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3 years ago

Let f(x, y) = (x + y)e x 2−y 2 and R be the rectangle enclosed by the lines x − y = 0, x − y = 2, x + y = 0, and x + y = 3.

Mathematics

1 answer:

dalvyx [7]3 years ago

7 0

Answer:

(1/4)*(e⁶ - 7)

Step-by-step explanation:

a) Given

x − y = 0 if x = 0 ⇒ y = 0

x − y = 2 if x = 0 ⇒ y = -2; if y = 0 ⇒ x = 2

x + y = 0 if x = 0 ⇒ y = 0

x + y = 3 if x = 0 ⇒ y = 3; if y = 0 ⇒ x = 3

then we show the region R in the pics 1 and 2.

b) We make the change of variables as follows

u = x + y

v= x - y

x - y = 0 ⇒ v = 0

x − y = 2 ⇒ v = 2

x + y = 0 ⇒ u = 0

x + y = 3 ⇒ u = 3

Where u is the horizontal axis and v is the vertical axis, the new region S is shown in the pic 3.

c) We evaluate ∫∫R (x + y)*e∧(x² - y²)dA

The procedure is shown in the pic 4, where we have to calculate the Jacobian in order to use it to get the answer.

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2 years ago

Please help me its about solving system by substitution

Andrew [12]

Answer:

(-3, 4)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
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Addition
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Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Terms/Coefficients
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y = -x + 1

2x + 3y = 6

Step 2: Solve for x

Substitution

Substitute in y: 2x + 3(-x + 1) = 6
Distribute 3: 2x - 3x + 3 = 6
Combine like terms: -x + 3 = 6
Isolate x terms: -x = 3
Isolate x: x = -3

Step 3: Solve for y

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6 0

2 years ago

52 ( Blank ) 2 ( Blank ) 31 = 73

nadezda [96]

Answer:

52 × 2 - 31 = 73

Step-by-step explanation:

Use PEMDAS

The way I remember is like this..

Please (Parentheses)

Excuse (Exponents)

My (Multiication)

Dear (Division)

Aunt (Addition)

Sally (Subtraction)

Multiply 52 × 2

which gives you 104.

Then subtract 31 from 101

and that will give you 73.

6 0

3 years ago

A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i

mars1129 [50]

Answer:

The absolute change in the height of the water is 9.5 inches

Step-by-step explanation:

Given

$l =24in$ --- length

$w = 15in$ --- width

$h =12in$ --- height

$V_1 = 900in^3$ --- the volume removed

Required

The absolute change in the height of the water

First, calculate the base area (b):

$b = l * w$

$b =24in * 15in$

$b =360in^2$

The height of the water that was removed is:

$H = \frac{V_1}{b}$ i.e. the volume of the water removed divided by the base area

$H = \frac{900in^3}{360in^2}$

$H = \frac{900in}{360}$

$H = 2.5in$

The absolute change in height is:

$\triangle H = |h - H|$

$\triangle H = |12in - 2.5in|$

$\triangle H = |9.5in|$

$\triangle H = 9.5in$

8 0

2 years ago

What is the solution to the system of equations shown below?

Alexxandr [17]

Answer:

b. (1, 3, -2)

Step-by-step explanation:

A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.

It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:

a: -1 -5(1) +2(-4) = -14 ≠ -18

b: 1 -5(3) +2(-2) = -18 . . . . potential choice

c: 3 -5(8) +2(1) = -35 ≠ -18

d: 2 -5(-3) +2(0) = 17 ≠ -18

This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:

2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1

-(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2

7 0

3 years ago