Use elimination to solve the system for 4x + 7 y equals -14 + 8 x + 5 y equals 8 for x
1 answer:
9514 1404 393
Answer:
(x, y) = (3.5, -4)
Step-by-step explanation:
Elimination is easiest if one of the coefficients of a variable is a multiple of the other coefficient of the variable. Here, we have x-coefficients of 4 and 8, so it will be easiest to eliminate x.
Subtract the second equation from 2 times the first.
2(4x +7y) -(8x +5y) = 2(-14) -(8)
9y = -36 . . . . . simplify
y = -4 . . . . . . . divide by 9
4x +7(-4) = -14 . . . . substitute for y in the first equation
4x = 14 . . . . . . . add 28
x = 3.5 . . . . divide by 4
The solution is (x, y) = (3.5, -4).
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Answer:
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Step-by-step explanation:
By congruence of triangles, the radius r of the cone base when its height is 200 cm satisfies the relation
r/200 = 400/600
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The volume of a cone with radius of the base = R is given by
So, the volume of water when it is 200 cm high is
One minute later, the height of the water is 200 cm + 20 cm = 220 cm
The radius now satisfies
r/220 = 400/600
and now the radius of the base is
r = 440/3
and the new volume of water is
So, the water is raising (being pumped) at a rate (speed) of
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