3. A box with a lid is to be made from a 96 cm by 48 cm sheet of metal. It is cut and folded as shown in the figure. If the box must be at least 12 cm high, what size squares should be cut from the corners in order for the box to have a volume of 9600 cm³? (2.3 12) 4. a) Determine an equation for a family of functions with zeros at 1± √5, -3, and 1/3. b) Determine an equation for the family member whose graph passes through the point (-2,-7). x x 1 1 II I II II II II II II 1 96 1 48
3. A box with a lid is to be made from a 96 cm by 48 cm sheet of metal. It is cut and folded as shown in the figure. If the box must be at least 12 cm high, what size squares should be cut from the corners in order for the box to have a volume of 9600 cm³? (2.3 12) 4. a) Determine an equation for a family of functions with zeros at 1± √5, -3, and 1/3. b) Determine an equation for the family member whose graph passes through the point (-2,-7). x x 1 1 II I II II II II II II 1 96 1 48
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:factor form.
f(x)=3x³ - x² - 3x + 1
3. A box with a lid is to be made from a 96 cm by 48 cm sheet of metal. It is cut and
folded as shown in the figure. If the box must be at least 12 cm high, what size squares
should be cut from the corners in order for the box to have a volume of 9600 cm³?
(2.3 12)
4. a) Determine an equation for a family of
functions with zeros at 1 ± √5, -3, and 1/3.
b) Determine an equation for the family member
whose graph passes through the point (-2,-7).
(2.4 12)
X
96
x
-
48
5. A square-based pyramid has a height that is twice its base length.
a) Determine an equation to represent the volume of the pyramid, in terms of the base
length.
b) What are the domain and range of the function if the base must be at least 1 cm²
and the volume cannot exceed 60 cm³? (2.5 14)
6. Ten-year-old Kayla's lemonade stand has experienced rises and falls in sales caused
by temperature changes over the last few summers. Her sales over the first two weeks
thu modal S(x) = x³ - 12x² + 36x, where x is the
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