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choli [55]
3 years ago
11

Popcorn kernels pop independently (i.e. unimolecularly). For one brand at constant temperature, 12 kernels pop in 5 seconds when

235 kernels are present. After 140 kernels have popped, how many kernels will pop in 5 seconds? (Your answer may include fractions of a kernel).
Mathematics
1 answer:
likoan [24]3 years ago
7 0

Answer:

no of kernels  pop = 4.34

Step-by-step explanation:

given data

kernels pop in 5 second  = 12

kernels are present = 235

solution

we get here kernels are pop at rate of here

kernels are pop at rate = 12  ÷  235  

kernels are pop at rate = 0.051063

and

we get here maximum kernels are remaining that is

maximum kernels remaining = 235 - 140

maximum kernels remaining = 85

so

no of kernels  pop in 5 second will be

no of kernels  pop = 0.051063   × 85

no of kernels  pop = 4.34

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Step-by-step explanation:

Let's look at choice 1.

x=t+1

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I'm going to subtract 1 on both sides for the first equation giving me x-1=t. I will replace the t in the second equation with this substitution from equation 1.

y=(x-1)^2+2(x-1)

Expand using the distributive property and the identity (u+v)^2=u^2+2uv+v^2:

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So this not the desired result.

Let's look at choice 2.

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Let's plug this into equation 2:

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y=4(\frac{x^2}{4})+2x-3

y=x^2+2x-3

This is the desired result.

Choice 3:

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Solve the first equation for t by adding 3 on both sides:

x+3=t.

Plug into second equation:

y=(x+3)^2+2(x+3)

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y=(x^2+6x+9)+(2x+6)

y=(x^2)+(6x+2x)+(9+6)

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Not the desired result.

Choice 4:

x=t^2

y=2t-3

I'm going to solve the bottom equation for t since I don't want to deal with square roots.

Add 3 on both sides:

y+3=2t

Divide both sides by 2:

\frac{y+3}{2}=t

Plug into equation 1:

x=(\frac{y+3}{2})^2

This is not the desired result because the y variable will be squared now instead of the x variable.

Choice 5:

x=t+1

y=t^2+4t

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x-1=t.

Plug into equation 2:

y=(x-1)^2+4(x-1)

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y=(x^2)+(-2x+4x)+(1-4)

y=x^2+2x+-3

y=x^2+2x-3.

This is the desired result.

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3 years ago
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