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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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$cos (30) = \frac{a}{c}$

Where,

a: apothema of the hexagon

c: Hexagon radius.

Clearing the radio we have:

$c = \frac{a}{cos (30)}$

Substituting values:

$c = \frac{12}{cos (30)} c = 13.85$

Rounding to the nearest whole number we have:

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Answer:

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7 0

2 years ago

Read 2 more answers

A newspaper is conducting a statewide survey concerning the race for governor. The newspaper will take a simple random sample of

katen-ka-za [31]

Answer:

Larger sample size gives less std error and hence test statistic is larger.

Step-by-step explanation:

Given that a newspaper is conducting a statewide survey concerning the race for governor. The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate. Is there evidence that a clear majority of the population will vote for the Democratic candidate

Group I II

Success 640 64

Total 1200 120

p 0.533333333 0.533333333

q 0.466666667 0.466666667

se 0.014401646 0.045542003

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3 0

2 years ago

Round each factor to the nearest ten to estimate the product of 34 . 39

aev [14]

Answer:

Round 34 down to 30 then round 39 up to 40

Step-by-step explanation:

34 ⟶ 30 34 is rounded down to 30

39 ⟶ 40 39 rounded up to 40

34 ⟶ 30

39 ⟶ 40

34 is rounded down to 30

39 rounded up to 40

Calculate mentally 34 × 39 = 1326

The estimated product is 1326.

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2 years ago

PJ will begin her cake deliveries at 12:20 . She asked to remind her 30 minutes before she has to leave. What time should I remi

mojhsa [17]

Answer:

At 11:50

Step-by-step explanation:

1. Subtract the hours and the minutes separately

12: 20

- 0: 30

12: -10

2. If the minutes are negative, subtract 1 from the hours and add 60 to the minutes.

12: -10

- 1: + 60

11: 50

You should remind PJ about her deliveries at 11:50.

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3 years ago

Write an equation in slope-intercept form for this line.

sineoko [7]

Answer:

y = $\frac{3}{2}$ x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = $\frac{3}{2}$ , then

y = $\frac{3}{2}$ x + c ← is the partial equation

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2 years ago