4y - x = 5 + 2y ..... (1)
3x + 7y = 24 ..... (2)
by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
<span>-x + 2y = 5 </span> ..... (1a)
by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x - 6y = -15 ..... (1b)
by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
13y = 39
⇒ y = 3
by substituting y=3 into (2)
3x + 7(3) = 24
3x = 24 - 21
3x = 3
⇒ x = 1
∴ solution to the system is x=1 when y = 3
Answer:
D. 16 times.
Step-by-step explanation:
Volume of a cylinder = π r^2 h
π r^2 h = 432
Now if the diameter is reduced by 1/4 then the radius is reduced by a fourth also.
Let the new height be H, then:
432 = π (r/4)^2 H
so π r^2 h = π(r/4)^2 H
r^2 h = r^2 H / 16
h = H/16
H = 16h.
Step-by-step explanation:
volume of a cylinder is
ground area × height = pi×r²×h
r = 4
what we need to calculate is how high the water stands with one "serving" of 2m³.
that height is then added every minute (with the additional 2m³ during that minute).
so,
2 = pi×4²×h = pi×16×h
2/16 = 1/8 = pi×h
h = (1/8) / pi = 1/(8pi) = 0.039788736... m
that is rounded about 0.04 m or 4 cm.
therefore, the water rises by 0.04 m or 4 cm per minute
0.04m/min
Answer:
all work is shown and pictured
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