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Archy [21]
3 years ago
7

Two cars, car X and car Y , start moving from the same point P on a cross intersection. Car X is travelling east and car Y is tr

avelling north. Some time later car X is 60 km east of point P and travelling in an easterly direction at 80 km/h and car Y is 80 km north of point P and travelling in a northerly direction at 100 km/h. How fast is the distance between car X and car Y changing?
Mathematics
1 answer:
agasfer [191]3 years ago
5 0
Let the distance traveled by car X be x km 
<span>let the distance traveled by car Y by y km </span>
<span>their paths form a right-angled triangle. </span>
<span>Let the distance between them be D km </span>
<span>D^2 = x^2 + y^2 </span>
<span>2D dD/dt = 2x dx/dt + 2y dy/dt </span>
<span>dD/dt = (x dx/dt + y dy/dt)/D </span>

<span>at the given case: </span>
<span>x = 60, y = 80 , dx/dt = 80, dy/dt = 100 </span>
<span>D^2 = 60^2 + 80^2 = 10000 </span>
<span>D = 100 </span>

<span>dD/dt = (60(80) + 80(100))/100 </span>
<span>= 128 </span>
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Let X be the mean of a random sample of size n = 64 from the uniform distribution on the interval (0, 3), i.e. f(x) = ( 1 3 , 0
allochka39001 [22]

Answer:

P ( 1.2 < X < 2.1 ) = 0.3

Step-by-step explanation:

Given:

Uniform distribution over interval (0,3) can be modeled by a probability density function f(x)

f(x) = 1 / (b - a)

Where a < x < b is the domain at which function is defined:

f(x) = 1 / (3) = 1 / 3

Where, X - U ( u , δ )

u = ( a + b ) / 2 = (0 +3) / 2 = 1.5

δ = ( b - a ) / sqrt (12) = (3 - 0) / sqrt (12) = 0.866

Hence,

X - U ( 1.5 , 0.866 )

There-fore calculating P ( 1.2 < X < 2.1 ):

P ( 1.2 < X < 2.1 ) = \int\limits^b_a{f(x)} \, dx

Where, a = 1.2 and b = 2.1

P ( 1.2 < X < 2.1 ) = x / 3 |

P ( 1.2 < X < 2.1 ) = 2.1 /3 - 1.2 / 3 = 0.3

Answer: P ( 1.2 < X < 2.1 ) = 0.3

6 0
2 years ago
Mr. Foster is starting a new job. His salary for the first year is $30,000. He will receive a 5% raise each year after that. Wri
stira [4]

Answer:

s= 30000+1500x

Step-by-step explanation:

Given data

Le the number of years be x

His salary for the first year is $30,000

5% of $30,000

=5/100*30000

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s= 30000+1500x

6 0
3 years ago
What Is the sequence of 5,10,15
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Add 5
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2 years ago
After two consecutive years of 5% rates of return, what rate of return in the third year will produce a cumulative gain of 16%?
murzikaleks [220]

Using decimal multipliers, it is found that a rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

The <u>decimal multiplier</u> for a increase of a% is given by:

M = \frac{100 + a}{100}

In this problem, two increases of 5%, thus:

M = \frac{100 + 5}{100} = 1.05

Another of x, that we want to find, and the result is a increase of 16%, thus:

M = \frac{100 + 16}{100} = 1.16

The three increases(5%, 5% and x%) result in a increase of 16%, thus:

1.05(1.05)(x) = 1.16

x = \frac{1.16}{(1.05)^2}

x = 1.052

1.052 - 1 = 0.052

A rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

A similar problem is given at brainly.com/question/21806362

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