greens theorem. find the max value of the line integral where f=(13x^2y+3y^3-y)i-12x^3j and C is any positively oriented closed curve. max=?

Answers

Answer 1

The line integral is given by

[tex]\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int_C((13x^2y+3y^3-y)\,\mathrm dx-12x^3\,\mathrm dy)[/tex]

By Green's theorem, the line integral along [tex]C[/tex] is equivalent to the double integral over [tex]R[/tex] (the region bounded by [tex]C[/tex])

[tex]\displaystyle\iint_R\left(\frac{\partial(-12x^3)}{\partial x}-\frac{\partial(13x^2y+3y^3-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_R(-36x^2-(13x^2+9y^2-1))\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_R(1-49x^2-9y^2)\,\mathrm dx\,\mathrm dy[/tex]

Now consider the function [tex]g(x,y)=1-49x^2-9y^2[/tex]. We can think of the double integral above as a volume integral; namely, it's the volume of the region below [tex]g(x,y)[/tex] and above the region [tex]R[/tex] in the [tex]x[/tex]-[tex]y[/tex] plane (i.e. [tex]z=0[/tex]). This volume will be maximized if [tex]C[/tex] is taken to be the intersection of [tex]g(x,y)[/tex] with the plane, which means [tex]C[/tex] is the ellipse [tex]49x^2+9y^2=1[/tex].

For the double integral, we can convert to an augmented system of polar coordinates using

[tex]\begin{cases}x=\frac17r\cos\theta\\\\y=\frac13r\sin\theta\end{cases}[/tex]

where [tex]0\le r\le1[/tex] and [tex]0\le\theta\le2\pi[/tex]. We have the Jacobian determinant

[tex]\det\mathbf J=\left|\dfrac{\partial(x,y)}{\partial(r,\theta)}\right|=\begin{vmatrix}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta}\\\\\frac{\partial y}{\partial r}&\frac{\partial y}{\partial\theta}\end{vmatrix}[/tex]
[tex]\det\mathbf J=\begin{vmatrix}\frac17\cos\theta&-\frac17r\sin\theta\\\\\frac13\sin\theta&\frac3r\cos\theta\end{vmatrix}=\dfrac r{21}[/tex]

So the double integral, upon converting to our polar coordinates, is equivalent to

[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\left(1-49\left(\frac r7\cos\theta)^2-9\left(\frac r3\sin\theta\right)^2\right)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}(1-r^2\cos^2\theta-r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}(r-r^3)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac{2\pi}{21}\int_{r=0}^{r=1}(r-r^3)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\dfrac\pi{42}[/tex]

Answer 2

Final answer:

To find the max value of a line integral over a closed curve using Green's Theorem, consider the curl of the given vector field and apply the theorem to express the result. The maximum value of the line integral is -2y²dy, determined through vector calculus and Green's Theorem application.

Explanation:

Green's Theorem states that for a vector field f in the form given, the max value of the line integral over any positively oriented closed curve C can be found by considering the curl of f.

By applying Green's Theorem, we can find that the maximum value of the line integral is -2 y²dy.

This computation involves utilizing vector calculus and understanding how to apply Green's Theorem to find the extremum of the line integral.

Related Questions

Analyzing the graphs of a periodic functions (need help)

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\[/tex]

[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

now, with that template above in mind, let's see.

reflected over the x-axis, that means A is negative.

vertically shrunk by 0.25 or 1/4, that means A is negative 4, or -4.

shifted to the left, that means C/B is positive

shifted by 65°, that means, we could use the default B = 1, and C = 65°, that way we end with C/B = 65/1 or just +65

and shifted downwards by 1 unit, that means D = -1.

[tex]\bf f(x)=-4sin(1x+65^o)-1\implies f(x)=-4sin(x+65^o)-1[/tex]

and looks more or less like the picture below.

Autumn is thinking about buying a car. The table below shows the projected value of two different cars for three years.

