R = m - v + 2, where r = faces, v = vertices, and m = edges
r = 28 - 13 + 2
r = 15 + 2
r = 17, so the first answer is correct.
7. The surface area of a cone is A = pi*r*sqrt(r^2 + H^2)
A = pi*(7)(sqrt(49 + 1849)
A = pi*(7)(43.57)
A = pi*305 = 959 m^2, so the first answer is correct.
13. The volume of the slab is V = HLW
V = (5 yards)(5 yards)(1/12 yards)
V = 25/12 cubic yards
So it costs $46.00*(25/12) = $95.83 of total concrete. The third answer is correct.
21. First, find the volume of the rectangular prism. V = HLW
V = (15 cm)(5 cm)(7 cm)
V = 525 cm^3
Next, find the volume of the pyramid. V = 1/3(BH), where H is the height of the pyramid and B is the area of the base of the pyramid. Note that B = (15 cm)(5 cm) = 75 cm^2
V = (1/3)(75 cm^2)(13 cm)
V = 325 cm^3
Add the two volumes together, the total volume is 850 cm^3. The fourth answer is correct.
22. The volume of a square pyramid is V = 1/3(S^2)(H), where S is the side length and H is the height.
V = (1/3)(20^2 in^2)(21 in)
V = 2800 in^3
Now that we know the volume of this pyramid, and that both pyramids have equal volume, we plugin our V to the equation for the volume.
2800 = (1/3)(84)(S^2)
2800 = 28S^2
100 = S^2
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10 in = S, so we have a side length of 10 in, and the first answer is correct. </span>
Answer:
12.5
Step-by-step explanation:
Hello from MrBillDoesMath!
Answer:
Domain: x >=0 for both cases
Discussion:
Assuming we are dealing with real valued functions, the domain of
y = x^(1/2) +4
is the set of all "x" such that x>= 0 (so we are taking the square root of a positive, or zero, real number)
The domain of x^(1/2) +6 -7 is the same as for the last function and for the same reason.
Thank you,
MrB
Answer:
2 cis (7/6 pi)
Step-by-step explanation:
r = sqrt( a^2 + b^2)
r = sqrt (-sqrt(3) )^2 + (-1)^2)
= sqrt(3 +1)
= sqrt(4)
= 2
theta = arctan (b/a)
theta = arctan (-1/-sqrt(3))
theta = 30
but this is in the third quardrant -a and -b
so add 180
theta = 210 degrees
convert this to radians
210 * pi/180 = 210/180 * pi = 21/18 * pi = 7/6 * pi
r cis (theta)
2 cis (7/6 pi)
