Find the function f whose gradient is equal to the vector function f, then evaluate the line integral of f along the given hyperbolic arc from (1,1) to (3,1/3). This involves calculus and the concept of vector fields.
Explanation:This problem involves calculus, specifically the concept of vector fields and line integrals. First, we are asked to find a function f(x, y) such that its gradient is equal to a given vector function f(x, y). To find this scalar function, we need to perform the integral of each component of the vector function f in terms of x and y.
Then we need to evaluate the line integral of the vector function f along a curve c, which is given as an arc of the hyperbola y = 1/x. The definite integral from point (1,1) to point (3,1/3) should be calculated. This integral represents the work done by the field f along the curve c.
Keep in mind that when you perform a line integral, you are adding up the contributions of a field (in this case, the vector field f) along a path (here, the hyperbola). Therefore, the path must be parameterized, and the limits of integration should be the parameter values that correspond to the points (1, 1) and (3, 1/3).
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What is the explicit formula for the sequence? 6, 5, 4, 3, 2, . .
Answer: [tex]a_n=5+n[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by:-
[tex]a_n=a+d(n-1)[/tex], where a is the first term , di sthe common difference and n is the number of terms.
The given sequence : 6, 5, 4, 3, 2, . .
Common difference d = 1
First term = 1
Now, the explicit formula for given arithmetic sequence will be:
[tex]a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n[/tex]
Hence, the explicit formula for given arithmetic sequence : [tex]a_n=5+n[/tex]
How to find the of each figure #5,6,7,8
Yahtzee is played with 5 dice player attempt to score point buy rolling various combinations. when all 5 dice show the same nubmer
25 pt question amd will mark brainliest
Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
2,000
1 + e3 − t
where P(t) is the total number of people infected after t hours. What does 2,000 represent in equation?
A) the rate at which the disease spreads
B) the number of the people in the school
C) the expected change in number of people infected
Eliminate
D) the total number of people infected after t hours
if 3 m equals 12 what is the value of 6(m-1)
Cable hangs between two poles of equal height and 37 feet apart. at a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is
What is the LCD of the following rational expressions?
x/x+1 , 7x/x-1
please help I'm so confused!?
the lengths of three line segments are 4 centimeters,5 centimeters,and 9 centimeters?is it 1,
No triangles can be constructed from line segments of 4 cm, 5 cm, and 9 cm in length, because the Triangle Inequality Theorem requires the sum of any two sides to be greater than the third side, which is not the case here.
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. To determine how many triangles can be constructed with these segments as sides, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the sum of the two shortest sides, 4 cm and 5 cm, is 9 cm, which is equal to the length of the longest side. Because one condition for the Triangle Inequality Theorem is not strictly being met (the sum must be greater, not equal), we can conclude that no triangles can be constructed using these three segments as sides.
When constructing triangles from three measures of angles or sides, it's important to realize that these conditions determine whether you can create a unique triangle, more than one triangle, or no triangle at all.
I don't understand this problem can you help?
what are the discontinuities of the function f(x) = x^2+5x+6/2x+16
Answer:
The discontinuity of the function is at x=-8.
Step-by-step explanation:
Given : Function [tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
To find : What are the discontinuities of the function?
Solution :
Discontinuity of the function is happen when denominator is zero.
First we factor the function,
[tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
[tex]f(x)=\frac{(x+2)(x+3)}{2(x+8)}[/tex]
Denominator = 0
[tex]2(x+8)=0[/tex]
[tex]x+8=0[/tex]
[tex]x=-8[/tex]
The discontinuity of the function is at x=-8.
To test upper h 0: muequals50 versus upper h 1: muless than50, a random sample of size nequals22 is obtained from a population that is known to be normally distributed. complete parts (a) through (d) below.
The question relates to a statistical hypothesis test, specifically comparing a sample mean to a known population mean. This involves recognizing null and alternative hypotheses, identifying and calculating a test statistic, deciding a significance level, determining a critical value, and finally comparing the test statistic to this critical value to decide whether to reject or not reject the null hypothesis.
Explanation:The subject matter posed in the question concerns a statistical hypothesis test.
In these cases, we have two contradictory hypotheses about a population: the null hypothesis, denoted as 'H₀', which generally represents the status quo or a statement of no effect (e.g. a population mean is equal to 50), and the alternative hypothesis, denoted 'H₁', the contrary of the null hypothesis (population mean is not equal to 50). In your specific case, the null hypothesis 'H₀' is that the mean is equal to 50 (μ = 50) and the alternative hypothesis 'H₁' is that the mean is less than 50 (μ < 50).
