<h3>
Answer: ds/dt = 11</h3>
================================================
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
-----------
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
-----------
Side note: The information t = 40 is never used. It's just extra info.
Answer:
0.75 hours
Step-by-step explanation:
Time taken by my pump = 6 hours
Time taken by friend's pump = x
Combined time = 1.5 hours
Rate :
my pump = 1/6
Combined rate = 1/1.5
Combinwd rate = 1/6 + 1/x
Hence :
1/6 + 1/x = 1/1.5
(x + 6) / 6x = 1.5
x + 6 = 9x
x - 9x = - 6
-8x = - 6
x = - 6 / - 8
x = 0.75 hours
Answer:
B: -a > -b
Step-by-step explanation:
a = 1, -a = -1
b = 3, -a = -3
-1 > -3
Therefore, -a > -b
If it's just an equation you have to write, then write: t = 0.002n
Karen is moving at 81.2 miles per hour while Melinda is moving at 71.2 miles per hour.
<h3>Equation for
speed</h3>
Speed is the ratio of total distance travelled to total time taken. It is given by:
Speed = distance / time
Let a represent Karen speed and b represent Melinda speed, hence:
a = b + 10
a - b = 10 (1)
Also:
a = d₁ / 1
d₁ = a
b = d₂/ 1 hour
d₂ = b
Since they are 108 miles apart, using Pythagoras:
108² = d₁² + d₂²
a² + b² = 11664
(b + 10)² + b² = 11664
b = 71.2 mph, a = 81.2 mph
Karen is moving at 81.2 miles per hour while Melinda is moving at 71.2 miles per hour.
Find out more on speed at: brainly.com/question/4931057