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3 years ago

Determine whether each quadrilateral is a parallelogram rectangle rhombus and Dory Square list of all that apply.

Mathematics

1 answer:

jeka943 years ago

3 0

Answer: see below

<u>Step-by-step explanation:</u>

(1)

$a)\quad EF = 3\sqrt2,\quad FG = 3\sqrt2,\quad GH = 3\sqrt2,\quad HE = 3\sqrt2$

b) FH = 6, EG = 6

c) Square (which means it is also a rectangle and parallelogram)

(2)

$a)\quad m_{EF}=3,\quad m_{FG}=-\dfrac{1}{2},\quad m_{GH}=3,\quad m_{HE}=-\dfrac{1}{2}$

$b)\quad \text{Midpoint}_{EG}=(4.5, 1.5),\quad \text{Midpoint}_{FH}=(4.5, 1.5)$

c) Parallelogram

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Step-by-step explanation:

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3 years ago

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3 years ago

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Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
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Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
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We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

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3 years ago

What is (7-4i)+(-2+5i)

Alla [95]

Answer:

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Answer = 5 + i

Step-by-step explanation:

Group the real part and the imaginary part of the complex number

( 7 - 4i ) + (-2 + 5i )

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Refine = 5 + i

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3 years ago

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adelina 88 [10]

Answer:

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Step-by-step explanation:

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3 years ago

Determine whether each quadrilateral is a parallelogram rectangle rhombus and Dory Square list of all that apply.​

Determine whether each quadrilateral is a parallelogram rectangle rhombus and Dory Square list of all that apply.