To test these hypotheses, you could follow these steps:
Identify a test statistic: Since we know the population is normally distributed and we are comparing the sample mean to the population mean, we can use a z-test statistic.
Compare the test statistic to the critical value to decide whether to reject or fail to reject the null hypothesis.
After these steps, interpret the results in terms of the problem.
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The histogram shows the number of vacation days taken by employees in the past year. Based on the histogram, which statement is true?
A.)Four employees took 20 vacation days in the past year.
B.) Four employees took 25 vacation days in the past year.
C.) Four employees took between 20 and 25 vacation days in the past year.
D.) Between 20 and 25 employees took four vacation days in the past year.
Answer:
Option(C)
Step-by-step explanation:
As per histogram, given below
3 students took holidays between 5-10 days.
5 students took holidays between 10-15 days.
5 students took holidays between 15-20 days.
4 students took holidays between 20-25 days.
3 students took holidays between 25-30 days.
therefore, option (C) is correct.
Please help me understand this.
Quadrilateral ABCD is an isosceles trapezoid. If AB || CD, AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m - 16, solve for m.
A.) 2
B.) 3
C.) 4
D.) 5
Answer:
C.) 4
Step-by-step explanation:
we are given ABCD is an isosceles trapezoid
AB || CD
AB = m + 6
CD = 3m + 2
BC = 3m
AD = 7m - 16
Since, ABCD is an isosceles trapezoid
so, two sides must be equal
[tex]BC=AD[/tex]
now, we can plug values
[tex]3m=7m-16[/tex]
now, we can solve for m
[tex]3m-7m=7m-16-7m[/tex]
[tex]-4m=-16[/tex]
Divide both sides by -4
and we get
[tex]m=4[/tex]
Answer:
M= 4
Step-by-step explanation:
In Ms. Dole's class, students received grades of 87, 72, 99, 93, and 84 on yesterday's quiz. What was the mean of the quiz grades?
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
Answer:
13.
Step-by-step explanation:
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth. 6, 7, 19, 7, 18, 7
Answer:
The mean is 10.7 and the standard deviation is 5.6.
Step-by-step explanation:
To find the mean, add together all of the data and divide by the number of data points:
(6+7+19+7+18+7)/6 = 64/6 = 10.7
To find the standard deviation, subtract each data point from the mean, square them and find the sum:
(6-10.7)²+(7-10.7)²+(19-10.7)²+(7-10.7)²+(18-10.7)²+(7-10.7)²
=(-4.7)²+(-3.7)²+(8.3)²+(-3.7)²+(7.3)²+(-3.7)²
=22.09+13.69+68.89+13.69+53.29+13.69 = 185.34
Next divide this by 6, the number of data points:
185.34/6 = 30.89
Lastly, take the square root:
√30.89 = 5.6
Which of the following points are more than 5 vertical units away from the point left-parenthesis 0 comma negative 2 right-parenthesis? Choose all that apply. (2 points) left-parenthesis 6 comma negative 2 right-parenthesis left-parenthesis negative 8 comma negative 2 right-parenthesis left-parenthesis 0 comma negative 8 right-parenthesis left-parenthesis 0 comma 4 right-parenthesis
Given point is (0, -2).
Given options are A(6, -2); B(-8, -2); C(0, -8); D(0, 4).
It says to select the options that are more than five units vertically away from the given point.
"Vertically away" means the x-coordinate would be same and y-coordinate would be shifted up or down.
Since it says to shift more than five units vertically away, so we must have :-
y > -2 + 5 or y < -2 - 5.
Therefore, y > 3 or y < -7.
Hence, option C and D are correct i.e. (0, -8) and (0, 4).
Estimate the probability that if the company books 225 persons. not enough seats will be available. 1-.81^225
1. demand for product
2. example of fixed cost buyer's
3. sales receipts
4. credit discount
5. example of variable cost
6. moves slow-moving goods
7. business upturn
8. used for business expansion
9. depends on prime rate
10. assures profit on item sold
2/10, net 30
credit
interest rate
workers' wages
revenue
recovery
rent
markdown
markup
buyer's willingness to pay
Answer:
Interest rate - 9
Revenue - 3
Recovery - 7
Markdown - 6
Buyer's willingness to pay - 1
Markup - 10
Worker's wages - 5
2/10 net 30 - 4
Credit - 8
Rent - 2
Step-by-step explanation:
Just did this on odyssey
78 million in scientific notation
Answer:
[tex]78\ million=7.80\times 10^7[/tex]
Step-by-step explanation:
A number N can be written in scientific notation as :
[tex]N=p{\circ}0\times 10^q[/tex]
Where
p is the any real number
q is any integer
Here, the given number is 78 million. Firstly, we must know meaning of 1 million.
