The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be mod
1 answer:
You might be interested in
Answer:
a) t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
b) x = 0,97 miles
c) t (min) = 1,24 hours
Step-by-step explanation: See Annex
Figure in annex shows a clear description of the situation
Let x be distance in miles between point P and where boat lands
A woman has to row a distance L
L = √ (4)² + (x)²
and the part to get to the town (which she has to walk)
d = ( 7 - x)
But we are required to give time as a function of x
distance = speed * time ⇒ t = distance / speed
Therefore
t(x) = [ √ (4)² + (x)²]/ 4 + ( 7 - x ) / 5
t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
Taking derivatives both sides of the equation
t¨(x) = ( 2x)*4 / 16√ (4)² + (x)²] - 5/25
t¨(x) = x/ 2√ (4)² + (x)²] - 1/5
t¨(x) = 0 x/ 2√ (4)² + (x)²] - 1/5 = 0
[ 5 x - 2√ (4)² + (x)²] = 0 ⇒ 5x = 2√ (4)² + (x)²] or
25 x² = 4 ( 4 + x²)
25 x² = 16 + 8x²
17x² = 16
x² = 16/17
x² = 0,941
x = 0,97 miles
And the distance walking to get to town
d = 7 - x d = 7 - 0,97
d = 6,03 miles
The least travel time is t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
t (min) = √ 16 + 0,94) /4 + 1,4 - 0,97/5
t (min) = 1,03 + 1,4 - 0,194
t (min) = 1,24 hours
Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769 </u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.