Number of years 1 2 3
Car 1 (value in dollars) 38,000 32,000 26,000
Car 2 (value in dollars) 38,000 32,300 27,455

Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Autumn wants to purchase a car that would have the greatest value in 6 years. Will there be any significant difference in the value of either car after 6 years? Explain your answer, and show the value of each car after 6 years. (4 points)

Answers

PART A

The value of car A decreases by 6000 every year. Since the decrease is the same every year, the function is linear

The value of car B decreases by the ratio of [tex] \frac{17}{20} [/tex] every year. Since the decrease is by the same ratio every year, the function is exponential

PART B

Car 1: the function is [tex]y=-6000x+44000[/tex], where [tex]y[/tex] is the value after [tex]x[/tex] years. Negative 6000 shows the decrease every year and 44000 is the value of the car in Year 0

Car 2: the function is [tex]y=(38000) ( \frac{17}{20}) ^{x-1} [/tex], where [tex]y[/tex] is the value after [tex]x[/tex] years. 38000 is the value of the car after Year 1 and [tex] \frac{17}{20} [/tex] is the ratio of depreciation

PART C

Value of car 1 after 6 years is [tex]-6000(6)+44000=8000[/tex]
Value of car 2 after 6 years is [tex](38000) ( \frac{17}{20}) ^{6-1} =16860.8[/tex]

There is a significant difference in the values of the cars after 6 years

Final answer:

The value of Car 1 decreases linearly and can be described by a linear function. Without an exact exponential function for Car 2, we'll assume it may have a slower depreciation rate compared to Car 1. Autumn should consider Car 2 to likely have greater value after 6 years.

Explanation:

Part A: Identifying the Type of Function

To determine which type of function best describes the value of each car after a fixed number of years, we must look at the rate at which the car's value decreases. For Car 1, the value decreases by a constant amount each year ($6,000), which suggests a linear function. Conversely, Car 2 does not decrease by the same amount each year, but rather by amounts that seem to be getting progressively larger, hinting at an exponential function.

Part B: Writing the Functions

The linear function for Car 1 can be represented as f(x) = -6,000x + 44,000, since we start at $44,000 and decrease by $6,000 each year. For Car 2, an exponential decay function may fit the data; however, with only three points provided, determining the exact exponential function would require more complex regression analysis which we do not perform here. Assuming the rate of depreciation remains similar, we might estimate the function for Car 2 using a linear approximation for simplicity.

Part C: Future Car Value Comparison

Extending the linear depreciation model for Car 1, its value after 6 years would be f(x) = -6,000(6) + 44,000 = $8,000. A precise prediction for Car 2 after 6 years cannot be determined without an accurate exponential function, but it's apparent that Car 2 depreciates less rapidly than Car 1. Therefore, Autumn would likely find that Car 2 retains more value over 6 years.

Solve for v 14v-8v=24

Answers

14v-8v=24
Subtract 8v from 14v
6v=24
Divide 24 by 6
Final Answer: v = 4

14v - 8v = 24

Reorganize this problem to: 14(v)-8(v)-24 ➡️?
6v ➡️ 24
6(1)➡️ 6
6(2) ➡️ 12
6(3) ➡️18
6(4) ➡️24
✅v ➡️ 4 ✅

or you can do this method

v - 4 ➡️0
✔️v ➡️4 ✔️

The number of solution is 1 and v=4

Ivan was given two data sets, one without an outlier and one with an outlier.

Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61

How is the median affected by the outlier?

Answers

Answer:

Step-by-step explanation:

The outlier affects the median of the data sets collected by Ivan by reducing the median.

What is an outlier?

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier in the data set is 62. Median is the number at the center of a data set.

Median without an outlier is 113Median with an outlier is 111

To learn more about outliers, please check: https://brainly.com/question/27197311

#SPJ2

Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchases

Pleaseee helppppppp

Answers

15.98*3 + 39.95 + 24.99 = 112.88

7% taxes (always taxes!): 112.88 * 1.07= 120.7816

Rounded to cents: 120.78

3(15.98) + 39.95 + 24.99 = 112.88
112.88(1.07) = 120.78 <=

Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of?

