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malfutka [58]
2 years ago
14

Type the correct answer in each box. A music company is introducing a new line of acoustic guitars next quarter. These are the c

ost and revenue functions, where x represents the number of guitars to be manufactured and sold: R(x) = 120x C(x) = 100x + 1,840 The company needs to sell at least guitars for a total revenue of $ to start making a profit.
Mathematics
1 answer:
andre [41]2 years ago
7 0

Answer:

The company has to produce more than 92 guitars and sell them for making a profit.

Step-by-step explanation:

These are the cost and revenue functions, where x represents the number of guitars to be manufactured and sold: R(x) = 120x, and  C(x) = 100x + 1840.

Therefore, the condition for no loss-no gain for manufacturing x number of guitars is

R(x) = C(x)

⇒ 120x = 100x + 1840

⇒ 20x = 1840

⇒ x = 92

Therefore, the company has to produce more than 92 guitars and sell them for making a profit. (Answer)

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-86989.
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so........
83524+4365+(-86989)=900
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1 year ago
se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y
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Answer:

It is proved that f_x, f_y exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)

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f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

And,

f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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The height of a baseball thrown from the catcher to first base is modeled by the function h(t) = -0.09t^2 + 0.72t + 6, where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds

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