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vagabundo [1.1K]

3 years ago

14

Find the extreme values of the function f(x,y)=5x2−1y2−2y subject to the constraint 5x2 1y2=1.

1 answer:

KatRina [158]3 years ago

3 0

You just have to get x and y by themselves so solve and plug in

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Y=x^2+3x-4 and y=4x-4

sweet [91]

The answer is (0,-4),(1,0)

8 0

3 years ago

The endpoints of a diameter of a circle are (6,2) and (−2,5) . What is the standard form of the equation of this circle?

Paul [167]

Answer:

The standard form of the given circle is

$(x-2)^2+(y-\frac{7}{2})^2=73$

Step-by-step explanation:

Given that the end points of a diameter of a circle are (6,2) and (-2,5);

Now to find the standard form of the equation of this circle:

The center is (h,k) of the circle is the midpoint of the given diameter

midpoint formula is $M=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

Let $(x_{1},y_{1})$ and $(x_{2},y_{2})$ be the given points (6,2) and (-2,5) respectively.

$M=(\frac{6-2}{2},\frac{2+5}{2})$

$M=(\frac{4}{2},\frac{7}{2})$

$M=(2,\frac{7}{2})$

Therefore the center (h,k) is $(2,\frac{7}{2})$

now to find the radius:

The diameter is the distance between the given points (6,2) and (-2,5)

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

$=\sqrt{(-2-6)^2+(5-2)^2}$

$=\sqrt{(-8)^2+(3)^2}$

$=\sqrt{64+9}$

$=\sqrt{73}$

Therefore the radius is $\sqrt{73}$

i.e., $r=\sqrt{73}$

Therefore the standard form of the circle is

$(x-h)^2+(y-k)^2=r^2$

Now substituting the center and radiuswe get

$(x-2)^2+(y-\frac{7}{2})^2=(\sqrt{73})^2$

$(x-2)^2+(y-\frac{7}{2})^2=73$

Therefore the standard form of the given circle is

$(x-2)^2+(y-\frac{7}{2})^2=73$

5 0

3 years ago

Use distributive property to evalúe 3(78) show all steps !

Semmy [17]

Answer: 234

Step-by-step explanation: 78 * 3 = 210 + 24 = 234

3 0

2 years ago

Fill in the blanks to write the solutions to the quadratic equation. x2 + 2x + 10 = 0

Arada [10]

X2 + 2x + 10 =0
Can also be written as 2x +2x + 10 =0
4x + 10 =0
4x = -10
x= -10/4
x= -5/2

8 0

3 years ago

A sine function has the following key features:

il63 [147K]

Try the suggested solution with short explanation; red line means the curve between the first point (on the midline) and the closest maximum; the - - - - line means the curve between the first point (on the midline) and the closest minimum.

8 0

3 years ago