Answers

The zero with a multiplicity of 1 is x = 1, and the zero x = -2 has a multiplicity of 2.

How to find the multiplicity of zeros in a polynomial?

For a general polynomial like:

[tex]p(x) = (x - x_1)^n*(x - x_2)^m*...[/tex]

The zero x₁ has a multiplicity of n (same as the exponent in the term where the zero appears), while the zero x₂ has a multiplicity m.

Now let's go to our polynomial:

[tex]f(x) = (x - 3)^2(x + 2)^2(x - 1)[/tex]

Here we can see that the only zero with a multiplicity of 1, is x = 1, while the zero x = -2 has a multiplicity of 2.

If you want to learn more about polynomials, you can read:

https://brainly.com/question/4142886

Answer:

first one is 1 and second is 2

Step-by-step explanation:

just got it right

Find the area of the equilateral triangle if a side is 14√3 ft. Round to the nearest whole number.

Answers

Answer:

Answer is C

Step-by-step explanation:

Area of an equilateral triangle can be found by the following formula,

A=[tex]\frac{\sqrt{3}} {4} a^{2}[/tex]

Where "a" is the length of one side of the triangle.

Now we can substitute the value given to the equation above and find the area of the given equilateral triangle.

A=[tex]\frac{\sqrt{3}} {4}(14\sqrt{3})^ {2}[/tex]

=[tex]\frac{\sqrt{3}} {4} 196*3[/tex]

=[tex]\frac{\sqrt{3}*196*3} {4}[/tex]

=[tex]254.611[/tex]

A=[tex]255[/tex] square feet.

Answer is C

What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)

Answers

check the picture below

you can pretty much just count how many units for the base, and height.

Answer: 10 square units.

Step-by-step explanation:

The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-

[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]

Given : The vertices of triangle : (2,0), (6,0), (8,5)

Then , the area of the triangle will be :_

[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]

Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10

With 400,000 sq ft or 16% of total office space. How much space did the city have

Answers

if 400,000 is 16%, and "x" is say the 100%

well then [tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 400,000&16\\ x&100 \end{array}\implies \cfrac{400000}{x}=\cfrac{16}{100}[/tex]

solve for "x".

Given the Vectors s=(-3,2) and t= (-9,-4), find 6s and s+t

Answers

hello :
s=(-3,2) and t= (-9,-4),
6s = (-3×6 , 2×6 ) = (-18 , 12)
s+t = ( -3-9 , 2-4 ) = (-12,-2)

6s=(-18,12), and t+s=(-12,-2).

The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side is 14 more than the shortest side, find the lengths of the three sides?

Answers

side 1 = x

side 2 = x+5

side 3 = x+14

perimeter = side 1 + side 2 + side 3

133 = x + (x+5) + (x +14)

133=3x + 19

114=3x

x=114/3 = 38

side 1 = 38

side 2 = x+5 = 38+5 = 43

side 3 = x+14 = 38+14 = 52

38+43+52 = 133

side lengths are 38, 43 & 52

subtract, 8 3/8 - 10 1/6

Answers

[tex] 8\frac{3}{8} = \frac{67}{6} \\ 10\frac{1}{6} = \frac{61}{6} [/tex]

[tex] 8\frac{3}{8} - 10\frac{1}{6}[/tex]

[tex]convert [/tex] them to: [tex] \frac{67}{8} - \frac{61}{6} [/tex]

[tex] \frac{67}{8} - \frac{61}{6} = \frac{-43}{24} [/tex]

Your [tex]answer[/tex]: [tex] -1\frac{19}{24} [/tex]

Good luck on your assignment & enjoy your day

~[tex]MeIsKaitlyn :)[/tex]

Find the surface of a cylinder with a base diameter of 4yd and a height of 6yd

Answers

pi*radius squared= area of a circle
3.14*2^2=12.56yd^2

pi*diameter=circumference
3.14*4=12.56yd

area of surface around the cylinder=circumference*height
12.56*6=75.36yd^2

area of surface around the cylinder+ (area of circle*2)= surface area
75.36+(12.56*2)=100.48

the answer should by 100.48 yards squared

hope this helps

Set up a system of equations for the following scenario. Then solve for the system. Three students buy different combinations of tickets for a baseball game. The first student buys 2 senior, 1 adult, and 2 student tickets for $51. The second student buys 1 adult and 5 student tickets for $55. The third student buys 2 senior, 2 adult, and 7 student tickets for $75. Set up a system of equations to find the price of each ticket.

