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3 years ago

What is the equation of a circle with center (-4,7) and radius 8?

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

6 0

The equation of the circle would be (x−(−4))2+(y)2=6or (x+4)2+(y−72=36.

Explanation:The equations of the circle is(−h)2+y−k)2=r2

where h is the x of the center of the circle and k is the y of the center of the circle, and r is the radius(-4,7) radus is 6h = -4k = 7r = 6plug in the values(x−(−4))2+(y−7)2=62simplify(x+4)2+(y−7)2=36.

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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

There are 96 strawberries in a basket. Each of the 12 children received an equal number of strawberries. Which equation gives s,

MAXImum [283]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Since the expression (x-4)^2+(y+1)^2 evaluated at (3,6) is

stiks02 [169]

$\bf (x-4)^2+(y+1)^2\qquad (3,6)~~ \begin{cases} x = 3\\ y = 6 \end{cases}\implies (3-4)^2+(6+1)^2 \\\\\\ (-1)^2+7^2\implies 1+49\implies 50$

5 0

3 years ago

Divide.<br>(3x4 - 3x2 - 6x - 10) = (x - 2)

alekssr [168]

Answer:

3x^3 + 6x^2 + 15x + 36 + 62 / 3x^4 +3x^2 +6x + 10

Step-by-step explanation:

Use Syenthetic Division

4 0

3 years ago

Some number added to seventeen

Oksanka [162]

Answer:

x+17

Step-by-step explanation:

x + 17 is the answer

5 0

4 years ago