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

Answers

Answer 1

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

Our double integral will become

[tex]\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[/tex]

Evaluate The Double Integral Int Int Y^3 DA Where D Is The Triangular Region With Vertices (0,1), (7,0)

Related Questions

PLEASE HELP AND EXPLAIN (WILL MARK BRAINLYIST)
Figure JKLMN is a scaled version of PQRST. The two figures are shown below.
The scale factor of figure JKLMN to figure PQRST is 3:2. If KL = 27 cm and MN = 45 cm, what is the length of side ST?
A.
30 cm
B.
40.5 cm
C.
67.5 cm
D.
18 cm

Answers

Answer: the answer is 40.5 cm

Step-by-step explanation:

first your gonna want to look at the numbers given and then solve.

Need help with this geometry question.What is HK?

Answers

Answer:

Step-by-step explanation:

use a protractor if you have one or ask for one

Find the greatest common factor (GCF) of 12x and 18x3.

Answers

Answer:

the answer to that question is 6x squared.

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x and 18x3

first, simplify 18x3

12x and 54x

Now, cancel the x, we'll add it on in the end

12 and 54

Factor it!

(2 * 3 * 2) and (2 * 3 * 3 * 3)

2 and 3 remain common, so multiply = 6

Add on x from before.

6x is the answer.

Shahida has seen an eagle landing at the top of the tree in her backyard. She places a camera on a tripod a distance of 12 feet from the
trunk of the tree. She angles the camera to the top of the tree so she can get a picture of the eagle. The height of the tree is 31 feet. The
height of the tripod is 4 feet.

Answers

The angle of elevation from the tripod to the top of the tree is about 66 degrees

What is trigonometric ratio?

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle of elevation. Since the tripod is at a height of 4 feet, hence:

tanФ = (31 - 4) / 12

Ф = 66 degrees

The angle of elevation from the tripod to the top of the tree is about 66 degrees

Find out more on trigonometric ratio at: https://brainly.com/question/24349828

hello help me with this question thanks in advance

Answers

Answer:

B. 98 ft

Step-by-step explanation:

x^2 + y^2 = z^2

z = sqrt(84^2 + 50^2) = 97.7 ft ~ 98 ft

Question #5 Answer:

B. 98 feet

Step by-step explanation:

[tex]Solution:\ From\ question\\ 84\ feet\ long\ and\ 50\ feet\ wide\\ so\ he\ will\ run\ \sqrt{{84}^2+{50}^2}\ \approx98\ feet[/tex]

ratio of a rectangle's length to its width is 4:7. If the longer side is 31.5in., find the width, the perimeter, and the area of this rectangle.

Answers

Answer:

Step-by-step explanation:

Ratio of length : width = 4 : 7

Length = 4x

Width = 7x

Longer side = 31.5 in

⇒ 7x = 31.5

Divide both sides by 7

x = 31.5/7

x = 4.5

length = 4x

= 4*4.5

l = 18 in

width = 31.5

w = 31.5 in

[tex]\boxed{ \text {Perimeter of rectangle }= 2*l + 2*w}[/tex]

= 2*18 + 2*31.5

= 36 + 63

= 99 in

[tex]\boxed{ \text{Area of rectangle = l*w}}[/tex]

= 18*31.5

= 567 in²

jan saw 9 full moons in 252 days write each statement as a rate

Answers

i honestly don’t know sorry

Is ABSE- ATES? If so, identify the similarity postulate or theorem that
applies.

Answers

Hope it helps best of luck

6 8/10 + 1 7/10 =
please help meee

Answers

Answer:

8.2

Step-by-step explanation:

Hope this helps....

Answer:

The answer is 8 1 / 2

Step-by-step explanation:

See the Image

Option 1 is easier to understand

Whcih choice best describes the group this shape belongs in, based on the kinds of sides and angles it has? Angela chose A as the correct answer. How did she get that answer?

