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natta225 [31]
3 years ago
13

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. a stop w

atch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s. what is the height of the cliff? (g = 9.8 m/s2 and air resistance is negligible)
Mathematics
1 answer:
stellarik [79]3 years ago
3 0
To solve this problem you must apply the proccedure shown below:
 1. You must apply the following formula:
 yo=-(Voy)t+gt²/2
 2. You have that:
 Voy=VoxSin(30°)
 Voy=(12 m/s)(Sin(30°))
 Voy=6 m/s
 t=5.6 s
 g=9.8 m/s²
 2. When you susbtitute these values into the formula, you obtain:
 yo=-(6 m/s)(5.6 s)+(9.8 m/s^2)(5.6 s)²/2
 yo=120.06 m
 Therefore, the answer is: 120.06 m
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The number of motor vehicles registered in millions in the US has grown as follows:
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Answer:

a) Figure attached

b) r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=10 \sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274  

r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989  

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=10 \sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274  

r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989  

So then the correlation coefficient would be r =0.989

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Answer:

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Answer:

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Step-by-step explanation:

24+1=25

25-1=24

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