Answer:i dont know
Step-by-step explanation:
Is the integral ſ A. dr path independent if A = (2x - y)i + (x + y)j?
Evaluate A dr around a unit circle centered at the origin. What is t
value of the integral if we take a clockwise direction?
The integral is path-independent if we can find a scalar function f such that grad(f ) = A. This requires
[tex]\dfrac{\partial f}{\partial x}=2x-y[/tex]
[tex]\dfrac{\partial f}{\partial y}=x+y[/tex]
Take the first PDE and integrate both sides with respect to x to get
[tex]f(x,y)=x^2-xy+g(y)[/tex]
where g is assumed to be a function of y alone. Differentiating this with respect to x gives
[tex]\dfrac{\partial f}{\partial y}=-x+\dfrac{\mathrm dg}{\mathrm dy}=x+y\implies\dfrac{\mathrm dg}{\mathrm dy}=2x+y[/tex]
which would mean g is *not* a function of only y, but also x, contradicting our assumption. So the integral is path-dependent.
Parameterize the unit circle (call it C) by the vector function,
[tex]\mathbf r(t)=\cos t\,\mathbf i+\sin t\,\mathbf j[/tex]
with t between 0 and 2π.
Note that this parameterization takes C to have counter-clockwise orientation; if we compute the line integral of A over C, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.
Then
[tex]\mathrm d\mathbf r=-\sin t\,\mathbf i+\cos t\,\mathbf j[/tex]
and the (counter-clockwise) integral over C is
[tex]\displaystyle\int_C\mathbf A\cdot\mathrm d\mathbf r[/tex]
[tex]\displaystyle=\int_0^{2\pi}((2\cos t-\sin t)\,\mathbf i+(\cos t+\sin t)\,\mathbf j)\cdot(-\sin t\,\mathbf i+\cos t\,\mathbf j)\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}1-\sin t\cos t\,\mathrm dt=2\pi[/tex]
and so the integral in the direction we want is -2π.
By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.
(HALP PLS WILL 100% MARK BRAINLIEST!) Sage has $26 and wants to download some songs from a music
Web site. Each song costs $1.79 to download. By rounding the
cost of the songs up to the nearest whole dollar, estimate the
greatest number of songs she can download.
A) 11
B) 13
C) 15
D) 17
Answer:
≈ 13Step-by-step explanation:
First ,we round 1.79 to the nearest whole dollar:
since 7 ≥ 5 then 1.79 rounded to the nearest whole dollar is 2
now ,we can estimate the greatest number she can download:
26/2 = 13
A 6) Set both given equations equal to zero, then combine them into one standard form
equation. Simplify if possible.
7x + 3 = 5 and y-1 = 6
The equation in standard form is given by:
[tex]7x + y - 9 = 0[/tex]
------------------
The general equation in standard form is:
[tex]Ax + By + C = 0[/tex]
------------------
The first equation is:
[tex]7x + 3 = 5[/tex]
Setting equal to zero:
[tex]7x + 3 - 5 = 0[/tex]
[tex]7x - 2 = 0[/tex]
------------------
The second equation is:
[tex]y - 1 = 6[/tex]
[tex]y - 1 - 6 = 0[/tex]
[tex]y - 7 = 0[/tex]
------------------
Combining them, and placing in standard form:
[tex]7x - 2 + y - 7 = 0 + 0[/tex]
[tex]7x + y - 9 = 0[/tex]
A similar problem is given at https://brainly.com/question/14664782
A board game has a spinner divided into sections of equal size. Each section is labeled with a number between 1 and 5. Which number is a reasonable estimate of the number of times the spinner will land on a section labeled with a 5 over the course of 300 spins?
Answer:
75
Step-by-step explanation:
first, there are three 5's on the spinner, with a total of 12 sections. 3/12 = 0.25, so you multiply 0.25 times 300 (the total spins) and get 75
QUESTION 4
What kind of passenger would be considered a false negative?
A) Someone with dangerous material that pass through security
B) Someone with dangerous material thpt is stopped by security
C) Someone without dangerous material that pass through security
D) Someone without dangerous material that is stopped by security
which side lengths form a right triangle
Answer:
A and C
Step-by-step explanation:
A right triangle consists of two legs and a hypotenuse.To find hypotenuse, we use The Pythagorean TheoremThe Pythagorean Theorem = [tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]two legs meet at a 90° angle and the hypotenuse is the longest side3 - 4 - 5
6 - 8 - 10
7 - 24 - 25
5 - 12 - 13
are some basic right triangle
(about more, look picture)
Just use hypotenuse formula :
3 x 3 = 9
4 x 3 = 12
5 x 3 = 15
Option C is correct
[tex] {5}^{2} + { \sqrt{6} }^{2} = { \sqrt{31} }^{2} [/tex]
Option A is correct
[tex] {5}^{2} + {5}^{2} = { \sqrt{50} }^{2} [/tex]
But B isn't correct
Hope this helps ^-^
2x + 3y = 12
Complete the missing value in the solution to the equation.
