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2 years ago

MAKE SURE TO SHOW YOUR WORK (please)

Mathematics

2 answers:

creativ13 [48]2 years ago

8 0

Answer:

9.11 x 10^-28

Step-by-step explanation:

if you divide 9.11 x 10^-28 by 1.67 x 10^-24 you get .000546

if you divide 1.67 x 10^-24 by 9.11 x 10^-28 you get 1,833

therefore, 1.67 x 10^-24 is 1833 times greater than the other value

MrRa [10]2 years ago

8 0

9.11 x 10^-28
Is the answer hope this helps

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3. A sign company is building a sign with the dimensions shown. What is the area, in square feet, of the sign? Round to the near

Aleks04 [339]

Answer:

84.87sq ft

Step-by-step explanation:

Let ABC be the triangle and AD be the perpendicular on BC such that BD=DC=7ft.

Now, it is known that $\frac{DC}{AC}=cos60^{0}$

$AC=\frac{7}{\frac{1}{2}}$

$AC=7ft$

Now, in triangle ADC, we have

$(AC)^{2}=(AD)^{2}+(DC)^{2}$

$(14)^{2}=(AD)^{2}+(7)^{2}$

$196-49=(AD)^{2}$

$AD=12.12ft$

Now, area of the triangle= $\frac{1}{2}{\times}b{\times}h$

= $\frac{1}{2}{\times}14{\times}12.12$

= $84.87sq ft$

Thus, area of the building is 84.87sq ft.

8 0

2 years ago

48:80 in simplest form

vivado [14]

The answer is 16

.......

8 0

3 years ago

Four brothers each bought two hot dogs and a bag of chips at the football concession stand. If the bag of chips was $1.25, and t

IRISSAK [1]

Items bought in total:
4 brothers X two hot dogs and one bag of chips=
4X3=
12.

Hot dogs- x, chips- y.
4y + 8x= $18.20

Chips= $1.25 each so
4($1.25) + 8x= $18.20
5 + 8x= $18.20
8x= $18.20-5
8x= $13.20
x= $13.20/8 [13.20 divided by 8]
x= $1.65

This means that one hot dog= $1.65.

If you’re unsure what to write as the answer I’d suggest that you put all the working out down in your copy/notes.

3 0

2 years ago

Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He

ZanzabumX [31]

Answer:

cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

<h3>Rectangular Prism</h3>

The relevant formulas are ...

V = LWH

A = 2(LW +H(L +W))

for length L, width W, and height H.

<u>a)</u><u> prism 1</u>

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

V = (8 in)(8 in)(5 in) = 320 in³

A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

<u>b)</u><u> prism 2</u>

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

V = (10 in)(8 in)(4 in) = 320 in³

A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

<h3>Cylinder</h3>

The relevant formulas are ...

V = πr²h

A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

<h3>Square Pyramid</h3>

The relevant formulas are ...

V = 1/3s²h

A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

A = (10 in)(10 in + 2×14 in) = 380 in²

<h3>Summary</h3>

The proposed figures have volume and area (rounded to the nearest unit) as follows:

$\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}$

The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

<em>Additional comment</em>

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

3 0

1 year ago

Solve x^2 + 4x + 8 = 0

Mkey [24]

Answer:

x = -2 + 2 i or x = -2 - 2 i

Step-by-step explanation:

Solve for x:

x^2 + 4 x + 8 = 0

Subtract 8 from both sides:

x^2 + 4 x = -8

Add 4 to both sides:

x^2 + 4 x + 4 = -4

Write the left hand side as a square:

(x + 2)^2 = -4

Take the square root of both sides:

x + 2 = 2 i or x + 2 = -2 i

Subtract 2 from both sides:

x = -2 + 2 i or x + 2 = -2 i

Subtract 2 from both sides:

Answer: x = -2 + 2 i or x = -2 - 2 i

8 0

2 years ago