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2 years ago

Find the sum of the measure of the interior angles of the polygon below.

Mathematics

1 answer:

lana [24]2 years ago

4 0

Answer:

900

Step-by-step explanation:

(n – 2)180 where n is the number of sides

since this is a 7 sided polygon

(7-2) * 180

5 * 180

900

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

4 0

3 years ago

PLEASE HELP THANKS YOU

kondaur [170]

U must find the median, the range, and the mode. And that is your answer

8 0

2 years ago

Read 2 more answers

Write functions for each of the following transformations using function notation. Choose a different letter to represent each f

kupik [55]

Answer:

$(a)\ T_{a,b} =(x +a,y+b)$

$(b)\ F_{y\ axis} = (-x,y)$

$(c)\ F_{x\ axis} = (x,-y)$

$(d)\ R_{o,90^o} = (-y,x)$

$(e)\ R_{o,180^o} = (-x,-y)$

$(f)\ R_{o,270^o} = (y,-x)$

Step-by-step explanation:

Solving (a): Translate a units right, b units up

When a function is translated a units right, the number of units will be added to the x coordinate

When a function is translated b units up, the number of units will be added to the y coordinate.

So, we have:

$T_{a,b} =(x +a,y+b)$

Solving (b): Reflect across y-axis

When a function is translated across the y-axis, the x coordinate gets negated.

So, we have:

$F_{y\ axis} = (-x,y)$

Solving (c): Reflect across x-axis

When a function is translated across the x-axis, the y coordinate gets negated.

So, we have:

$F_{x\ axis} = (x,-y)$

Solving (d): 90 degrees rotation counterclockwise

When a function is rotated 90 degrees counterclockwise, the y-coordinates gets negated and then swapped with the x-coordinate.

So, we have:

$R_{o,90^o} = (-y,x)$

Solving (e): 180 degrees rotation counterclockwise

When a function is rotated 180 degrees counterclockwise, the coordinates are negated.

So, we have:

$R_{o,180^o} = (-x,-y)$

Solving (f): 270 degrees rotation counterclockwise

When a function is rotated 270 degrees counterclockwise, the x-coordinates gets negated and then swapped with the y-coordinate.

So, we have:

$R_{o,270^o} = (y,-x)$

6 0

3 years ago

Find the value of x plsss the people that answerd this got it wrong.

liubo4ka [24]

X=145. If its wrong lmk

6 0

2 years ago

Read 2 more answers

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Vanyuwa [196]

Answer:

The integral diverges

Step-by-step explanation:

Consider the integral from 0 to infinity of

$xe^{4x}$

We can do this in parts

$\int {xe^{4x} } \, dx =\int {x} \, d(e^{4x})/4\\ = x/4 e^{4x}-e^{4x}/16$

When we substitute limits infinity we find that the values become infinity

Hence the integral diverges

The given improper integral diverges

8 0

3 years ago