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slava [35]
3 years ago
15

Is the following a Proportion 15/40 = 5/8

Mathematics
2 answers:
Semenov [28]3 years ago
8 0
No, because 5/8=15/24 and 15/24≠15/40 
LuckyWell [14K]3 years ago
4 0
15/40 = 5/8
cross multiply
(15)(8) = (40)(5)
120 = 200...incorrect...so it is not a true proportion

little tip : proportions are nothing but equivalent fractions...15/40 is not equivalent to 5/8.....now if it would have been 15/40 = 3/8 , since these are equivalent fractions, this would have been a true proportion
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3 years ago
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Harrizon [31]

Answer:

  • <u>0.075 m/min</u>

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

<u>1. Write the equation for the volume of the cone:</u>

      V=\dfrac{1}{3}\pi r^2h

<u />

<u>2. Find the relation between the radius and the height:</u>

  • r = diameter/2 = 5m/2 = 2.5m
  • h = 5.2m
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<u>3. Filling the tank:</u>

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

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        V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3

<u>4. Find the derivative of the volume of water with respect to time:</u>

            \dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}

<u>5. Find x² when the volume of water is 8π m³:</u>

       V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\  11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062m²

<u>6. Solve for dx/dt:</u>

      1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}

      \dfrac{dx}{dt}=0.03596m/min

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<u>7. Find dh/dt:</u>

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