n casts a bakera fed cost of $420 and variable cost of $2.10 per cupcake.A cupcake is sold for $490 each ) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes. (ü) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes. üi) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold. (v) Graph both functions on the same coordinate axes. (vi) From your graph find coordinatae at which cost equals revenue. (vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1.029. How much profit is made for this number of cupcakes? Q2. if x < 2 ) Discuss the continuity of the function f(x) = },* 2x+4 if x> 2 on the open interval 0 < x<2 and on the closed interval 0 0, it is found that У 3 0.5(x2 + 3x) Assuming the oil slick is continuously distributed, how x + x2 +4x thick would you expect it to be at the source?

n casts a bakera fed cost of $420 and variable cost of $2.10 per cupcake.A cupcake is sold for $490 each ) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes. (ü) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes. üi) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold. (v) Graph both functions on the same coordinate axes. (vi) From your graph find coordinatae at which cost equals revenue. (vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1.029. How much profit is made for this number of cupcakes? Q2. if x < 2 ) Discuss the continuity of the function f(x) = },* 2x+4 if x> 2 on the open interval 0 < x<2 and on the closed interval 0 0, it is found that У 3 0.5(x2 + 3x) Assuming the oil slick is continuously distributed, how x + x2 +4x thick would you expect it to be at the source?

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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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Permutations and Combinations

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Counting Theory

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Question

The questions is in the picture

n casts a bakera fed cost of $420 and variable cost of $2.10 per cupcake.A cupcake is
sold for $490 each
) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes.
(ü) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes.
üi) Write an algebraic expression representing the cost C as a function of the number of
cupcakes x that are produced.
(iv) Write an algebraic expression representing the revenue R as a function of the number of
cupcakes x sold.
(v) Graph both functions on the same coordinate axes.
(vi) From your graph find coordinatae at which cost equals revenue.
(vii) Using your graph, determine how many cupcakes need to be made to produce revenue
of at least $1.029. How much profit is made for this number of cupcakes?
Q2.
if x < 2
) Discuss the continuity of the function f(x) = },*
2x+4
if x> 2
on the open interval 0 < x<2 and on the closed interval 0 <x<2.
(ii) An efficiency study of the morning shift at a certain factory indicates that an average
worker arriving on the job at 7:00 A. M. will have assembled f (x) = x³ + 6x² + 15x
units x hours later. Approximately how many units will the worker assemble
between 8: 00 and 8: 15 A M. ?
(iii) Amanufacturer's total cost is C(q) = 0.1q² + 0.5q² + 500q +200
dollars when the level of production is q units.
The current level of production is 4 units. and the manufacturer is planning to increase this to
4.1 units. Estimate how the total cost will change as a result.

Q3
Use a matrix method to find the equilibrium prices and quantities where the supply and demand functions
for Good 1, Good 2 and Good 3 are as
Qai = 50 – 2P, + 5P, – 3P3,
Qs1 = 8P, - 5
Qaz = 22 + 7P, – 2P, + 5P3,
Qs2 = 12P, - 5
Qd3 = 17 + P, + 5P, - 3P,,
Qs3 = 4P,-1
Q4
(i) A business manager determines that t months after production begins on a new product,
6t2 + 5t
the number of units produced will be P thousand, where P(t) =
(t + 1)2
What happens to production in the long run ?
(ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a
distance x meters from the rupture. Turbulence makes it difficult to directly measure the
thickness of the slick at the source (where x = 0), but for x > 0, it is found that
У 3
0.5(x2 + 3x)
Assuming the oil slick is continuously distributed, how
x + x2 +4x
thick would you expect it to be at the source?

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