<h3>
Answer: ds/dt = 11</h3>
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Work Shown:
Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)
s^2 = x^2+y^2
s^2 = 15^2+20^2
s^2 = 225+400
s^2 = 625
s = sqrt(625)
s = 25
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Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.
s^2 = x^2 + y^2
d/dt[s^2] = d/dt[x^2 + y^2]
d/dt[s^2] = d/dt[x^2] + d/dt[y^2]
2s*ds/dt = 2x*dx/dt + 2y*dy/dt
2(25)*ds/dt = 2(15)*5 + 2(20)*(10)
50*ds/dt = 150 + 400
50*ds/dt = 550
ds/dt = 550/50
ds/dt = 11
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Side note: The information t = 40 is never used. It's just extra info.
Y - 2 = -2/5(x - 5)......distribute thru the parenthesis
y - 2 = -2/5x + 2....add 2 to both sides
y = -2/5x + 2 + 2
y = -2/5x + 4 <== slope intercept form
$8.77 will be the total cost after the 20% tip.
ANSWER
The distance is 10 units.
EXPLANATION
Let us use the distance formula to find the distance between,
and
The distance formula is given by,
We plug in the values to get,