Figure 2 shows a solid piece of wood in the shape of a triangular prism of length y cm. The cross-section is an equilateral triangle of side x cm. The total surface area of the piece of wood is 96√3 cm². a) Express y in terms of x. [You are advised to write any non-integers in surd form]. b) C) Show that the volume, V, of the piece of wood is given by 3x² /32 4 X V = - Use calculus to i) find the value of x which gives the maximum volume. ii) confirm that your value of x gives a maximum.
Figure 2 shows a solid piece of wood in the shape of a triangular prism of length y cm. The cross-section is an equilateral triangle of side x cm. The total surface area of the piece of wood is 96√3 cm². a) Express y in terms of x. [You are advised to write any non-integers in surd form]. b) C) Show that the volume, V, of the piece of wood is given by 3x² /32 4 X V = - Use calculus to i) find the value of x which gives the maximum volume. ii) confirm that your value of x gives a maximum.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.4: Powers Of Monimials
Problem 43WE
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11. Solve part C only
Transcribed Image Text:x cm
x cm
x cm
Figure 2
y cm
![The total surface area of the piece of wood is 96√3 cm².
a) Express y in terms of x. [You are advised to write any non-integers in surd
form].
b)
Figure 2 shows a solid piece of wood in the shape of a triangular prism of
length y cm. The cross-section is an equilateral triangle of side x cm.
c)
Show that the volume, V, of the piece of wood is given by
/32
v = 3x² (²²-²)
4
Use calculus to
i) find the value of x which gives the maximum volume.
ii) confirm that your value of x gives a maximum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffde3be69-de28-4603-8c9e-8f0acba98c9a%2F0c5e27f8-6cea-4dd8-abad-2502f590fbf0%2Fumdomoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The total surface area of the piece of wood is 96√3 cm².
a) Express y in terms of x. [You are advised to write any non-integers in surd
form].
b)
Figure 2 shows a solid piece of wood in the shape of a triangular prism of
length y cm. The cross-section is an equilateral triangle of side x cm.
c)
Show that the volume, V, of the piece of wood is given by
/32
v = 3x² (²²-²)
4
Use calculus to
i) find the value of x which gives the maximum volume.
ii) confirm that your value of x gives a maximum.
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