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WITCHER [35]
3 years ago
5

For a special event, a restaurant charges a one-time setup fee, plus a charge for each person attending the event. The charge fo

r 5 people is $100. The charge for 10 people is $162.50.
Part 1) Write a linear function that models the cost, y, of the total event cost based on the number of people, x, attending the event.

Part 2) Describe what the rate of change and initial value mean in this situation.
Mathematics
1 answer:
Rashid [163]3 years ago
7 0

Any linear function is of the form y=mx+b

Here m is slope and b is y intercept.

Slope is difference in y divided by different in x values .

In the question for 5 persons cost is $100 and for 10 persons cost is $162.50

So the points are (5,100) and (10,162.50)

Slope m=\frac{162.50-100}{10-5}=12.50

We can find the value of b by taking m=12.50 and (x,y)=(5,100)

Substitute these values in y=mx+b

100=12.50(5)+b

100=62.50+b

Subtracting 62.50 both sides

b=100-62.50

b=37.5

a) Put m=12.50 and b=37.50 to get the equation

y=12.50x+37.50

b)Rate of change is the m value or the slope of the function.

Initial value that is (5,100) gives us one of the points to find the rate of change.

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Step-by-step explanation:

Substitute 2 for x:

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3 years ago
Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En
ArbitrLikvidat [17]

Answer:

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Step-by-step explanation:

The equation of the circle is:

x^{2} + (y-1)^{2} = 16

After some algebraic and trigonometric handling:

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t

Where:

\frac{x}{4} = \cos t

\frac{y-1}{4} = \sin t

Finally,

x = 4\cdot \cos t

y = 1 + 4\cdot \sin t

a) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

b) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

c) x = 4\cdot \cos t'', y = 1 + 4\cdot \sin t''

Where:

4\cdot \cos t' = 0

1 + 4\cdot \sin t' = 5

The solution is t' = \frac{\pi}{2}

The parametric equations are:

x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right)

y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)

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Answer:

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Given:

Current stock price = $50

Divided d = $2

Growth rate g = 5 %

Find:

Expected rate of return

Computation:

Expected rate of return = D(1+g)/Current Price + g

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Expected rate of return  =7.1% (Approx.)

6 0
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First of all why is there 2 similar equation connected to one another?

Second in order to solve this all you need to do is plug in the number and solve for x

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6 0
3 years ago
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Dennis_Churaev [7]

Answer: 15/32

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5/8 of the vegetable sold where green.

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Then the 3/4 is applied to the 5/8 of green vegetables.

Then the fraction (of the total number of vegetables) that were string beans was:

F  = (3/4)*(5/8) = (3*5)/(4*8) = 15/32

3 0
3 years ago
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