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Leni [432]
3 years ago
12

A jeweler wants to minimize business costs and has found that the average cost in dollars per necklace is given by C(x)=0.5x^2-7

x+65.5, where x is the number of necklaces that are created.
Mathematics
1 answer:
Vika [28.1K]3 years ago
8 0

Answer:

The maximum cost is 41 dollars per necklace.

Step-by-step explanation:

The average cost in dollars/necklace is given by :

C(x)=0.5x^2-7x+65.5  .....(1)

Where

x is the number of necklaces that are created

To maximize the cost, find the value of x by putting dC/dx = 0

\dfrac{d}{dx}(0.5x^2-7x+65.5)=0\\\\x-7=0\\\\x=7

Now put the value of x = 7 in equation (1).

C(x)=0.5(7)^2-7(7)+65.5\\\\=41\ \text{dollars per necklace}

Hence, the maximum cost is 41 dollars per necklace.

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9+3v is greater than or equal to 6
kondaur [170]

Answer:

If you take it in terms of integers,

9+3v may or may not be greater or equal to 6. It depends on the value of the variable you put in.

For eg:- if you substitute the value for v as 2 then 9+3x2=15 which is greater than 6 but if you put in -1 for v then you will get 9+3x(-1)=6


8 0
3 years ago
Which statement best describes the area of Triangle ABC shown below?
PolarNik [594]

Answer:

it is half the area of a square of side length 8

Step-by-step explanation:

area of a square = l × b

= 8 × 8

= 64 cm^2

area of a triangle = b × h ÷ 2

= 8 × 8 ÷ 2

= 64 ÷ 2

= 32 cm^2

hope you can understand ☆☆☆

8 0
3 years ago
The expression 3n^2+n+2. What is the coefficient of n?
Lera25 [3.4K]
The coefficient of n is 1
3 0
3 years ago
Which fraction represents the decimal 0.12
ryzh [129]

Answer:

\dfrac 3{25}

Step-by-step explanation:

0.12 = \dfrac{12}{100}=\dfrac{3}{25}

8 0
2 years ago
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24
VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let r be the radius and \theta be the angle of a circle.

According with the graph, the area of the sector is given by

A=\frac{1}{2}r^2\theta

The arc lenght of a circle with radius r and angle \theta is r \theta

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

2r+r\theta=24 \:in

We need to express the area as a function of one variable, to do this we use the above equation and we solve for \theta

2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}

Next, we substitute this equation into the area equation

A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2

The domain of the area is

0

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r

12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6

To check if r=6 is a maximum we use the Second Derivative test

if f'(c)=0 and f''(c), then f(x) has a local maximum at x = c.

The second derivative is

\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2

Because A''(r)=-2 the largest slice is when r = 6 in.

The diameter of the pizza is given by

D=2r=2\cdot 6=12 \:in

A 12 in diameter will reward you with the largest slice of pizza.

3 0
3 years ago
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