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Inga [223]
3 years ago
11

How would you go about solving for (3g - 25)(-5)?

Mathematics
1 answer:
Kay [80]3 years ago
3 0

Answer:

10t³ - 95t + 45

Step-by-step explanation:

  • Plug the g(t) and h(t) into the equation: (3(3t - 3) - 2(t³ - 5t)) (-5)
  • Distribute 3 & -2 through the prentheses : (9t - 9 2t³ + 10t) (-5)
  • Collect like terms : (19t - 9 - 2t³) (-5)
  • Distrubute -5 through the parentheses: -95t + 45 + 10t³
  • Use the commutative property to reorder the terms : 10t³ - 95t + 45

Solution : 10t³ - 95t + 45

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A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1
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Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

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2 years ago
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