SOLUTION: I have some problems I got wrong on my test. Please explain step by step what I should have done. I am allowed four, so here they are. 1.) Pizza Unlimited has the following pr

Question 129723: I have some problems I got wrong on my test. Please explain step by step what I should have done. I am allowed four, so here they are.

1.) Pizza Unlimited has the following prices for pizzas. Price is related to diameter by a quadratic equation. Fit a quadratic equation into the data points (8, 3.39), (12, 5.12), and (16, 7.29).
Diameter Price
8 inch $3.39
12 inch $5.12
16 inch $7.29
A.) Price =what quadratic equation?
B.) Using the equation find the price of a 14 inch pizza.
I know the answers, but I did the problem wrong, will you please show me the steps? How did they get the equation?
Answer A: 0.01375x^2 +0.1575x+1.25
Answer B: 14 inch pizza costs $ 6.15

2.) Solve for x. (x-6)^2 + (x+1)^2 = 0
The solutions are 5 + 7 i /2, 5-7 i/2
How do I know when to place the � I � one there?
Please show the step by step way to get this solution.

3.) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?
I put the max product at 9 (incorrect) and the numbers yielding this product at -3, -3 (correct)
However when I did the same problem with -16 instead of -6, I got 49 for the max product and it was correct. I thought the max product was the number in question squared. How do I get the max product?

4.) Solve the formula for the given number. Assume all variables represent positive numbers.
(N=n^2 � 19 n)/6; for n
I got n = (19 + sqrt sign 361 + 36 N)/2 (incorrect)
The answer is n = (19 + sqrt sign 361 + 24 N)/2
What did I do wrong, please show me the steps.
Thanks for all your help!!!!!!!!!! :o)

Found 2 solutions by stanbon, chitra:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have some problems I got wrong on my test. Please explain step by step what I should have done. I am allowed four, so here they are.
1.) Pizza Unlimited has the following prices for pizzas. Price is related to diameter by a quadratic equation. Fit a quadratic equation into the data points (8, 3.39), (12, 5.12), and (16, 7.29).
Diameter Price
8 inch $3.39
12 inch $5.12
16 inch $7.29
A.) Price =what quadratic equation?
--------------
Substitute the three x/y pairs into the quadratic form: y = ax^2+bx+c
to get three equations in the three unknows a,b,and c
Solve the three equations for a,b, and c
------------------------------------------------
B.) Using the equation find the price of a 14 inch pizza.
If the equation is f(x) = 0.01375x^2+0.1575x+1.25, find f(14)
to find the price of a 14 in. pizza.
----------------------
I know the answers, but I did the problem wrong, will you please show me the steps? How did they get the equation?
Answer A: 0.01375x^2 +0.1575x+1.25
Answer B: 14 inch pizza costs $ 6.15
=============================================
2.) Solve for x. (x-6)^2 + (x+1)^2 = 0
You get x^2-12x+36 + x^2+2x+1 = 0
2x^2-10x+37 = 0
x = [10 +- sqrt(100-4*2*37)]/4
x = [10 +- sqrt(-196)]/4
x = [10 +- 14i]/4
You get that "i" because i is the square root of -1.
---------------------------------
The solutions are 5 + 7 i /2, 5-7 i/2
How do I know when to place the � I � one there?
Please show the step by step way to get this solution.
=============================
3.) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?
I put the max product at 9 (incorrect) and the numbers yielding this product at -3, -3 (correct)
However when I did the same problem with -16 instead of -6, I got 49 for the max product and it was correct. I thought the max product was the number in question squared. How do I get the max product?
--------
Let one of the numbers be "x"; If the other number is "y"
the sum, x+y = -6
y = -(x+6)
---------
Their product is P(x) = x [-(x+6)]
Then P(x) = -x^2-6x
This is a quadratic with a = -1 and b = -6
The max occurs when x = -b/2a = 6/-2 = -3
Since x+y = -6
-3+y = -6
y = -3
And the product is 9
=========================
4.) Solve the formula for the given number. Assume all variables represent positive numbers.
(N=n^2 � 19 n)/6; for n
I got n = (19 + sqrt sign 361 + 36 N)/2 (incorrect)
The answer is n = (19 + sqrt sign 361 + 24 N)/2
What did I do wrong, please show me the steps.
Thanks for all your help!!!!!!!!!! :o)
------------------
I can't follow what you mean here.
=====================================
Cheers,
Stan H.

Answer by chitra(359) (Show Source): You can put this solution on YOUR website!
1) By data it is given that price is related to diameter by a quadratic equation.

A general quadratic equation is given by f(x) =

We shall write it as y = f(x) =

==> y =

So now lets plug in all the given set of values, in the form of co-ordinates. This implies that it forms 3 equations.

3.39 = 64a + 8b + c ------------(1)

5.12 = 144a + 12b + c -----------(2)

7.29 = 256a + 16b + c -----------(3)

Let solve them simlutaneously.

Subtracting (1) & (2), we get:

1.73 = 80a + 4b --------------(4)

subtracting (2) & (3), we get:

2.17 = 112a + 4b ------------(5)

subtracting (4) & (5)

0.44 = 32a

==> a = 0.01375

Now by back substituion we find b

1.73 - 1.1 = 4b

0.63 = 4b

==> b = 0.1575

substitute the a and b value in one of the equations. So we get:

3.39 = 0.88 + 1.26 + c

3.39 - 2.14 = c

c = 1.25

Thus the quadratic equation would be

y =

Price of a 14 inch pizza would be just plug in x = 14 in the above equation we get:

y = $6.15

==============================================================================

2) Solve for x. = 0

The given equation can be written as:

= 0

= 0

Using the quadratic formula we find the roots.

Substituting for the values we get:

Taking 2 as a common factor we get:

So the roots are: 5 + 7i/2 and 5 - 7i/2

The solutions are 5 + 7 i /2, 5-7 i/2

=============================================================================

3) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?

Let x and y be the two numbers.

It is given that the product is maximum and the sum is negative six.

so lets find the multiples of 6. They are + -1, +- 2, +-3, +-6

Taking them 2 at a time we find that -3 and -3 when added gives us -6

And their product gives us 9 which is the maximum number.

Hence the solution.

===========================================================================
4) solve for "n"
N = /6

This can be written as:

6N =

Using the quadratic formula we get:

Substituing for the values, we get:

Thus the solution.

Regards

If you stil have any doubts you can get back to me.. I'm a online teacher.. I'll help you..

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