Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin
Let's assume that Kirby walks with a speed

for a time

, and that he runs with a speed

for a time

.
The total time available for Kirby to catch the train is:

and this must be equal to the sum of the two times t1 and t2:
The distance Kirby should cover is

and this should be equal to the sum of the distances covered by walking and by running:

So we have a system of 2 equations:


If we solve the system, we find:


So, Kirby needs to run at least for 8 minutes in order to catch the train.
Answer:
6-ounce bottle for $3.49 because its
.58 per ounce
3.49 divided by 6 = .58
Step-by-step explanation:
9.59 divided by 14 is .69 per ounce
chegg
For this case we have the following expression:
(xy ^ -6) / (x ^ -4y ^ 2)
By power properties we can rewrite the expression as:
(x * x ^ 4) / (y ^ 6 * y ^ 2)
Then, for power properties:
Same exponents are added:
(x ^ (4 + 1)) / (y ^ (6 + 2))
(x ^ 5) / (y ^ 8)
Answer:
An expression after the negative exponents have been eliminated is:
(x ^ 5) / (y ^ 8)