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The Altitude of a triangle is increasing at a rate of 8cm/s while its area is increasing at the rate of 12cm^2/s. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 100 cm^2 ?
A cone of radius π centimeters and height β centimeters is lowered point first at
a rate of 1 cm/s into a tall cylinder of radius π centimeters that is partially filled with
water. How fast is the water level rising at the instant the cone is completely
submerged
If π(π₯) is a differentiable and π(π₯) = π₯ π(π₯) use the definition of the derivative to show
that πβ²(π₯) = π₯π'(π₯) + π(π₯).
Evaluate the following limits, if they exist, where βπ₯β is the greatest integer function.
(a)lim β2π₯β/π₯
π₯β0
(b) lim π₯ β1/π₯β
π₯β0
How may revolutions per minute must the body make about vertical axis so that the cord make an angle of 45 with the vertical
Let π(π₯) = βπ₯β + ββπ₯β, where βπ₯β is the greatest integer less than or equal to π₯.
(π) For what values of π, does limπ₯βπ
π(π₯)exist?
(π) At what numbers is π discontinuous?
Suppose we experiment with an Atwood Machine consisting of two masses m
and 2m connected by an inextensible non-slip string running over a pulley of
radius a and mass 4m, as shown below.
) Briefly discuss why no work is done by the forces of constraint. (5)
(d) What is the total energy of the system? (2)
(e) Find the acceleration dv/dt of the blocks.
Suppose we experiment with an Atwood Machine consisting of two masses m
and 2m connected by an inextensible non-slip string running over a pulley of
radius a and mass 4m, as shown below.
(a) Determine the total kinetic energy of the system. (6)
(b) Find the gravitational potential energy of the system.
What is the cardinality of the relationship between an event (such as a sale) and the store in which that event happened?
A. 1:1
B. 0:N
C. M:N
D. 1:N
Where would information (i.e., address, size, acquisition date, etc.) about a specific retail store in a chain (e.g., the store in Tempe, Arizona) be stored?
A. In a relationship entity
B. In a resource entity
C. In one or more agent entities
D. In one or more event entities
#339914 on Dec 2023