Two cars are driving towards an intersection from perpendicular directions. The first car's velocity is 101010 meters per second and the second car's velocity is 666 meters per second. At a certain instant, the first car is 444 meters from the intersection and the second car is 333 meters from the intersection. What is the rate of change of the distance between the cars at that instant (in meters per second)

D(L)/dt  = 407,6 m/s

Step-by-step explanation:

Let call A the intersection point.

As the cars are driving from perpendicular directions, they form with a coordinates x and y, a right  triangle, and distance between them is the hypotenuse (L), then

L² = x² + y²

Taking derivatives with respect to time we have:

2*L* D(L)/dt  =  2*x *D(x)/dt  + 2*y* D(y)/dt      (1)

In this equation we know: At a certain time

x  =  444 m       and  D(x)/dt  =  10 m/s

y  =  333 m       and  D(y)/dt  = 666 m/s

And   L = √(x)²  + (y)²    ⇒  L  = √ (444)² +( 333)² ⇒ L = √197136 + 110889

L = √308025

L = 555 m

Thn plugin these values in euatn (1) we get

2* 555 * D(L)/dt (m) =  2* 444* 10 + 2*333*666 (m*m/s)

D(L)/dt  = ( 4440 + 221778)/555  (m/s)

D(L)/dt  = 407,6 m/s

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step-by-step explanation:

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step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.