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jok3333 [9.3K]
3 years ago
15

Find the values if a and b such that x squared + 2x -7 = (x+a) squared + b​

Mathematics
1 answer:
stealth61 [152]3 years ago
6 0

Given:

x^2+2x-7=(x+a)^2+b

To find:

The values of a and b.

Solution:

We have,

x^2+2x-7=(x+a)^2+b

It can be written as

(x^2+2x)-7=(x+a)^2+b

Add and subtract square of half of coefficient of x in the parenthesis.

(x^2+2x+(\dfrac{2}{2})^2-(\dfrac{2}{2})^2)-7=(x+a)^2+b

(x^2+2x+1^2)-1-7=(x+a)^2+b

(x+1)^2-8=(x+a)^2+b     [\because (x+y)^2=x^2+2xy+y^2]

(x+1)^2+(-8)=(x+a)^2+b

On comparing both sides, we get

a=1

b=-8

Therefore, the value of a is 1 and the value of b is -8.

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2 years ago
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the
kenny6666 [7]

Given:

The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation

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To find:

The maximum amount of profit the company can make, to the nearest dollar.

Solution:

If a quadratic equation is f(x)=ax^2+bx+c, then the vertex is

Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)

If a>0, then vertex is the minimum point and if a<0, then the vertex is the maximum point.

We have,

y=-29x^2+1388x-10040

Here, a=-29,b=1388, c=-10040. Clearly, a<0. So, the vertex is the point of maxima.

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-\dfrac{b}{2a}\approx 23.931

Putting x=23.931 in the given equation, we get

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y=-16608.09+33216.228-10040

y=6568.138

The vertex is at (23.931,6568.138).

Therefore, the maximum profit is $6568.138 when x=23.931.

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Answer is 3.25h = m
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2 years ago
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