1,8)
Answer:
Step-by-step explanation:
[tex]\mathrm{Slope-Intercept\:form\:of}\:2x+3y=12:\quad y=-\frac{2}{3}x+4\\\mathrm{Domain\:of\:}\:-\frac{2}{3}x+4\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\mathrm{Range\:of\:}-\frac{2}{3}x+4:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Parity\:of}\:-\frac{2}{3}x+4:\quad \mathrm{Neither\:even\:nor\:odd}\\\mathrm{Axis\:interception\:points\:of}\:-\frac{2}{3}x+4:\quad \mathrm{X\:Intercepts}:\:\left(6,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:4\right)\\\mathrm{Inverse\:of}\:-\frac{2}{3}x+4:\quad -\frac{3x-12}{2}\\\mathrm{Slope\:of\:}-\frac{2}{3}x+4:\quad m=-\frac{2}{3}[/tex]
A shop sells boxes of chocolate. In total there are 252 dark chocolate and 180 milk chocolates.if every box is identical,how many boxes could there be?
Answer:
12 boxes.
Step-by-step explanation:
We need to find the greatest common factor of 251 and 180:
First find the prime factors :
252 = 2*2*3*3*7
180 = 2*2*3*3*5
So the GCF = 2*2*3*3 = 36.
So id each box is identical, there could be 7 boxes of dark chocolates and 5 boxes of milk chocolates each containing 36 chocolates.
Total number of boxes = 12.
Please answer this correctly
Answer:
54 9/10
Step-by-step explanation:
The perimeter is the sum of all the sides
13 1/4 + 12 1/5 + 18 1/4 + 11 1/5
Add up the whole numbers
13+12+18+11 = 54
1/4+1/5+1/4+1/5
2/4+2/5
1/2+2/5
Get a common denominator
1/2*5/5 + 2/5*2/2
5/10 + 4/10
9/10
Add them back together
54 9/10
Last week, the price of cherries at the corner deli was $4.99 per pound. This week, cherries at the same deli are on sale at a 15% discount. What is the total price of 3.75 pounds of cherries this week at the deli?
Answer:
The price for 3.75 pounds of cherries is $17.775.
Step-by-step explanation:
The price las week was $ 4.99 and it got a discount of 15% for this week, this means that the price for this week is 100% of the one prior minus 15%, therefore it is 85% of the last price. We need to calculate the price per pound with this discount as shown below:
[tex]\text{this week} = \text{last week}*\frac{95}{100}\\\\\text{this week} = 4.99*0.95 = 4.74 \text{ per pound}\\[/tex]
Since the price is $4.74 per pound and we want to buy 3.75 pounds, then the total amount we need to pay is:
[tex]\text{total amount} = 3.75*4.74 = 17.775[/tex]
The price for 3.75 pounds of cherries is $17.775.
Mr Smith had four daughters.Each daughter has four brothers.How many children does Mr Smith have
Starting off, you already know he has 4 daughters and for every daughter there are 4 sons.
So, we take the 4 daughters and add 4 to each one:
1 daughter + 4 sons = 5 children
We complete that equation 4 times for each daughter, and we end up with 20 children as our answer.
Hope this helps you out a bit! Stay safe and stay healthy! :D
What is the value of y?
-36
-108
-72
-54
Answer:
54°
Step-by-step explanation:
The overall angle degrees of a trinangle 180°
Since we know that once of the angles is 72° we subract that from 180°
That equals 108°
Then we divide 108° since that is the sum of both the angles.
108/2= 54, so y= 54°
Help, pls. it's due tomorrow night.
An airplane flies due north at 200 km/h, and the wind blows in a direction N30°E
at 40 km/h. Find the coordinates for the vector representing the resultant for
the airplane with the wind factored in, and the resultant airspeed. Report any
approximations to two decimal places accuracy and include a diagram.
Answer:
please please please please show please
Answer with Explanation please! Thank you!
Answer:
D
Step-by-step explanation:
2(x+b) = ax+c
2x+2b = ax+c
c = 2b
if u can do all 3 that will be great, TYSM!!
A: Five people each paying $14.50 means that the total bill was [tex]5\cdot\$14.50=\boxed{\$72.50}.[/tex]
B: Subtract the number of people he already has from the number of people he needs to get [tex]42-29=\boxed{13}[/tex] people.
