Suppose a,b,c represent three positive whole numbers. if a+b=13 and b+c=22 and a+c=19 what is the value of c

Mathematics

1 answer:

aivan3 [116]3 years ago

5 0

Answer: C = 14

Step-by-step explanation: You can assume the A is less than B, and if you just go down in numbers such as A=6 and B=7 (To solve A + B = 13), you will eventually get to A=5 and B=8. If you do B = 8 + C = 14 ( That you get after subtracting 8 by 22 ) You should get 22, and to proof check it, you do A + C which is going to be 5 + 14 and you get 19 thus proving that C = 14.

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You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week

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Answer:

a) The demand function is

$q(p) = -4 p + 107$

b) The nightly revenue is

$R(p) = -4 p^2 + 107 p$

c) The profit function is

$P(p) = -4 p^2 + 133.75 p - 939$

d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

Step-by-step explanation:

a) Lets find the slope s of the demand:

$s = \frac{79-43}{7-16} = \frac{36}{-9} = -4$

Since the demand takes the value 79 in 7, then

$q(p) = -4 (p-7) + 79 = -4 p + 107$

b) The nightly revenue can be found by multiplying q by p

$R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p$

c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)

$P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939$

d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P

$r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41$