Since, [tex]1\ million=10^6[/tex]
[tex]78\ million=78.0\times 10^6[/tex]
To convert the above number in scientific notation, we can shift the decimal before 8 such that,
[tex]78\ million=7.80\times 10^7[/tex]
Hence, this is the required solution.
Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. Using the formula A(t) =P*e^rt , how much will you have in the account after 4 years
Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)
Answer:
So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1
Ans: [tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
The standard form equation of a hyperbola with the center at the origin (0,0), a vertical axis, a vertex at (0, a), and a focus at (0, c) is given by:
[tex]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\][/tex]
where [tex]\(c\)[/tex] is the distance from the center to the focus, and [tex]\(b\)[/tex] is related to [tex]\(a\) and \(c\)[/tex] by the equation [tex]\(c^2 = a^2 + b^2\)[/tex].
In your case, the center is at (0,0), the vertex is at (0,60), and the focus is at (0,-65). The distance from the center to the focus is [tex]\(c = 65\)[/tex], and the distance from the center to the vertex is [tex]\(a = 60\)[/tex]. Using the relationship [tex]\(c^2 = a^2 + b^2\)[/tex], we can find b:
[tex]\[65^2 = 60^2 + b^2\][/tex]
Solving for b:
[tex]\[4225 = 3600 + b^2\][/tex]
[tex]\[b^2 = 625\][/tex]
[tex]\[b = 25\][/tex]
Now, substitute [tex]\(a\), \(b\), and \((h, k) = (0, 0)\)[/tex] into the standard form equation:
[tex]\[\frac{y^2}{60^2} - \frac{x^2}{25^2} = 1\][/tex]
So, the equation of the hyperbola is:
[tex]\[\frac{y^2}{3600} - \frac{x^2}{625} = 1\][/tex]
[tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin
If Henry's home has a market value of $145000 and the assessment rate is 35% what is its assessed valuation
Answer:
Assessment value of Henry's home is $50750
Step-by-step explanation:
Henry's home has a market value of $145000 and the assessment rate is 35%.
This means value of home is 35% of the total cost $145000
Now we will solve it by calculating percentage
Assessment = 35% of 145000 = [tex](145000)(\frac{35}{100})=(1450).(35)=50750[/tex]
So the answer is assessment of Henry's home = $50750.
The digits 1,2,3,4,5,6,7 and 8 are arranged randomly to form a three-digit number find the probability that the number is even and greater than 800
[tex] |\Omega|=8\cdot7\cdot6=336\\
|A|=\underbrace{1\cdot6\cdot3}_{\text{8,any,even}}=18\\\\
P(A)=\dfrac{18}{336}=\dfrac{3}{56}=5\% [/tex]
Look at the table. Make a conjecture about the sum of the first 15 positive even numbers.
The conjecture about the sum of the first 15 positive even numbers is 15 * 16
Making a conjecture about the sum of the first 15 positive even numbers.
From the question, we have the following parameters that can be used in our computation:
The table of values
Where, we have
2 = 1 * 2
2 + 4 = 2 * 3
2 + 4 + 6 = 3 * 4
And so on
This means that
Sum of first n positive even numbers = n * (n + 1)
So, for the first positive even numbers, we have
n = 15
This gives
Sum of first 15 positive even numbers = 15 * (15 + 1)
Evaluate
Sum = 15 * 16
Sum = 240
Hence, the sum is 15 * 16
Write the standard form of the equation of the circle with the given center and radius.
(-3, 6); 10
Answer:
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
[tex](x+3)^2+(y-6)^2=100[/tex]
Step-by-step explanation:
This is the general standard equation for the circle centered at (h, k) with radius r
[tex](x-h)^2+(y-k)^2=r^2[/tex]
It shows all the important information at a glance: the center (h, k) and the radius r.
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
Start with:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put in (h, k) and r
[tex](x-(-3))^2+(y-6)^2=10^2\\(x+3)^2+(y-6)^2=100[/tex]
find the value of q in the following system so that the solution to the system is(4,2) 3x-2y=8
2x+3y=Q