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Nata [24]
2 years ago
8

SOMEONE HELP ME BEFORE I PASS OUT 1. |X|≤8 2. |X|≤27

Mathematics
1 answer:
g100num [7]2 years ago
4 0

Answer: 1. [-8, 8]

2. [-27, 27]

Step-by-step explanation:

1. |X|≤8

x≤8 or x>=-8

-8<=x<=8 ==> [-8, 8]

2. |X|≤27

x≤27 or x>=-27

-27<=x<=27 ==> [-27, 27]

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Georgia [21]
V=LWH
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8 0
3 years ago
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h
mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed  = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere  =\frac{2}{3}\pi r^3

Volume of a Cylinder =\pi r^2 h

Therefore:

The Volume of the Solid formed

=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}

Area of the Hemisphere =2\pi r^2

Curved Surface Area of the Cylinder =2\pi rh

Total Surface Area=

2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh

Cost of the Hemispherical Ends  = 2 X  Cost of the surface area of the sides.

Therefore total Cost, C

=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh

Recall: h=\frac{4640}{\pi r^2}-\frac{4r}{3}

Therefore:

C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}

The minimum cost occurs at the point where the derivative equals zero.

C^{'}=\frac{-27840+32\pi r^3}{3r^2}

When \:C^{'}=0

-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518

Recall:

h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

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How many grams are in 1 pound
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The electronic Store sold for laptopComputers in one day. The total cost of laptops was $3600. If each laptop cost the same amou
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sp2606 [1]

Area of the figure = 27 square units

Solution:

Number of full squares shaded = 24

Number of half squares shaded = 0

Number of more than half square shaded = 3

Number of less than half square shaded = 4

Area of the figure = Number of full square + Number of more than half square

                               + Half of number of half squares

                             =24+3+\frac{1}{2}(0)

                             = 24 + 3

                             = 27 square units.

Area of the figure = 27 square units

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3 years ago
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