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vekshin1
3 years ago
9

Express the following numbers as a ratio between an integer and a natural number:

Mathematics
1 answer:
olasank [31]3 years ago
7 0

9514 1404 393

Answer:

  • 7/5
  • 3/10
  • -13/4
  • -27/1
  • 0/1

Step-by-step explanation:

The mixed numbers can be expressed as improper fractions in the usual way. The integer portion can be expressed as a multiple of the fraction denominator divided by itself.

Integers can be expressed as a ratio with 1 as the denominator.

1 2/5 = (1×5/5) +2/5 = (5+2)/5 = 7/5

0.3 = three tenths = 3/10

-3 1/4 = -(3×4/4 +1/4) = -(12+1)/4 = -13/4

-27 = -27/1

0 = 0/1

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Answer:

B) 36 ft

Step-by-step explanation:

Given:

The height as a function of time is given as:

f(t)=-16t^2+48t

At maximum height, the instantaneous velocity becomes 0. The instantaneous velocity is the first derivative of the height function.

So, the derivative of the the given function is 0 at the maximum height.

Differentiating the above function with time, we get

f'(t)=\frac{d}{dt}(-16t^2)+\frac{d}{dt}(48t)\\f'(t)=-32t+48

Now, equating the derivative to 0 and finding time.

f'(t)=0\\-32t+48=0\\32t=48\\t=\frac{48}{32}=1.5\ s

Therefore, time taken to reach maximum height is 1.5 s.

Now, maximum height is obtained by plugging in t=1.5 in the height equation.

Maximum height is given as:

h_{max}=-16(1.5)^2+48(1.5)\\h_{max}=-16\times 2.25+72\\h_{max}=-36+72\\h_{max}=36\ ft

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Step-by-step explanation:

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