Answers

The shape in the figure has 6 sides

The choice that describes the group the shape belongs to is (a) parallel sides, acute angles

How to determine the group of the shape?

From the figure, we have the following highlights

The shape has 6 sidesThe direct opposite sides are equalThe direct opposite sides are parallelThe measure of angles between adjacent sides are less than 90 degrees i.e. acute angles

The above highlight mean that:

The shape belongs to parallel sides, acute angles group of shapes

Hence, Angela's conclusion is correct

Answers

Answer:

please see photo for details

Select ALL the expressions that have the same value as the expression 0.5 ÷ 0.25
A. 1,200 ÷ 60
B. 1.2 ÷ 0.6
C. 0.012 ÷ 0.06
D. 2.5 ÷ 2.25
E. 0.05 ÷0.025

Answers

Answer:

B and E

Step-by-step explanation:

0.5 ÷ 0.25 = 2

A. NO because it's 20

B. Yes

C. NO because it's 0.2

D. NO because it's 1.1 repeating

E. Yes

what is a question that is easier to answer using a stem-and-leaf plot than a dot plot?

Answers

Answer:

steam plot

Step-by-step explanation:

because the stem plot is easy to use

Answer:

When you use large numbers and don't have categories.

Step-by-step explanation:

Take these: 23, 27, 29, 35, 36, 41, 47, 48, 52. It is better as a stem and leaf.

---------------------------------------------------------------------------------------------------------

2 ][ 3 7 9

3 ][ 5 6

4 ][ 1 7 8

5 ][ 2

---------------------------------------------------------------------------------------------------------

If you use dot plot, it is recommended use amounts under 10.

Darren's rectangle measures 3 1/4 units by 4 1/3 units. what is its area

area = ? ?/?

Answers

Answer:

14 1/13

Step-by-step explanation:

13/4*13/3=169/12=14 1/13

The hypotenuse of a triangle is 10 inches long. One of the legs is 6.5 inches long. what is the measurement of the missing leg? round to the nearest tenth, if necessary

Answers

Answer:

7.6

Step-by-step explanation:

a^2 + b^2 = c^2

6.5^2 + x^2 = 10^2

42.25 + x^2 = 100

isolate x by subtracting 42.25 on both sides

x^2 = 57.75

square root of 57.75 or 7.6

a family makes gumbo to serve during jazz fest.the gumbo recipe requires twice as many cups of chopped tomatoes as diced onions.Which expression can be used to represent the number of cups of diced onions based on the number of cups of chopped tomatoes,t?
A) t^2
B)2+t
C) t÷2
D)2t

Answers

Answer:

D: 2t

Step-by-step explanation:

a coefficient next to a variable is an automatic multiplication equation

The solution is Option D.

The number of cups of diced onions A to the number of cups of chopped tomatoes t is represented by the equation A = 2t

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = total number of cups of diced onions

Let the total number of cups of chopped tomatoes be = t

Now , the recipe requires twice as many cups of chopped tomatoes as diced onions

Substituting the values in the equation , we get

A = 2t

where A = number of cups of diced onions

t = number of cups of chopped tomatoes

Therefore , the value of A is 2t

Hence ,

The equation will be A = 2t where t is the number of cups of tomatoes

To learn more about equations click :

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#SPJ2

simplify the expression 30x^6/3x^-2

Answers

Answer:

[tex]30x^{4}[/tex]

Step-by-step explanation:

Which equation represents the graphed function?

-3x + 2 = y
-2/3x+2=y
3/2x-3=y
2x-3 = y

Answers

The linear equation that represents the graph is 3/2x - 3 = y

Data;

-3 + 2 = y-2/3x + 2 = y3/2x - 3 = y2x - 3 = y

Linear Equation

From the given graph, we can see at the x-axis that the line touches at point 2 and at the y-axis, the line touches at point 3.

If we decide to multiply through by 3 to eliminate the fraction, the equation would look like this.

