Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
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The number of full periods and classes does a 202-digit number have are 1 and 3 respectively.
<h3>What are periods?</h3>
Periods are simply groups of three digits separated by commas when writing numbers in standard form.
The digit number, 202 has 1 period.
Classes is simply the number of digits in a set.
Example: 500 has 3 classes
We can say that the 202 digit number has 1 period and three classes.
Thus, the number of full periods and classes does a 202-digit number have are 1 and 3 respectively.
Learn more about period here:
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Answer:
the point estimate of the true proportion of employees is 0.401
Step-by-step explanation:
Given data
plan A = ( 0.241 , 0.561 )
to find out
the point estimate for estimating the true proportion of employees who prefer that plan
solution
we know that given data 98% confidence interval for the proportion of employees who prefer plan A: (0.241, 0.561) so point estimate for estimating the true proportion o employees who prefer that plan is p^E
and we can say here
lower limit = 
= 0.241 ..............1
upper limit = 
= 0.561 ...............2
now add these two equations 1 and 2
= +
= + = 0.241 + 0.561
2 p = 0.802
2p = 0.806
p = 0.401
So the point estimate of the true proportion of employees is 0.401
