1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Radda [10]
3 years ago
9

Find the volume of the region bounded above by the paraboloid z equals 3 x squared plus y squared and below by the square R: min

us 1 less than or equals x less than or equals 1 comma negative 1 less than or equals y less than or equals 1.

Mathematics
1 answer:
RideAnS [48]3 years ago
5 0

Answer:

V=5.333cubit unit

Step-by-step explanation:

this problem question, we are required to evaluate the volume of the region bounded by the paraboloid z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1

The question can be interpreted as z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1 and we are told to evaluate the volume of the region bounded by the given paraboloid z

The volume V of integral evaluated along the limits of x and y for the 2-D figure, can be evaluated using the expression below

V = ∫∫ f(x, y) dx dy then we can now substitute and integrate accordingly.

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION:

You might be interested in
The graph below represents the solution set of which inequality?
natulia [17]

Answer:

option: B (x^2+2x-8) is correct.

Step-by-step explanation:

We are given the solution set as seen from the graph as:

(-4,2)

1)

On solving the first inequality we have:

x^2-2x-8

On using the method of splitting the middle term we have:

x^2-4x+2x-8

⇒  x(x-4)+2(x-4)=0

⇒ (x+2)(x-4)

And we know that the product of two quantities are negative if either one of them is negative so we have two cases:

case 1:

x+2>0 and x-4

i.e. x>-2 and x<4

so we have the region as:

(-2,4)

Case 2:

x+2 and x-4>0

i.e. x<-2 and x>4

Hence, we did not get a common region.

Hence from both the cases we did not get the required region.

Hence, option 1 is incorrect.

2)

We are given the second inequality as:

x^2+2x-8

On using the method of splitting the middle term we have:

x^2+4x-2x-8

⇒ x(x+4)-2(x+4)

⇒ (x-2)(x+4)

And we know that the product of two quantities are negative if either one of them is negative so we have two cases:

case 1:

x-2>0 and x+4

i.e. x>2 and x<-4

Hence, we do not get a common region.

Case 2:

x-2 and x+4>0

i.e. x<2 and x>-4

Hence the common region is (-4,2) which is same as the given option.

Hence, option B is correct.

3)

x^2-2x-8>0

On using the method of splitting the middle term we have:

x^2-4x+2x-8>0

⇒ x(x-4)+2(x-4)>0

⇒ (x-4)(x+2)>0

And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:

Case 1:

x+2>0 and x-4>0

i.e. x>-2 and x>4

Hence, the common region is (4,∞)

Case 2:

x+2 and x-4

i.e. x<-2 and x<4

Hence, the common region is: (-∞,-2)

Hence, from both the cases we did not get the desired answer.

Hence, option C is incorrect.

4)

x^2+2x-8>0

On using the method of splitting the middle term we have:

x^2+4x-2x-8>0

⇒ x(x+4)-2(x+4)>0

⇒ (x-2)(X+4)>0

And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:

Case 1:

x-2 and x+4

i.e. x<2 and x<-4

Hence, the common region is: (-∞,-4)

Case 2:

x-2>0 and x+4>0

i.e. x>2 and x>-4.

Hence, the common region is: (2,∞)

Hence from both the case we do not have the desired region.

Hence, option D is incorrect.




5 0
3 years ago
What are the two representations of the conversion factor used to convert between inches and feet? Select all that apply.
ipn [44]
B and C are the same thing and they would be the two representations of the conversion that shows 12 inches is equivalent to 1 foot, so B and C are your answers
6 0
3 years ago
No Explanation Please Don't Answer
vazorg [7]

Answer:

A) \frac{1}{2}(9+15)w

Step-by-step explanation:

Area of a trapezoid is \frac{1}{2}(base1+base2) *h

A=\frac{1}{2}(9+15)*w

8 0
2 years ago
Type SSS, SAS, ASA, SAA, or HL to
Tems11 [23]

9514 1404 393

Answer:

  ASA

Step-by-step explanation:

The shared angle, the marked angle, and the marked sides between those angles are congruent. That is, you have congruent Angle, Side, Angle, so the ASA postulate applies.

6 0
3 years ago
how many ninths does it take to make the same amount as 1/3.Explain your answer in words and pictures
docker41 [41]
The answers is 3/9 which you can check by reducing.  It reduces to 1/3.  Basically you go 1/3 = x/9 then cross multiple to get 9=3x do the division so 3x/3 and 9/3 and you get 3/9.
5 0
3 years ago
Other questions:
  • What is the value of n?<br> 121 144
    7·1 answer
  • How would you write 17/7 as a repeating decimal
    8·2 answers
  • Add. Simplify the answer to lowest terms before entering the numerator and denominator in their boxes. 47/148+29/148
    14·2 answers
  • After working for 24 hours,zoe made $234. After working for 40 hours, zoe made $390.predict how much she would make after 10 hou
    7·1 answer
  • Solve for x. x = log5 1 x =
    9·1 answer
  • I'LL GIVE BRAINLIEST. PLEASE HELP, IM BEGGIN U
    7·2 answers
  • Im on a girls basketball team , 3 are in sixth grade , 5 are in seventh grade , and 6 are in eighth grade . so which is the rati
    11·1 answer
  • Simplify the expression 7g+4p-3g-9p
    11·2 answers
  • Which equation is true when n = 4<br> a. 2n = 6<br> b. n + 3 = 7<br> c. 9 - n = 13<br> d. n/12 = 3
    13·2 answers
  • Help i give 5 stars and a crown​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!