Answers

Let
x = cost of a ticket for a senior
y = cost of a ticket for an adult
z = cost of a ticket for a student.

The first student buys 2 senior, 1 adult, and 2 student tickets for $51.
Therefore
2x + y + 2z = 51 (1)

Th second student buys 1 adult and 5 student tickets for $5.
Therefore
y + 5z = 55 (2)

The third student buys 2 senior, 2 adult, and 7 student tickets for $75.
Therefore
2x + 2y + 7z = 75 (3)

Answer:
The system of equation for determining x, y, and z is
2x + y + 2z = 51
y + 5z = 55
2x + 2y + 7z = 75

Warnng: The system of equations does not have a solution.

What are two numbers whose sum is 11 and whose product is -60?

Answers

Step 1:
Enumerate pairs of numbers whose product is 60
(1,60)
(2,30)
(3,20)
(4,15)
(5,12)
(6,10)
(10,6)
...
2. identify the pair whose components have a difference of 11.
(4,15)
3. attach a negative sign to the smaller component so that the sum is +11.
(-4,15)

Answer: the numbers are -4 and 15.

he IQ scores of 500 college football players are randomly selected. Which graph would be most appropriate for these data: histogram, bar chart, pie chart, multiple bar graph, or slack plot?

Answers

A histogram allows you to plug in data such as the occurrences of score frequencies in a continuous data set that has been equally divided into classes such as bins. Bar charts allows you to use numerous types of variables including nominal an ordinal data sets. Pie chart is a circle chart that allows you to see the numerical proportions of each data set. The chart that would be most appropriate in the IQ scores of 500 college football players that are randomly selected is the histogram. This is because the data is to be classified according to their IQ scores and it requires a distribution of sample from 500 college football players.

The radius of a circular park is 114 yd. To the nearest yard, what is the circumference of the park?

Answers

circumference = 2 x pi x r

using 3.14 for pi

2 x3.14x114=715.92

round to 716 yards

Answer:

The circumference of a circle is 715.92 yd.

Step-by-step explanation:

Formula

[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]

Where r is the radius of a circle.

As given

The radius of a circular park is 114 yd.

[tex]\pi = 3.14[/tex]

Put in the formula

[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 114[/tex]

Circumference of a circle = 715.92 yd

Therefore the circumference of a circle is 715.92 yd.

Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of?

Answers

I think the most difficult word to define in geometry is point.

Other words like line, segment, circle, angle may be defined from other word based of the notion of point.

But point is a very abstract notion, because it does not have length, so a point is an imaginary think.

Once, you have the notion of point, you can figure out that a line is an infinite succession of points, and from that define other concepts.

Angle may also be found a dificcult word to define because it is the opening or amount of turn between two lines that have a common end point.

The words typically associated with geometry are:

Points, Lines, Plane, and angle.

We have,

In geometry,

There are some words that can be challenging to precisely define or may have different interpretations.

Here are a few examples:

- Point: While a point is commonly understood as a location with no size or dimension, providing an exact definition can be difficult without relying on terms like "location" or "position."

- Line: A line is often described as a straight path extending infinitely in both directions. However, defining it without using similar geometric concepts like "straight" or "infinitely" can be challenging.

- Plane: A plane is typically defined as a flat, two-dimensional surface that extends infinitely in all directions. However, explaining it without referencing terms like "flat" or "two-dimensional" can be complex.

- Angle: An angle is formed by two intersecting lines or line segments. Describing it precisely without using terms like "intersects" or "measures" can be difficult.