C: Divide 96 by 8 to get [tex]\boxed{12}[/tex] packs.
Arithmetic is where it all begins, y'know?
Answer:
Hope this helps though I m not sure about the first one since I got another answer 72.5 but it isn't there
Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 5,000 and P'(1,000) = −3, what do these values tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 5,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the as a function of x. P'(1,000) = −3, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.
Answer:
Step-by-step explanation:
We are told that P(x) is the profit of saling x blu ray discs. P(1000) is our profit for selling 1000 blu ray discs. So, our profit is 5000. Recall that the derivative P'(x) represents the rate at which the function P(x) is increasing/decreasing (increasing if P'(x) is positive, or decreasing otherwise) by increasing the values of x. In this case P'(1000)=-3, so the profit will decrease -3 if we increase x in one unit.
What’s the correct answer for this question?
Answer:
E : x=12
Step-by-step explanation:
ACCORDING TO THE THEOREM
(PD)(PC) = (AP)(PB)
8(3+x)=10x
24+8x=10x
24=10x-8x
24 = 2x
x = 12
Answer:
12
Step-by-step explanation:
PD * PC = AP * PB
= 8 * (3 + x) = 10 * x
= 24 + 8x = 10x
= 10x - 8x = 24
= 2x = 24
= 12
Anja stands by the side of the road counting the wheels on the vehicles that go past her if she counts 250 wheels tie many cars and bikes has she seen?
Answer:
50 cars and 25 bikes
Step-by-step explanation:
Given
Total wheels = 250
Required:
Number of cars and bikes
Let C represent Cars and B represents Bike
A car has 4 wheels and a bike has 2 wheels;
So,
[tex]4C + 2B = 250[/tex]
Divide through by 2
[tex]\frac{4C + 2B}{2} = \frac{250}{2}[/tex]
[tex]2C + B = 125[/tex] ---- Equation 1
The ratio of wheels of cars to wheels of bike is 1:2
Meaning that
1C = 2B
So, C = 2B
Substitute 2B for C in equation 1
[tex]2(2B) + B = 125[/tex]
[tex]4B + B = 125[/tex]
[tex]5B = 125[/tex]
Divide both sides by 5
[tex]\frac{5B}{5} = \frac{125}{5}[/tex]
[tex]B = \frac{125}{5}[/tex]
[tex]B = 25[/tex]
Recall that C = 2B
So,
[tex]C = 2 * 25[/tex]
[tex]C = 50[/tex]
Hence, Anna has seen 50 cars and 25 bikes
Cuanta cartulina se necesita para construir un prisma rectangular para cuya base mide 10cm y tiene 6cm de altura
Answer:
i dont understand the language
Step-by-step explanation:
Alicia made her aunt a garden. The width is 6 5/7 ft ft and the length is 7 3/5 ft. What is the area of the garden
Please answer!
Step-by-step explanation:
Area=Length×width
=6 5/7×7 3/5
change the improper fraction to proper
=47/7 ×38/5
=1786/35
=51.03ft²
PLEASE ANSWER I NEED THIS NOW The blue dot is at what value on the number line?
Answer:
-10
Step-by-step explanation:
goes up by 4 each value
Answer:
-10
Step-by-step explanation:
in that chain,
it is 10,6,2,-2,-6,-10
Which of the following is graphed below
Answer:
The answer is C
An archaeologist locates a fossil of an early human skeleton. To determine the age of the fossil, the archaeologist utilizes a technique called carbon dating, where the relative amount of carbon-14 can help determine the age of the fossil. Carbon-14 has a half-life of about 5700 years. He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size. The decay of carbon-14 can be calculated as shown below, where N0 is original amount of carbon-14, t is the time of decay, in years, r represents the rate of decay, and N(t) represents the amount of carbon-14 remaining. Rounded to the nearest year, the skeleton is approximately years old.
Answer:
The skeleton is approximately 18970 years old.
Step-by-step explanation:
The amount of Carbon-14 remaining after t years is given by the following equation:
[tex]N(t) = N(0)(1-r)^{t}[/tex]
In which N(0) is the initial amount and r is the decay rate, as a decimal.
Carbon-14 has a half-life of about 5700 years.
This means that [tex]N(5700) = 0.5N(0)[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]0.5N(0) = N(0)(1-r)^{5700}[/tex]
[tex](1-r)^{5700} = 0.5[/tex]
[tex]\sqrt[5700]{(1-r)^{5700}} = \sqrt[5700]{0.5}[/tex]
[tex]1-r = 0.9999[/tex]
[tex]r = 1 - 0.9999[/tex]
[tex]r = 0.0001[/tex]
So
[tex]N(t) = N(0)(1-r)^{t}[/tex]
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size.
