is: (0.63)(0.3) = 0.189.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.
Given that the probability of identifying white is 0.63.
Then the probability of not white is:
1 - 0.63 = 0.37
Given that the probability of being a senior citizen is 0.3.
Then the probability of not a senior citizen is:
1-0.3 = 0.7
Hence, the probability of being a senior citizen and white is:
(0.63)(0.3) = 0.189
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Compared to lat yer, the population of Boom Town ha increaed by 25%. The population i now 6,000. What wa the population lat year
Compare to last year the population of the Boom town increased by 25% which is equal to 6000 then population of the last year is 4800.
As given in the question,
Present year population of the Boom town is equal to 6000
Let us consider 'y' be the population of Boom town last year.
Percentage of increase in population = 25%
Equation formed for the given condition is :
y + 25%y = 6000
⇒ y + (25/100)y = 6000
⇒ (100 + 25 / 100 )y = 6000
⇒ y = ( 600,000 / 125 )
⇒ y = 4,800 population of Boom town last.
Therefore, last year population of the Boom town is equal to 4,800.
The above question is incomplete, the complete question is:
Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?
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Use the drawing tools to graph the solution to this system of inequalities
y> 2x + 4
x+y≤6
A collection of two or more inequalities in one or more variables is known as a system of inequalities.
What does it mean to solve a system of inequalities?Two or more inequalities in one or more variables make up a system of inequalities. When a problem calls for a variety of answers and those answers are constrained by multiple factors, systems of inequalities are used.
The intersection region of every solution in the system of inequalities is the system's solution.
Comparable to solving a system of linear equations, solving a system of linear inequalities involves locating the point (or points) of intersection, however this is not the case with inequalities. Instead, the area that fulfils each linear inequality will make up the solution set.
An inequality system's graph shows how the inequalities are resolved.
The system of inequality needs to be fixed by [tex]$y > \frac{2}{3}$ \\ and $x \leq \frac{16}{3}$[/tex]
Following is a description of the inequality system:
[tex]$y > 2 x+4$$x+y \leq 6$[/tex]
The charts for these are in the attached.
[tex]$y > 2 x+4$ and $x+y \leq 6$[/tex]
The graph shows us:
[tex]$y > \frac{2}{3}$$x \leq \frac{16}{3}$[/tex]
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how many radians are there in 3 circles
Answer:
There are 6
Step-by-step explanation:
There are two within each circle.
Answer: 18.84 radians
Step-by-step explanation:
What circles are drawn on the score sheet at the end of a set?
In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
Following are the circles that are drawn at the end of a set on the NCAA women's volleyball scorecard:
who has the first opportunity to serve:
Based on our existing knowledge of how NCAA Women's Volleyball functions, we can see that each period is divided into sets and that there is a scorecard where each team's points are given. In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
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Aerial has 0.60$ worth of nickles and dimes he has a total of 7 nickles and dimes altogether
Find the coordiantes of the vertices for the figure after the given transformation
Dilation of 2.
Answer:
[tex]I'(-2,-4), J'(-4,4), K'(4,4)[/tex]
Step-by-step explanation:
Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].
How do you represent 2 is greater than 1?
To represent 2 is greater than 1 in math is presented as 2 > 1.
How to represent a comparative between to two number in math?In math, there is a certain symbol to describe a certain condition of comparison. Here some of them:
a < b. The symbol of < represent the number on the left side has lower value than the right side. Example: 3 < 4 which is mean 3 has lower value than 4. a = b . The = symbol represent the number on the left side is equal with the right side. Example: 6 = 3 x 2 which is mean 6 has equal value to 3 x 2.a ≤ b. The ≤ symbol represent the number on the left is equal or smaller than the right side. Example 6 = 3 x 2y where y > 0.Learn more about math symbol here
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What is 2 with an exponent of 1?
The 2 with an exponent of 1 is represented as 2¹ and the value of 2 with an exponent of 1 is 2 .
When the number "a" is multiplied by itself "n" number of times , then it can be represented in Exponential Form as "aⁿ " , the number "a" is called the base and the number "n" is called the exponent or power .
we have to find the value of 2 with an exponent of 1 ;
So , it is represented as ⇒ 2¹ ;
and the value of this exponential expression is ⇒ 2 .
Therefore , the value of 2 with an exponent of 1 is 2 .
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Five friends together earned $165 raking leaves. They divided the money evenly among the 5 of them. Maria earned another $10 walking a neighbor's dog. How much money did Maria earn in all?Enter your answer in the box.
Answer:
$43
Step-by-step explanation:
each friend:
$165/5 = $33
Maria:
$33 + $10 = $43
Answer: $43
Step-by-step explanation:
First, divide the money amongst the friends.
165/5 = 33
Then add the ten.
33 + 10 = 43
8x to the third power -9x
The value of the expression is 512x³-9x²
How to find the value of the expression?You should be aware that an expression is a mathematical statement that is not an equation but have variables. It is also an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
The given expression is
8x to the third power -9x
This is expressed as follows
(8x)³-9x²
In this expression, every term inside the bracket is raised to the third power
⇒8³ * x³ - 9 *x
= 512*x - 9x²
= 512x³-9x²
In conclusion, the value of the expression is 512x³-9x²
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1. Bennet is getting in shape for football season. He runs 400 yards 3 times a day for 5 days. How many feet did he run in 5 days?
2. The Russel family is keeping track of the milk they drink each week:
- The first week they drank 2 gallons, 1 quart and 1 cup of milk
- the second week they drank 3 gallons of milk
which week did they drink more milk?
Drag and drop the angle measures below.
122
142
38
44
58
84
96
Type here to search
122%
/R
14101
960
EE
43
96
P
hp
122
Q
The measures of the angle are a = 84°, b = 84°, c = 96°, d = 58°, e = 38° and f = 142°
How to determine the angle measures?
Angle geometry is a branch of mathematics that deals with the properties and relationships of angles in geometric figures.
Check the attached image for labeling
d = 180 - 122 = 58° (sum of angles on a straight line)
c = 96° (vertically opposite angles are equal)
a = 180 - 96 = 84° (sum of angles on a straight line)
b = a (vertically opposite angles are equal)
b = 84°
e = 180 - b -d (sum of angles in a triangle)
e = 180 - 84 - 58 = 38°
f = 180 - e (sum of angles on a straight line)
f = 180 - 38 = 142°
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