Thus,

These words require a level of understanding of basic geometric concepts and often rely on other geometric terms for precise definitions.

Learn more about geometry here:

https://brainly.com/question/31408211

#SPJ6

Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one fourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7

Answers

1/4x + 2 = 2x - 7.....this has been broken down...ur system of equations is : y = -1/4x + 2 and y = 2x - 7
-1/4x + 2 = 2x - 77 + 2 = 2x + 1/4x9 = 8/4x + 1/4x9 = 9/4x9 * 4/9 = x4 = x
y = 2x - 7y = 2(4) - 7y = 8 - 7y = 1
solution is : -1/4x + 2 = 2x - 7 letter c

The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance.

Answers

The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called the partitioning variance. This is used in the statistical tool ANOVA- between groups variance. It is abbreviated to SSB which means the sum of squares between groups.

The Jurassic Zoo charges $14 for each adult admission and $9 for each child. The total bill for the 214 people from a school trip was $2081. How many adults and how many children went to the zoo?

Answers

a=adult

c=child

a+c=214

c=214-a

9c+14a=2081

9(214-a)+14a=2081

1926-9a+14a=2081

5a=155

a=155/5=31

31 adults

183 children

check

31*14 = 434

183*9=1647

1647+434=2081

In Ellen's math class, there are 2 boys for every 3 girls . What is the the following ratio of boys to girls in the class ?
A . 17/21
B . 14/21
C . 7/14
D. 11/17

Answers

Based on the ratio of boys/girls We can infer that the only possibility for Ellen's math class would be answer B. 14/21

Dennis ran a mile in 593.7 seconds. Martina ran a mile in 573.36 seconds. What was the difference in their running times ?
A . 5.14 seconds
B . 6.01 seconds
C . 20.34 seconds
D . 26.01 seconds

Answers

The answer would be C.20.34

Choose the fraction that goes in the blank? 1/2 < _ < 4/5

I don't understand how they got 2/3

Answers

2/3 works here because its value is greater than 1/2 but less than 4/5. An easy way to visualize this is to take the decimal value of each number as decimals are often easier to understand than fractions.

1/2=.50
2/3=.67
4/5=.80

This inequality could be rewritten as .50 < .67 < .80 and would have the same value.

1/2 < __ < 4/5

1/2 = 0.5
4/5 = 0.8

they got 2/3 because 2/3 = 0.66 and it falls in between 1/2 and 4/5.

The other answer choices obviously did not fall in the solution range

if I have 3 layers of 14 cases per layer of an item,how many total cases should I have

Answers

3 layer 14 cases multiply
3×14=42 cases

The total number of cases I should have is 42.

How many cases should I have?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

Total number of cases = number of layers x cases per layer

14 x 3 = 42

To learn more about multiplication, please check: https://brainly.com/question/3385014

#SPJ6

You are hiking on a trail that leads to the top of a mountain. At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet. What is your mean hourly change in elevation?

Answers

average rate=(change in height)/(change in time)

r=(4500-3700)/(4+12-12)

r=800/4

r=200 ft/hr

200 feet per hour.

Answer: 200 ft per hour

Step-by-step explanation:

Given : You are hiking on a trail that leads to the top of a mountain.

At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet.

The formula for the mean hourly change in elevation is :-

[tex]\dfrac{\text{Change in elevation}}{\text{Time in hours}}[/tex]

From the given information, the change in elevation=4500 ft-3700 ft= 800 ft

Time taken = 4 hours [From 12 pm to 4 pm]

Now, Mean hourly change in elevation=[tex]\dfrac{800}{4}=200[/tex]

Hence, the mean hourly change in elevation = 200 ft

At a certain time, the length of a rectangle is 5 feet and its width is 3 feet. At that same moment, the length is decreasing at 0.5 feet per second and the widthis increasing at 0.4 feet per second.

What is the length of the diagonal at that time?
How fast is the length of the diagonal changing? Is this length increasing or decreasing?

