Step-by-step explanation:
x+5=3(x-3)
X+5= 3x-3
x-3x=-3-5
-2x=-8
X= -8/-2
X=4 Answer
Answer:
Step-by-step explanation:
Answer:
Elena's running speed is 5 miles/hour
Explanation:
The speed is defined as the covered distance per unit time
In the problem, we have:
The distance covered is the length (circumference) of the circular track which is given as of a mile.
We are also given that she completes each lap (she completes of a mile) in of an hour
To get her speed, we will divide the distance covered by the time taken to cover this distance
This is done as follows:
speed = miles/hour
This means that:
Elena can run 5 miles each hour
Hope this helps :)
Step-by-step explanation:
A cross-section is a washer with an inner radius of 8sin(x) - (-1) and an outer radius of 8cos(x) - -(1), so its area would be:
A(x) = π[(8cos(x) + 1)^2 − (8sin(x) + 1)^2]
= π[64cos^2(x) + 16cos(x) + 1 - 64sin^2(x) − 16sin(x) − 1]
= π[64cos(2x) + 16cos(x) - 16sin(x)]
=> V(x) = ∫[0,π/4] π[64cos(2x) + 16cos(x) - 16sin(x)] dx
= π[32sin(2x) + 16sin(x) + 16cos(x)] |[0,π/4]
= π[32sin(π/2) + 16√2/2 + 16√2/2 - 16]
= π(32 - 16 + 16√2) = π(16 + 16√2)
The volume of the region is π(16 + 16√2).
