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IceJOKER [234]
2 years ago
12

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on

a certain object, the acceleration of the object is 5 /ms2 . If the acceleration of the object becomes 6 /ms2 , what is the force
Mathematics
1 answer:
Step2247 [10]2 years ago
5 0

Answer:

The force is 12 N

Step-by-step explanation:

* Lets explain how to solve the problem

- Direct variation is a relationship between two variables that can

 be expressed by an equation in which one variable is equal to a

 constant times the other

- If y ∝ x , then y = kx , where k is the constant of variation

* Lets solve the problem

- The force acting on the object varies directly with the object's

  acceleration

∵ The force is F in newtons and a is the acceleration is m/s²

∴ F ∝ a

∴ F = ka

- To find k substitute F and a by the initial values of them

∵ A force of 10 N acts on a certain object, the acceleration of the

  object is 5 m/s²

∵ F = 10 N when a = 5 m/s²

∵ F = ka

∴ 10 = k(5)

- Divide both sides by 5

∴ K = 2

- Substitute the value of k in the equation

∴ F = 2a

- Lets find the force when the acceleration is 6 m/s²

∵ a = 6 m/s²

∴ F = 2(6) = 12

* The force is 12 N

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i^i=\left(e^{i\pi/2}\right)^i=e^{i^2\pi/2}=e^{-\pi/2}\approx0.2079

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3 years ago
If t varies 1/s and t=2 when s=60 find the relationship between t and s, b, find the value of t when s=90 c, find s when t=2,1/2
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Answer:

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3 years ago
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The number of major earthquakes in a year is approximately normally distributed with a mean of 20.8 and a standard deviation of
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Answer:

a) 51.60% probability that in a given year there will be less than 21 earthquakes.

b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 20.8, \sigma = 4.5

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This is the pvalue of Z when X = 21. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 20.8}{4.5}

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Z = 0.04 has a pvalue of 0.5160.

So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.

b) Find the probability that in a given year there will be between 18 and 23 earthquakes.

This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:

X = 23

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Z = -0.62 has a pvalue of 0.2676

So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

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