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5. A spherical snowball with an outer layer of ice melts, so that the radius of the snowball
decreases at the rate of 1/5 cm/sec. Find the rate at which the volume decreases when the
diameter is 50 cm.
3. An open rectangular box w/ square ends to hold 6400 cu ft, is to be built at a cost of
Php 75.00 per sq ft. for the base and
Php 25.00 /sq ft for the sides. Find the most economical dimensions.
2. A boy is flying a kite at a height of 150 ft. If the kite moves horizontally away from the
boy at the rate of 20 ft/sec, how fast is the string being paid out when the kite is 250 ft from him?
Find the area between y=x^2 and x+y-2=0
A wall "h" meters high is 2m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6m. How high is the wall in meters?
Minimum distance. Find the minimum distance from a point on the
positive x-axis (a, 0) to the parabola y^2 = 8x.
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
(a) Evaluate∫[
𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙.
(b) Use MATLAB to generate some typical integral curves of 𝑓(𝑥) =
𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙over the interval (−5,5).
Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 − 2xy + y2, (1, 5, 16) with maple lab please
Find an approximate value of the double integral below where 𝑅 is the rectangular region having
vertices (−1, 1) and (2, 3). Take a partition of 𝑅 formed by the lines 𝑥 = 0, 𝑥 = 1, and 𝑦 = 2, and take (𝑢𝑖
, 𝑣𝑖) at the
center of the 𝑖th sub region.
∬(3𝑦 − 2𝑥
2)𝑑𝐴
𝑅
