5. A poster is to be made with a 1-inch margin on each of the left and right sides and a 1.5-inch margin on the top and bottom. The printed area, within the margins, must be 216 square inches. Find the dimensions of the poster of smallest total area (including the margins) that fits these specifications. 1' 1.5' 216 sq in 1.5' 1'

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question

Can you solve #5?

10
X
tong is
the shape of a rectangle. A
child squeezes the top and bottom so that the rectangle be-
comes wider and shorter while its perimeter remains 100 cm.
How fast is the area of the rectangle decreasing when the
height is 20 cm and decreasing at 4 cm/sec? Include the
units.
5. A poster is to be made with a 1-inch margin on each of the left
and right sides and a 1.5-inch margin on the top and bottom. The
printed area, within the margins, must be 216 square inches. Find
the dimensions of the poster of smallest total area (including the
margins) that fits these specifications.
4. A radioactive element decays to 80% of its original amount after 2 days. What is the half-life
of this element? (An exact answer is preferred but not required.)
+
++++
F
++
Some possibly useful data:
个
(ƒg)'(x) = f(x)g'(x) + f'(x)g(x)
y = yo = m(x - x0)
个
1'
1.5'
6. Consider the two curves y = x² and y = x + 12. Set up, but do not evaluate,
a definite integral that represents the area bounded by the two curves. Don't
forget the limits of integration.
216 sq in
1.5'
1'
cos 2x = 2 cos²x - 1
Transcribed Image Text:10 X tong is the shape of a rectangle. A child squeezes the top and bottom so that the rectangle be- comes wider and shorter while its perimeter remains 100 cm. How fast is the area of the rectangle decreasing when the height is 20 cm and decreasing at 4 cm/sec? Include the units. 5. A poster is to be made with a 1-inch margin on each of the left and right sides and a 1.5-inch margin on the top and bottom. The printed area, within the margins, must be 216 square inches. Find the dimensions of the poster of smallest total area (including the margins) that fits these specifications. 4. A radioactive element decays to 80% of its original amount after 2 days. What is the half-life of this element? (An exact answer is preferred but not required.) + ++++ F ++ Some possibly useful data: 个 (ƒg)'(x) = f(x)g'(x) + f'(x)g(x) y = yo = m(x - x0) 个 1' 1.5' 6. Consider the two curves y = x² and y = x + 12. Set up, but do not evaluate, a definite integral that represents the area bounded by the two curves. Don't forget the limits of integration. 216 sq in 1.5' 1' cos 2x = 2 cos²x - 1
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