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makvit [3.9K]
2 years ago
6

Write "yes" or "no" to state whether or not the given side lengths would form a right triangle.

Mathematics
1 answer:
ser-zykov [4K]2 years ago
6 0

Answer:

"yes" or "no"

Step-by-step explanation:

You might be interested in
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
Can u please find the value of X and both missing angle measures? It’s just notes I was absent when she explained it.
KIM [24]
Heres a tip---- if it has a square its 90 degrees if it doesnt its 180 and if its in an x shape theyre equal
8 0
3 years ago
What is the equation of the following line? be sure to scroll down first to see all answer options
andreyandreev [35.5K]

Answer:

The equation for the following graph:

y = -\frac{1}{5}x

Step-by-step explanation:

- You first need to find the slope by using the <u>slope formula</u>:

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

(where (x_{1},y_{1}) is the first point and (x_{2}, y_{2}) is the second point)

-Use the given points (0,0) and (10, -2) from the graph for the formula:

m = \frac{-2 - 0}{10 - 0}

Then, you solve:

m = \frac{-2 - 0}{10 - 0}

m = -\frac{1}{5}

After you have found the slope, use the slope -\frac{1}{5} and the first point (0,0) for the <u>point-slope formula:</u>

y - y_{1} = m ( x - x_{1})

<u>(</u>where m is the slope and (x_{1}, y_{1}) is the first point)

y - 0 = -\frac{1}{5}  ( x - 0)

Then, you solve:

y - 0 = -\frac{1}{5}  ( x - 0)

y - 0 = -\frac{1}{5}x - 0

y - 0 + 0 = -\frac{1}{5} - 0 + 0

y = -\frac{1}{5}x

So, the equation for the following graph is y = -\frac{1}{5}x .

7 0
2 years ago
Graph the data below and then answer the questions that follow. year 1=$20,000, year 2=$21,750, year 3=$23,500, year 4=$25,250,
Mariana [72]

Answer:

Since the difference between the value for each year is constant, this is an arithmetic sequence.

Step-by-step explanation:

Year 2 - Year 1 = 21,750 - 20,000 = 1,750

Year 3 - Year 2 = 23,500 - 21,750 = 1,750

Year 4 - Year 3 = Year 5 - Year 4 = 1,750

3 0
2 years ago
Need help with number 5 plz and thank you
____ [38]
Yes, my dear~♥️.
x=1, y=7
x=2, y=9
x=3, y=11
x=4, y=13
So your answer is point B.)
4 0
2 years ago
Read 2 more answers
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