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DanielleElmas [232]
3 years ago
10

The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the

parabolic function shown below. On which planet would the ball go the highest? On which planet would the ball take the longest to return to the ground? Explain your reasoning.
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
3 0

Answer:

If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.

Step-by-step explanation:

Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:

v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2

the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.

Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:

v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}

When we use this to replace the 't" in the displacement formula, we et:

y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}

This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)

And we can also answer the question about time, since given the same initial velocity v_0 , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)

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Answer:

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Read the statement, and identify the expressions that are equivalent.
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I have 31 stamps in total. I have 4 more 1 cent stamps than 8 cent stamps and twice as many one cent stamps as 12 cent stamps. I
Neko [114]

Answer:

There area 14 one cent stamps

Step-by-step explanation:

Let

x -----> the number of 1 cent stamps

y -----> the number of 8 cent stamps

z -----> the number of 12 cent stamps

we know that

0.01x+0.08y+0.12z=1.78 -------> equation A

x=y+4 ------> y=x-4 -----> equation B

x=2z -----> z=0.5x ------> equation C

substitute equation B and equation C in equation A and solve for x

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3 years ago
A contractor is calculating the number of decorative stones for a new rectangular patio. The bids always include a count for the
babunello [35]

Answer:

The number of edge stones needed has a constant rate of change, but the number of stones for the center does not.

Step-by-step explanation:

The complete question is shown in the picture attached below.

Two functions E(x) and C(x) are given in the table along with some of the function values. We have to identify if any of these functions show constant rate of change or not.

By constant rate of change we mean that the slope is constant or in other words, a linear relationship is shown by the function. For a Linear function, the  first differences of the function values are same.

By first differences we mean the difference between two consecutive output values. We can see that difference between consecutive input values is constant i.e. 1. If the difference between consecutive output values of any of the functions is same, then that function will be a Linear Function and, therefore, the rate of change for that function will be constant.

Lets analyze E(x) first. The output values are:

34, 52, 70 and 88

The difference between consecutive output values is:

18, 18 and 18

Since, this difference is constant, we can conclude that E(x) is a Linear function with a constant rate of change.

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The difference between consecutive output values is:

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Since, the differences are not constant, C(x) is not a Linear Function and , therefore, the rate of change of C(x) is not constant.

Conclusion:

The number of edge stones which is represented by E(x) has a constant rate of change, but the number of stones for center which is represented by C(x) does not have constant rate of change. This makes the first option our correct answer.

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