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Taya2010 [7]
3 years ago
10

The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is

the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0
The function is graphed as shown below

Part A:

We use the formula - \frac{b}{2a} to find the vertex of the function. A quadratic function of the form of a x^{2} +bx+c and equating this form to the given function - x^{2} +20x-75, we have
b=20 and a=-1.

Substituting a and b into the vertex formula, we have
x=- \frac{20}{2(-1)}=10, as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

- x^{2} +20x-75=0
-( x^{2} -20x+75)=0
x^{2} -20x+75=0
(x-5)(x-15)=0
x=5 and x=15, as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos

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Slav-nsk [51]

Answer:

x = 5 units.

Step-by-step explanation:

In a parallelogram. diagonals bisect each other.

This means $ \overline{CE} = \overline{BE} $.

$ \implies 15 - x = 2x $

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3 years ago
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Yuliya22 [10]

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3 years ago
Does anyone know how to solve this? It’s really starting to stress me out.
bekas [8.4K]

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

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Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

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lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

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lim(u→0) (π sin(πu) / (πu)) − 12

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π (1) − 12

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3 years ago
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Vanyuwa [196]

Answer:

Answer: -0.008

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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