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2 years ago

Evaluate the double integral int int y^3 dA where D is the triangular region with vertices (0,1), (7,0) and (1,1).

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

7 0

Answer:

1/5

Step-by-step explanation:

Refer to the image for the region. I've chosen to "scan" the region horizontally for convenience sake, so x varies for values between the green and the red line, and y varies from 0 to 1.

The two lines have equations $x=7-6y$ (red line) and $x=7-7y$ (green line). Since we're integrating first with respect to x, it's easier to write the equation like that and not as $y=mx+q$ since they will become our new limits of integration

Our double integral will become

$\int \limits_0^1 \ \ \int \limits_{7-7y}^{7-6y}y^3dxdy = \int \limits_0^1 y^3x|\limits_{7-7y}^{7-6y} dy =\\\int \limits_0^1 y^3[(7-6y)-(7-7y)]dy = \int \limits_0^1y^3(y)dy =\\\int \limits_0^1 y^4dy =\frac15y^5|\limits_0^1=\frac15$

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bixtya [17]

Answer:

Cost of one roll of plain wrapping: $\$5$

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Step-by-step explanation:

Let be "p" the cost in dollars of one roll of plain wrapping paper and "h" the cost in dollars of one roll of holiday wrapping paper.

Based on the information given, we can set up this system of equations:

$\left \{ {{5p+13h=272} \atop {11p+16h=359}} \right.$

In order to solve it, we can use the Substitution method. The steps are:

1. Solve for "p" from the first equation:

$5p+13h=272\\\\5p=272-13h\\\\p=\frac{272-13h}{5}$

2. Substitute the above into the second equation and solve for "h":

$11(\frac{272-13h}{5})+16h=359\\\\598.4-28.6h+16h=359\\\\-12.6h=359-598.4\\\\h=\frac{-239.4}{-12.6}\\\\h=19$

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7 0

3 years ago

Help me with this problem please

padilas [110]

Answer:

The second one

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Can someone tell me what I did wrong here

Stels [109]

Answer:

should have divided it directly ........ maybe or it's just messy........ maybe

Step-by-step explanation:

..........

...........

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2 years ago

Which relation is not a function?

velikii [3]

Answer:

Step-by-step explanation:

That would be D because there is a repetition of x = -6.

-6 maps to -6, 5 and -5 which is not allowed in a function.

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3 years ago

Currently, Lupe and Hector are 61 and 67 years old, respectively. They have two daughters and a grandson, who are 37, 31 and 7 y

RSB [31]

Answer:

2 years

Step-by-step explanation:

We can check all the possibilities. Necessarily, Hector's age in years must be prime, then we consider the years when this happens and test for the other members of the family.

Hector is 67 years old, so in 25 years he will be 92 years old. The prime numbers between 67 and 92 are 71, 73, 79, 83 and 89.

When Hector is 71 years old, four years have passed the Lupe is 65 years old, so this case fails.

When Hector is 73 years old, six years have passed. Lupe is 67 years old, an their daughters and grandson are 43, 37 and 13 years old. All of these are prime numbers, therefore in this year the statement holds.

When Hector is 79, twelve years have passed. Then, the eldest daughter is 49, which is not a prime number thus this case fails.

When Hector is 83, sixteen years have passed, so Lupe is 77 which is not prime. This case fails too.

Finally, when Hector is 89, 22 years have passed. Lupe is 83, the daughters are 59 and 53 resp; the grandson is 29. All of these are primes, so the statement is true.

3 0

3 years ago