The age is t for which N(t) = 0.15N(0). So
[tex]N(t) = N(0)(0.9999)^{t}[/tex]
[tex]0.15N(0) = N(0)(0.9999)^{t}[/tex]
[tex](0.9999)^{t} = 0.15[/tex]
[tex]\log{(0.9999)^{t}} = \log{0.15}[/tex]
[tex]t\log{0.9999} = \log{0.15}[/tex]
[tex]t = \frac{\log{0.15}}{\log{0.9999}}[/tex]
[tex]t = 18970.25[/tex]
Rounding to the nearest year.
The skeleton is approximately 18970 years old.
Answer:
Mark as Brainliest Please :)
Step-by-step explanation:
What is the greatest common factor of 60, 45 and 82? HALPPPPPPPPPPPPPPPPPPp
Answer:
GCF: 1
Step-by-step explanation:
Factors are numbers that can be evenly divided into another number. The greatest common factor of a set of numbers is the biggest number than can evenly divide into all the the numbers.
Let's list the factors of 60, 45 and 82
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 45:
1, 3, 5, 9, 15, 45
Factors of 82:
1, 2, 41, 82
The greatest factor that all 3 numbers share is 1.
The right answer is 1.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
Explain how you will solve the pair of equations by substitution.show all steps and write the solution in (x,y) form.
Answer:
(-2, -3)Step-by-step explanation:
The question is incomplete. Here is the complete question.
Consider the following pair of equations:
y = 3x + 3 ... 1
y = x − 1 ... 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form .
From both equations, we will substitute y = 3x+3 in equation 1 into 2 to have;
3x+3 = x-1
collecting the like terms;
3x-x = -1-3
2x = -4
Dividing both sides by 2 will give;
2x/2 = -4/2
x = -2
Substituting x = -2 into equation 1;
y = 3x+3
y = 3(-2)+3
y = -6+3
y = -3
The solution in (x, y) form is (-2, -3)
The solution of the system of equations Ax+y=5 and Ax+By=20 is (2,-3). What are the values of A and B
Answer:
A = 4B = -4Step-by-step explanation:
Put the values of x and y in the equations and solve the resulting system.
A(2) +(-3) = 5
A(2) +B(-3) = 20
__
The first equation tells the value of A:
2A = 8 . . . . add 3
A = 4 . . . . . .divide by 2
This and the second equation tells the value of B:
(4)(2) -3B = 20
-3B = 12 . . . . . subtract 8
B = -4 . . . . . . . divide by -3
The values of A and B are 4 and -4, respectively.
Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the votes were for blue, 5/9 of the remaining votes were for green 48 votes were for red. How many votes were for blue? how many votes were for green? if every student got one vote, but there were 25 students absent on the day of the vote, how many students are there at Riverside Elementary School
Answer:
288 votes
Step-by-step explanation:
wright out what you know
Blue: 5/8
Green: 5/9 (of 3/8 because it is the remaining parts) so 5/24
Red: 1 - (5/8 + 5/24) = 1/6
Find the total amount of people
You know that 1/6 of the population is 48, so the total population is 288 (48×6)
Multiply the total population by the fractions to get the number of votes
A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let Y be the number of the trial on which the lock is opened. Find the probability function for Y.
The "density of probability" is represented by the Y-axis in the normal distribution.It indicates the likelihood of finding values close to comparable places on the X-axis.
Find the probability f ?Y is the number of trial on which lock is opend so, P(Y=y) be the probability that key opens the lock on y th trial Lets draw first key
p(1 st key opens the lock) =1-1/5= 4/5
Hence p(1 st key does not open the lock = 1- 1/5 =4/5
Since p (Lock is opened on 1 st triual ) = p(1st key opens the lock )
Hence , P(Y =2 ) 1/4 .4/5 = 1/5
p( y = 4) = 1/5
p(y = 5 ) =1/5
To learn more about probability function refer
https://brainly.com/question/28021875
#SPJ2
The radius of a circle is 6.5cm What is the diameter
The diameter of a circle is twice the radius.
Diameter = radius x 2
= 6.5 x 2
= 13 cm
Answer:
13
Step-by-step explanation:
diameter is two times the radius
6.5 x 2 = 13
Bartholomew went hiking over the weekend. He hiked all 4 trails in 3 hours. Which is the best estimate for the number of miles he hiked per hour
Answer:
a?
Step-by-step explanation:
