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frutty [35]
3 years ago
11

The cost, Y (in dollars) to provide for guests at a dinner party is proportional to the number x of guests attending the party.

It costs 30 dollars to provide food for 4 guests.
Mathematics
1 answer:
Annette [7]3 years ago
4 0

Maybe you missed to add the complete question. After a little research I was able to find the complete question which is as follows:

<em>''The cost y(in dollars) to provide food for guests at a dinner party is proportional to the number x of guests attending the party. It costs $30 to provide food for 4 guests. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to provide food for 10 guests?'' </em>

So, I am solving based on this complete question.

Answer:

Please check the explanation.

Step-by-step explanation:

<em>a. Write an equation that represents the situation. </em>

As the cost and the number of guests are proportional.

So the equation of the form

y = mx

Plug in the values y = 30 and x = 4 to find m

y = mx

30 = m (4)

m = 30/4

    = 7.5

Now, substituting m = 7.5 in the equation y=mx

y = mx

y = 7.5x

<em>b) Interpreting Slope</em>

Given that the units for y are dollars, and the units for x are guests.

Thus, the slope 7.5 means it costs $7.5 per guest.

<em>c) How much does it cost to provide food for 10 guests?'' </em>

We know the equation

y = 7.5x

put x = 10

y = 7.5(10)

y = $75

Thus, it costs 75 dollars for 10 guests.

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Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
Calculate the loss on selling 50 shares of stock originally bought at 133/4 and sold at 12.
Anarel [89]
Here is the solution of the given problem above:
The first thing we should do is to multiply 50 and 13 3/4 
13 3/4 is equivalent to 13.75 .
So, we then multiply 
50 x 13.75  and we get 687.50.
so, $687.50 was the amount spent on the stock. 
Now, lets find out how much they sold them for:
What we do is multiply 12 and 50 
50 x 12 would be 600
We can find out the loss by subtracting 
$687.50 - $600 and that gives us $ 87.50.
Therefore, the amount that is loss in selling is $87.50. The correct answer would be option B. Hope this answer helps.
5 0
3 years ago
Read 2 more answers
1 + 1? <br> .......……………………
masya89 [10]
Hmm difficult one but I think ima have to go with 2?????
4 0
3 years ago
Read 2 more answers
Cellus
mote1985 [20]

Answer:

y = 6 when x = 18

Step-by-step explanation:

The appropriate formula for this direct proportion is y = kx, where k is the constant of proportionality.

We know y = 3 when x = 9:  3 = k(9)

This yields k = 3/9, or k = 1/3

Then the formula is y = (1/3)x

and when x = 18, y = (1/3)(18) = 6

y = 6 when x = 18

4 0
2 years ago
What’s the value for 2.3 + 4.09 =n
Rashid [163]
Answer:

n = 6.39

Explanation:

2.3 + 4.09 = n
6.39 = n

Swap the sides of the equation
n = 6.39
6 0
2 years ago
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