"What is the input value for which f (x) = 3?" <br><br> Please Help!!!!! URGENT!!!

Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2)

Leya [2.2K]

he volume of the solid under a surface

z

=

f

(

x

,

y

)

and above a region D is given by the formula

∫

D

f

(

x

,

y

)

d

A

.

Here

f

(

x

,

y

)

=

6

x

y

. The inequalities that define the region D can be found by making a sketch of the triangle that lies in the

x

y

−

plane. The bounding equations of the triangle are found using the point-slope formula as

x

=

1

,

y

=

1

and

y

=

−

x

3

+

7

3

.

Here is a sketch of the triangle:

Intersecting Region

The inequalities that describe D are given by the sketch as:

1

≤

x

≤

4

and

1

≤

y

≤

−

x

3

+

7

3

.

Therefore, volume is

V

=

∫

4

1

∫

−

x

3

+

7

3

1

6

x

y

d

y

d

x

=

∫

4

1

6

x

[

y

2

]

−

x

3

+

7

3

1

d

x

=

3

∫

4

1

x

[

y

2

]

−

x

3

+

7

3

1

d

x

=

3

∫

4

1

x

[

49

9

−

14

x

9

+

x

2

9

−

1

]

d

x

=

3

∫

4

1

40

x

9

−

14

x

2

9

+

x

3

9

d

x

=

3

[

40

x

2

18

−

14

x

3

27

+

x

4

36

]

4

1

=

3

[

(

640

18

−

896

27

+

256

36

)

−

(

40

18

−

14

27

+

1

36

)

]

=

23.25

.

Volume is

23.25

.

4 0

3 years ago

Which number sentence is true?A.-1.5 + (-0.5) = 2.0B.2.5 + (-1.5) = 1.0C.-1.5 + (-0.5) = -1.0D.-2.5 + 3.5 = -1.0

Anni [7]

Answer: B

Step-by-step explanation: the other ones are wrong.

4 0

3 years ago

Find the center of the circle whose equation is x² + y² = 4.

Varvara68 [4.7K]

Answer:

The center of circle is $(0,0)$

Step-by-step explanation:

We need to find the center of the circle of the equation $x^{2}+y^{2}=4$

Since, the general equation of circle is $(x-h)^{2}+(y-k)^{2} = r^{2}$

Where (h,k) is center of circle and r is radius.

Re-write the circle equation is $x^{2}+y^{2}=4$ as,

$x^{2}+y^{2}=2^{2}$

Compare $x^{2}+y^{2}=2^{2}$ with $(x-h)^{2}+(y-k)^{2} = r^{2}$

so, $(x-0)^{2}+(y-0)^{2} = 2^{2}$

Hence, the center of circle is $(0,0)$

4 0

3 years ago

Read 2 more answers

If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will

tiny-mole [99]

0 = -16t² + 36t + 4
0 = -8t² + 18t + 2 ← Complete the square to solve
-8(t² - 9t/2) = -2
8(t² - 9t/4 + 81/64) = 2 + 81/8
8(t - 9/8)² = 97/8
(t - 9/8)² = 97/64
t - (t = 0)
(h = 0) at:
<span>t = (9 + √97)/8 ≅ 2.356 seconds
</span>

3 0

3 years ago

Read 2 more answers

Please help me fast!!!. Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and

Nikolay [14]

Answer:

11:10 am.

Step-by-step explanation:

The first thing I'm going to do is to add all the given time together

Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping

Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes

Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes

Total time = 5 hours + 35 minutes

The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping

Time = total time + time spent driving

Time = 5 hours 35 minutes + 35 minutes

Time = 6 hours and 10 minutes

Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer

Needed time = dinner time - time

Needed time = 5:10 pm - 6:10

Needed time = 17:10 - 6:10

Needed time = 11:10

This means that they ought to start their tour by 11:10 am, so that they can meet their dinner

7 0

3 years ago

"What is the input value for which f (x) = 3?" Please Help!!!!! URGENT!!!