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2 years ago

What is the slope of the line that passes through the points (-2, 3) and (-14, -5) ? ( Write your answer in the simplest form.

Mathematics

1 answer:

Ronch [10]2 years ago

6 0

Answer:

⅔

Step-by-step explanation:

slope = (-5-3)/(-14+2) = -8/-12= ⅔

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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

(ASAPPP) The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the

prohojiy [21]

Answer:

The instantaneous velocity at $t = 2$ is $-6$ .

Step-by-step explanation:

We have the position as the function

$s(t) = -2 - 6t$

As we know that the velocity is the rate of change of position over time, so it is basically the derivative of the function.

so finding the derivate of $s(t) = -2 - 6t$

∴ $s'(t)=-6$

The instantaneous velocity at $t = 2$

$s'(2)=-6$

Therefore, the instantaneous velocity at $t = 2$ is $-6$ .

Please note that the negative value indicates the direction of movement, in this case, it would be backward.

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2 years ago

Make an equation that is equal to 2/3

wariber [46]

Answer:

Replace the 4 with a 3 to make the equation true

5 0

2 years ago

Read 2 more answers

Graph -2x = -60 please help I need to finish this assignment.

Cerrena [4.2K]

Answer:

-2x = -60

Isolate x and simplify.

2x = 60

x = 30

Straight vertical line through x=30.

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3 years ago

What is the area of the triangle?

liubo4ka [24]

Answer:

area of triangle : 1/2 x length x widht

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3 years ago