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3 years ago

What are the domain and points of discontinuity of y= x-4/x^2+8x-20? What are the x and y intercepts?

Mathematics

1 answer:

aleksklad [387]3 years ago

7 0

Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x.

x-intercept(s): (2.30581496,0)

y-intercept(s): None

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Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.

skad [1K]

Answer:

The absolute maximum and minimum is $20\; \text{and} -20.$

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

$f_x=y-4=0$

$f_y=x=0$

The only solution to this system of equations is the point (0, 4), which lies in the domain.

$f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1$

$\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1$

$\therefore (0,4)$ is a saddle point.

Boundary points - $(4,0), (-4,0), (0,16)$

Along boundary $y=16-x^2$

$f=x(16-x^2)-4x$

$=16x-x^3-4x$

$\Rightarrow f^'=16-3x^2-4=0$

$\Rightarrow 3x^2=12$

$\Rightarrow x=\pm2,\;\;y=14$

Values of f(x) at these points.

$\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}$

Therefore, the absolute maximum and minimum is $20\; \text{and} -20.$

6 0

3 years ago

CAN SOMEONE MULTIPLY THIS PLEASE, ITS URGENT

____ [38]

Let's factorise it :

$\: {\qquad \dashrightarrow \sf ( {x}^{3} - 5)(x + 3) }$

$\: {\qquad \dashrightarrow \sf {x}^{3} (x + 3) + [-5(x + 3)] }$

Using Distributive property we get :

$\: {\qquad \dashrightarrow \sf {x}^{3} + {3x}^{3} + ( - 5x - 15) }$

$\: {\qquad \dashrightarrow \sf {x}^{3} + {3x}^{3} - 5x - 15 }$

$\: {\qquad \dashrightarrow \sf 4{x}^{3} - 5x - 15 }$

⠀

Therefore,

$\: {\qquad \dashrightarrow \sf ( {x}^{3} - 5)(x + 3) =4{x}^{3} - 5x - 15}$

8 0

2 years ago

5. Enter the answer as a decimal

Hitman42 [59]

Answer:

6.5%

Step-by-step explanation:

I = prt

5616 = 7200 × r × 12

r = 5616/(7200 × 12)

r = 0.065

r = 6.5%

5 0

2 years ago

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT. Find m2C in the quadrilateral.

saul85 [17]

Answer:

m∠C = 107°

Step-by-step explanation:

there are 4 sides so we first need to find the total interior angle:

( 4 - 2 ) * 180 = 360°

m∠C = 360° - 90° - 90° - 73°

= 107°

8 0

3 years ago

2/3 : 1 in its simplest form

slamgirl [31]

Answer:

2 : 3

Step-by-step explanation:

You need to show the ratio using the smallest whole numbers possible.

Multiply both numbers by 3.

2/3 : 1

2/3 × 3 : 1 × 3

2 : 3

5 0

2 years ago