Which relation is a function?
2 answers:
let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function. Check the picture below.
A very easy way to find out if a graph is a function is to use the vertical line test.
Look at each graph and mentally draw a vertical line that goes through each of its points.
If that line goes through more than one point (2, 3, 4...) then that graph is not a function.
That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.
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Answer:
C. 450
Step-by-step explanation:
Plot the solution area for the system of four inequalities
You'll get the quadrilateral with vertices at points (0,0), (0,10), (2,8) and (4,0).
The maximum value of the function can be at vertices, so
The maximum value of the function is 450 at point (0,10)
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.
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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
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<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
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<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
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<h3>Summary</h3>The proposed figures have volume and area (rounded to the nearest unit) as follows:
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.
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<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.