Answers

check the picture below

[tex]\bf r^2=x^2+y^2\implies 2r\cfrac{dr}{dt}=2x\cfrac{dx}{dt}+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{x\frac{dx}{dt}+y\frac{dt}{dt}}{r} \\\\\\ \cfrac{dr}{dt}=\cfrac{(5\cdot -0.5)+(3\cdot 0.4)}{\sqrt{34}}[/tex]

if it's a negative value, thus a negative rate, thus is decreasing, if it is a positive value, then increasing.

The diagonal is the hypotenuse of a 5 by 3 triangle.
d = (L^2 + W^2)^.5 = SQRT(34) or 34^.5
Taking the derivative of d:
d' = (1/2)(2LL' + 2WW')(L^2 + W^2)^(-.5)
Solving for d' given the L=5, L'=-.5, W=3, W'=+.4
yields d is decreasing at a rate of -2229 feet/sec.

(15+23)+7=15+(___+7)

Answers

23 hope this helps!!

the answer is 23....

estimate the product 731+207

Answers

The answer would be 938. So yeah

The estimated sum of 731 and 207 is 900.

I know this because...
- 731 is rounded to 700
- 207 is rounded to 200
- 700 + 200 = 900

Hope this helps! :)

A local hamburger shop sold a combined total of 693 hamburgers and cheeseburgers on Wednesday. There were 57 fewer fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday

Answers

693-57 = 636

636/2 = 318

cheeseburgers sold = 318

hamburgers sold = 318 + 57 = 375

To determine the number of hamburgers sold on a specific day, an equation is set up and solved to find the value of hamburgers. In this scenario, 375 hamburgers were sold on Wednesday.

The question is asking how many hamburgers were sold on a specific Wednesday given the total combined sales of hamburgers and cheeseburgers and that fewer cheeseburgers were sold than hamburgers. To find the number of hamburgers sold, we can set up a system of equations. Let's define H as the number of hamburgers and C as the number of cheeseburgers. From the information provided, we have the following equations:

H + C = 693 (Total sales of both types of burgers)C = H - 57 (There were 57 fewer cheeseburgers sold than hamburgers)

Substituting the second equation into the first gives us:

H + (H - 57) = 693

2H - 57 = 693

Adding 57 to both sides, we get:

2H = 693 + 57

2H = 750

Now divide both sides by 2:

H = 375

Therefore, 375 hamburgers were sold on Wednesday.

Other Questions

Can somebody help me on finding the constants if this experiment? When did jesus send the holy spirit to guide the church? Which of the following has helped preserve resources while cutting the demand for energy?A. water treated with chlorineB. energy efficient appliancesC. landfills rather than burning wasteD. legislation against the use of chlorofluorocarbons Your professor wants you to construct a phylogenetic tree of orchids. she gives you tissue from seven orchid species and one lily. what is the most likely reason she gave you the lily? Which of the following rifle sights provides magnification of the game animal which helps to ensure an accurate shot? A, Telescopic sight B, Aperture (peep) sight C, Open sightD, Binoculars When you mix negro and blanco, you get ________. A.rojo B.verde C.gris D.azul If tan y = 3 over y and cos x = y over z what is the value of sin x??A. sin x = 3/zB. sin x = 3yC. sin x = z/3D. sin x = 3z Negative reinforcement _____ the likelihood of a behavior being repeated, and positive punishment _____ the likelihood of a behavior being repeated. How writers from the harlem renaissance used irony to convey the message of incompleteness of the american dream? How to solve 19-4c=17? the question is............ The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing The nature of a volcanic eruption is determined largely by the ________ of the magma. The so-called "unalienable rights" found in the declaration of independence may also be described as _______ rights. Which is the following is responsible for the exchange of gases in a leaf John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use? In the case of __________, the supreme court held that police departments are allowed to regulate officer appearance. What would happen over the following fifty years if a fire burned off all of the vegetation in the area If a cone and a sphere have the same radius and the same height what is the relationship among the volumes of the two shapes The type of chemoreceptor responsible for our sense of smell is called a(n) ________. Steam Workshop Downloader