The complex polygon below represents the layout of a parking lot. Find the area of the parking lot in square meters.

Answer:

a) [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b) The volume of the box is maximized when 'x' is approximately 1.585 feet

Step-by-step explanation:

a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;

The length of the side of the square cut from the corners of the rectangular sheet of paper = x

The length of the box formed after cutting the square sides are;

The length of the box, l = a - 2·x

The width of the box, w =  b - 2·x

The height of the box, h = x

The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x

The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;

At the extremum, dV/dx = 0

∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0

12·x² - 4·(a + b)·x + a·b = 0

[tex]x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b), When a = 8.5 inches and b = 11 inches, we have;

x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914

x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

We get;

When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15

When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65

Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

(The value of 'x' in terms of 'a' and 'b' is therefore;

[tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex])

The volume of the box is maximized when, x ≈ 1.585 feet

Answer:

[tex]50~in[/tex]

Step-by-step explanation:

[tex]perimter=AB+AM+BM[/tex]

[tex]AM=2EM=2(9in)=18in[/tex]

[tex]BM=25E=2(7in)=14in[/tex]

∠m= [tex]180-[/tex] (∠A+∠B)= 180-(70+40)

∠m= 70⇒ AB= AM⇒AB=18

[tex]perimeter=18+14+18=[/tex]

[tex]50~in[/tex]

--------------------------

hope it helps...

have a great day!!

Answer:

your answer will be 50 in

Step-by-step explanation:

Answer:

2 cm

Step-by-step explanation:

V=πr2h = 20π

-π                -π

r2h = 20

h= 5

r2(5) = 20

/5         /5

r2=4

/2  /2

r=2cm

(my work is complicated, but trust me 2 cm is the answer)  

true (I don't know if this is the answer but it would be my guess)

Answer:

2411.52 mm²

Step-by-step explanation:

[tex]40^{2} =32^2+d^2[/tex]

→ [tex]d^2= 1600-1024[/tex]

→[tex]= 576[/tex]

→ [tex]d= 24[/tex]      [tex]so, (radius=12[/tex]

[tex]Total~ surface ~ area= (2\pi r)*height[/tex]

→ [tex](2*3.14*12*82)[/tex]

[tex]= 2411.52 mm^2[/tex]

-------------------------------

hope it helps...

have a great day!!

Answer:

2411.52 mm²

Step-by-step explanation:

hope its helpful

Answer:

x = 90, y = 12

Step-by-step explanation:

The key to this problem is the fact that opposite sides of a parallelogram are congruent (their lengths are equal).

Set up and solve two equations, one for x and one for y.

x + 80 = 2x - 10

80 = x - 10

90 = x

--------------------------

3y - 4 = y + 20

2y - 4 = 20

2y = 24

y = 12

Answer:

3

Step-by-step explanation: First, you find the mean of the data set. Then you take that mean and find the difference of that and each value, you add those up and find the mean of that number.

Answer:

I know the answer come follow me to see

Answer:

nsovurhnvurnvhfbsybvhnfshugb

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

I think I hope this helps

Answer:

A. B. and C.

(and hi again)

Answer:

No

Step-by-step explanation:

To find out if 2 is a solution, replace all the x's with 2.

4(2 - 1) - 3(2 - 2) =8

4(1) - 3(0) = 8

4 - 0 = 8

4 = 8

Nope!  False!  2 is not a solution.

Answer:

5/3 is the slope of the line.

Answer:

40 each i think maybe 30 if not

Answer:

m∠1 = 70°

Step-by-step explanation:

Step 1

Sum of angles on a straight line = 180°

Hence:

180° - 101°

= 79°

Sum of interior angles in a triangle = 180°

Hence

m∠1 = 180° - (79 ° + 31°)

m∠1 = 70°

Answer:

(-3,0)

Step-by-step explanation:

1) find the coordinate of x

x = -3

2) find the coordinate of y

the point lies on x axis so y = 0

The coordinates are (-3, 0)

:)

Answer:

1/9 or unlikely

Step-by-step explanation:

Answer:

8/9

Step-by-step explanation:

Answer:

(2,-3)

Step-by-step explanation:

2x + 2y = -2

3x - 2y = 12

Add the two equations to eliminate y

2x + 2y = -2

3x - 2y = 12

-----------------------

5x   = 10

5x/5 = 10/5

x = 2

Now find y

2x+2y = -2

2(2)+2y = -2

4+2y = -2

Subtract 4 from each side

4-4 +2y = -2-4

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

(2,-3)

Answer:

x=-2 and y=-24

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

50% of 12= 1/2 of 12= 6

Answer:

6 votes were for hunger relief.

Step-by-step explanation:

Total number of votes = 12

Percentage of votes for hunger relief = 50%

So, number of votes for hunger relief would be:-

50% of 12 votes

That equals--> [tex]\frac{50}{100}[/tex] x 12

= 0.5 x 12

= 6 votes

Answer:

4. x=0 x=5

5. x=-4 x=8

Answer:

21 km/h

Step-by-step explanation:

Answer:

I just need points sorry love But the answer is A.

Step-by-step explanation:

Answer:

$-23

77 - 100 = -23

Answer:

I can’t see the picture

Step-by-step explanation:

Answer:

i wrote "13 8/9 because 16 2/3 x 16 2/3= 50/3 x 50/3 = 250/9 then 250/9 ÷ 2 = 125/9 = 13 8/9"

Step-by-step explanation: if u add in some words or something so you teacher isnt sus hope you pass!!