[tex]\frac{3x}{2} -3 = y\\2(\frac{3x}{2}) -3(2) = 2(y)\\3x - 6 = 2y[/tex]

Kindly find the attached image of the graph.

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Which number is bigger: 0.135 or 0.14?

Answers

0.14 is the correct answer

A rectangular prism has a length of 12 meters, a width of 3 meters, and a height of
meters
Enter the volume of the prism as a mixed number in simplest form in the box
meters

Answers

Answer:

Volume of Prism = 1/2×h×l×b

I think the formula will help you.

There is no Height, I think question is incomplete

Find the values of x for which the denominator is equal to zero for 2x^2+5/x^2-2x .

x = 0, x = 2

x = 1, x = 2

none

x = 2

Answers

Let's see

[tex]\\ \rm\rightarrowtail x^2-2x=0[/tex]

[tex]\\ \rm\rightarrowtail x(x-2)=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x-2=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x=2[/tex]

꧁⫷ᴀɴsᴡᴇʀ⫸꧂

[tex] \green{••••••••••••••••••••••} \blue{••••••••••••••••••••••••••}[/tex]

[tex] \sf {x^2 - 2x = 0} [/tex]

[tex] \sf {x ( x - 2) = 0} [/tex]

[tex] \sf {x = 0 \: or \: x-2 = 0} [/tex]

[tex] \sf \green{ {x = 0 \: or \: x = 2}} [/tex]

#CarryOnLearning

#LibreAngMatuto

Express the set using interval notation.
x≥1

Answers

Answer:

[1,∞)

Step-by-step explanation:

Brackets indicate equal to while parentheses indicate not equal to this bound.

axis of symmetry f(x) = −4(x − 8)^ 2 + 3

Answers

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

For an equation in the form of [tex]y=a(x-h)^2+k[/tex], the axis of symmetry is where [tex]x=h[/tex]. In this case, the axis of symmetry is the line [tex]x=8[/tex]

prove that it is congruent

Answers

Answer:

The dashes on the side lengths mean that they are equal in length
⇒ PQ = RP

The triangles share one side PS

The figure also states that m∠QPS = m∠RPS

Therefore, the triangles are SAS congruent since they have two pairs of congruent sides and a congruent included angle.

Need help with this geometric question ASAP, Thank you

Answers

The error would be assuming the altitude is a bisector and divides the sides evenly.

[tex]x^{2} -36\frax+5/(x+6)[/tex]

Answers

the answer is

x^{2}-31x+5b

If 6/10 is multiplied by a fraction less than one what will be the product?

Answers

Answer:

If 6/10 is multiple by a fraction less then one the product would be 1/2

Step-by-step explanation:

6/10 is also equal to 0.6

If 0.6 is multipled by something less then one the product would not be able to be greater then 6/10

Resulting in 1/2 being the product.

Answer: All you gotta do is multiply 6x10 and then u get 60 so the product of of 6/10 is 60

What is the equation of a circle with center (−8, 3) and radius 8?

(x + 8)2 + (y − 3)2 = 64

(x − 8)2 + (y + 3)2 = 64

(x − 8)2 + (y + 3)2 = 8

(x + 8)2 + (y − 3)2 = 8

Answers

Answer:

(x + 8)² + (y - 3)² = 64

Step-by-step explanation:

(x - (-8))² + (y - 3)² = 8²

(x + 8)² + (y - 3)² = 64

Jayla just measured her pet snake and found out that it is 3.8 inches long, which is 52% longer than the last time Jayla measured. How long was the pet snake last time?

Answers

Let x be the original length.
x * (1+0.52) = 3.8
x * 1.52 = 3.8
x = 2.5 inches

Select the correct answer.
Which of the equations below represents a line perpendicular to the x-axis?
OA
I = 3
OB.
= = 3y
Зу
Ос.
1 = Y
=
OD
r = -3y

Answers

Answer:

0D r equals -3y

hope ts helpful

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