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3 years ago

−6−1.5(4b+8)=3(−6−2b)

Mathematics

1 answer:

____ [38]3 years ago

4 0

Answer:

-18 = -18 It is true.

Step-by-step explanation:

-6 -1.5(4b+8) = 3(-6 -2b)

-6 -6b - 12 = -18 -6b

-6b -18 = -18 -6b

+6b +6b

-18 = -18

It is true.

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Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

Looks like $f(x,y)=x^2+y^2-x^2y+7$ .

$f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1$

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

The latter two critical points occur outside of $D$ since $|\pm\sqrt2|>1$ so we ignore those points.

The Hessian matrix for this function is

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}$

The value of its determinant at (0, 0) is $\det H(0,0)=4>0$ , which means a minimum occurs at the point, and we have $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

$f(-1,y)=8-y+y^2$

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

If $y=-1$ , then

$f(x,-1)=2x^2+8$

which has 3 extreme values, but the previous cases already include them.

Hence $f(x,y)$ has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

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3 years ago

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IrinaVladis [17]

Answer:

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Step-by-step explanation:

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Mia bought 2 adult tickets and 4 kid's tickets. Each adult ticket cost $13.50 and each kid ticket cost $10.25. How much did Mia

Citrus2011 [14]

Answer:

Mia spent 68 dollars.

Step-by-step explanation:

The equation would be 2(13.50) + 4(10.25) = x

Solving for the first part, you get 27 for adult tickets and 41 for the children tickets. When you add the two values, you get 68.

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What is the density of an object that has a mass of 20 grams and has a length of 8cm and a width of 2cm and a height of 5cm????

Evgen [1.6K]

Answer:

Volume is the amount of space an object occupies. To determine the volume of any rectangular object, multiply the measurements of length, width, and height.

Volume = Length × Width × Height

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Volume = l × w × h

Volume = 3 cm × 3 cm × 12 cm

Volume = 108 cm3

Notice that the units for volume are cubic centimeters (cm3).

So 8 ÷ 25 = 0.32 and the units would be g/ cm3 . Other units of density could be g/L or g/ml or mg/ cm3 or kg/ m3 and the list could go on and on. Any unit of mass divided by any unit of volume.

Step-by-step explanation:

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3 years ago

Solve the equation in the image

Margaret [11]

Answer: 55

Step-by-step explanation:

$\sqrt[3]{4x-4}=6$