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GREYUIT [131]
2 years ago
13

Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he p

repared 20 cupcakes in 30 minutes.
A) Does the scenario represent a direct variation?
B) If yes, explain the meaning of the constant of proportionality in the scenario.

take your time if you want :)

Mathematics
1 answer:
attashe74 [19]2 years ago
5 0

a) As the constants are equal, the situation represents a proportional relationship.

b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constants for each situation are:

k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.

Since the constants are equal, the situation represents a proportional relationship.

The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

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Lyrx [107]

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Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

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h(t)=-16t^2+80t+64

where

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t is the time in seconds

Part A)  Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

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so

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-16t^2+80t+64=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

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x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+80t+64=0

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a=-16\\b=80\\c=64

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t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}

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The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

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Solve the quadratic equation

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a=-16\\b=80\\c=24

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t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}

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t=\frac{-80+\sqrt{7,936}} {-32}=-0.28

t=\frac{-80-\sqrt{7,936}} {-32}=5.28

therefore

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