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vredina [299]
3 years ago
15

Which of the graphs below correctly solve for x in the equation −x2 + 5x + 6 = 3x − 2? Graph of quadratic opening downward and l

inear sloping up to the right. They intersect at point negative 2, negative 8 and point 4, 10. Graph of quadratic opening upward and linear sloping up to the right. They do not intersect at point. Graph of quadratic opening downward and linear sloping down to the left. They intersect at point negative 0.9, 0.7. Graph of quadratic opening downward and linear sloping up to the right. They intersect at point negative 1.3, negative 2.2 and point 3.23, 11.73.

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
3 0
The first one. They intersect at (-2,-8) and at (4,10).
You can find this graphically or algebraically.
Graphically by inputting both equations and using the intersect function.
Or algebraically by setting the equation to 0.
Finding the x intercepts then by factoring.
Then inputting the x values into either original equation to find the y intercepts for each.

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You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o
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Answer:

Therefore the circumference of the circle is =\frac{20\pi}{4+\pi}

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

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\Rightarrow s=\frac{10-\pi r}{2}

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The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

A=\pi r^2+ (\frac{10-\pi r}{2})^2

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\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi

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\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}    > 0

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\frac{dA}{dr}=0

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\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0

Therefore at r=\frac{10}{4+\pi}  , A is minimum.

Therefore the circumference of the circle is

=2 \pi \frac{10}{4+\pi}

=\frac{20\pi}{4+\pi}

4 0
3 years ago
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