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laiz [17]
3 years ago
14

If using the method of completing the square to solve the quadratic equation x^2+13x+15=0 which number would have to be added to

"complete the square"?
Mathematics
1 answer:
Ray Of Light [21]3 years ago
8 0

Answer:

The number to be added to complete the square is (13/2)^2

But the solved value for x are:

x = 11.71 or -1.28

Step-by-step explanation:

x ^ 2 + 13x + 15 = 0

x^2 + 13x = -15

(The coefficient of x^2 is 1, hence needless diving through)

Add the square of half the coefficient of x to both sides

x^2 + 13x + (13/2)^2 = -15 + ( 13/2)^2

(x + 13/2)^2 = -15 + 169/4

(x + 13/2)^2 = 109/4

Take the square of both sides

x + 13/2 = +-10.44/ 2

x = 10.44/2 + 13 /2

x = 23.44/2

x = 11.71

OR

x = 10.44/2 - 13/2

x = -2.56/2

x = -1.28

Therefore x = 11.71 or -1.28

But the number to be added to complete the square is (13/2)^2

Lets keep learning, maths is fun

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Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an
Fantom [35]

9514 1404 393

Answer:

  about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

  h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

  s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

  sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

  α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

  h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

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<em>Additional comments</em>

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

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We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

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3 years ago
The perimeter of the square below is 36 yards. What is the length of each side? <br> yards
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Step-by-step explanation:

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The girls and boys' basketball teams sponsored a car wash that made $109. There were twice as many girls as
V125BC [204]

Answer:

Boys - 36$ 33 cents

Girls - 72$ 67 cents

Step-by-step explanation:

Boys x

Girls 2x

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Boys x =36$ 33c

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3 years ago
At an output level of 50 units per day, a firm has average total costs of $60 and average variable costs of $35. Its total fixed
e-lub [12.9K]

Answer:

$ 1250

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total cost = total fixed cost + total variable cost

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