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Pavel [41]
3 years ago
5

X² - 6x + y² + 2y = -1 find center & Radius

Mathematics
1 answer:
Fofino [41]3 years ago
8 0

Answer:

The answer to your question is Center = (3 , -1), radius = 3

Step-by-step explanation:

Equation

                       x² - 6x + y² + 2y = -1

-Process

1.- Leave a space between the like terms

                     x² - 6x           + y² + 2y          = -1

2.- Divide the middle term of each group by 2 and write the result to the power of 2 in both sides of the equation.

                     x² - 6x + (3)² + y² + 2y + (1)² = -1 + 3² + 1²

3.- Simplification

                     x² - 6x + 9 + y² + 2y + 1 = -1 + 9 + 1

4.- Factor

                     (x - 3)² + (y + 1)² = 9

5.- Find the center and the radius

     Center = (3 , -1)

     Radius = √9 = 3

                   

                     

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What is the number sentence for "1 less than N is the sum of Z and<br> 2"?
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          \rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}

        <em>What is the number sentence for "1 less than n is the sum of z and 2?"</em>

<em> </em>

<em>          </em>\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}

  ❖ First, Notice it says "1 less than n". This expression indicates that

        we subtract 1 from n, which  looks as follows:-

                                                     \Large\textit{n-1}

❖ Now, It also says "the sum of z and 2". This indicates that we add z and

     2:-

                                       \Large\textit{z+2}

❖ Now, Combine these two little expressions into one equation:-

\implies\sf{n-1=z+2}

<h3>Good luck with your studies.</h3>

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6 0
1 year ago
F(x) = 2x3 + 7x2 – 4x – 5
qaws [65]

Answer:

Its 3

Step-by-step explanation:

7 0
3 years ago
A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid
Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = 2 \times width

Base area = lb

= 2x^2

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}

Now, cost is

= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}

now we have to minimize C(x)

So, we need to compute the C'(x)

= 52x - \frac{648}{x^2}

C"(x)  = 52x - \frac{1,296}{x^3}

now for the critical points, we will solve the equation C'(x) = 0

= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}

C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0

So, x is a point of minima that is

= (\frac{648}{52} )^\frac{1}{3}

Now, Base material cost is

= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}

= 139.75

Side material cost is

= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3}  }

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

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