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Answer:
At a point X = 1.5 and Y = 4, the two lines will intersect
Explanation:
Given,
Two lines will intersect at the point with co-ordinates (X, Y) that will satisfy both the equations.
Hence,
y = 4x - 2 - Eq 1
y = 7 - 2x - Eq 2
Solving Eq 1 & 2, we get -
Eq 1 -Eq 2 will give
0 = 6X -9
6X = 9
X = 1.5
Y = 7 - 2*1.5 = 7-3 = 4
At a point X = 1.5 and Y = 4, the two lines will intersect
Answer:
0.027 cubic ft/min
Explanation:
Volume of water is V=V(t) Depth of water is h=h(t)
The relationship between V and h is
V=π/3.r2.h
Let
h0= the height of the cylinder = 24ft, r0= the radius of the opening = 10ft.
Since water level (h) rise with respect to flow rate we find an expression for r and substitute into V
r/h = r0/h0= 10/24 = 5/12
r = (5/12) h,
Substitute for r in V
so,
V=1/3.π.(h2)square = 1/3.π. 25/144.(h3)
When
h= 16ft
and dV/dt = 20ft3/min
,
dV/dt =1/3*π*25/144*h3*(dh/dt)
20ft3/min= 1/3*π* 25/144*h3*(dh/dt)
20 = 1/3*π*(16)3.(dh/dt)
Make dh/DT subject of formula
dh/dt=(20*3*144)/(25*π*4096) = 8640/321740.8
=
dh/dt= 0.027 ft3/min
The answer is T. The statement is true.
