Graph the image of the given triangle under a dilation with a scale factor of 12 and center of dilation (0, 0)

At what value of x does the graph of the following function F(x) have a

Free_Kalibri [48]

Answer:

B

Step-by-step explanation:

Given

f(x) = $\frac{1}{x+2}$

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

x + 2 = 0 ⇒ x = - 2

The equation of the vertical asymptote is x = - 2

6 0

3 years ago

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

Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another br

Serggg [28]

Answer:

dA/dt = 12 - 2A/(100 + t)

Step-by-step explanation:

The differential equation of this problem is;

dA/dt = R_in - R_out

Where;

R_in is the rate at which salt enters

R_out is the rate at which salt exits

R_in = (concentration of salt in inflow) × (input rate of brine)

We are given;

Concentration of salt in inflow = 4 lb/gal

Input rate of brine = 3 gal/min

Thus;

R_in = 4 × 3 = 12 lb/min

Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min

So, after t minutes, there will be (100 + t) gallons in the tank

Therefore;

R_out = (concentration of salt in outflow) × (output rate of brine)

R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min

R_out = 2A(t)/(100 + t) lb/min

So, we substitute the values of R_in and R_out into the Differential equation to get;

dA/dt = 12 - 2A(t)/(100 + t)

Since we are to use A foe A(t), thus the Differential equation is now;

dA/dt = 12 - 2A/(100 + t)

5 0

3 years ago

Is this an acute,obtuse or reflex angle

Ludmilka [50]

It will be a reflex angle

A reflex angle is an angle that is more than 180° and less than 360°

Obtuse: More than 90° but Less than 180°
Acute: Less than 90°

5 0

1 year ago

Read 2 more answers

The total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. If there are

mariarad [96]

Answer:

I think there are 23 students in the art class.

Step-by-step explanation:

You first subtract 9 from 101. Then, you divide by four to get 23.

4 0

3 years ago

Graph the image of the given triangle under a dilation with a scale factor of 12 and center of dilation ​ (0, 0)

Graph the image of the given triangle under a dilation with a scale factor of 12 and center of dilation (0, 0)