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4 years ago

7

Is 2x+7y=-12 linear or nonlinear

2 answers:

Hoochie [10]4 years ago

8 0

Answer: If you mean the mapping y(x) := 3x+4, then y(x) is not linear, because it does not satisfy the two properties of linearity. Only equations of the form y(x) := ax (for "a" being any real or complex number) are linear. Don't be confused with the plot of the graph of y(x) = 3x+4 being a line - this does not mean linear in the sense of the definition in Linear Algebra. Some authors define such function as "affine-linear".

skad [1K]4 years ago

3 0

Answer:

If you plot this on a graph it would be a linear equation...

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The equation of circle having a diameter with endpoints (-2, 1) and (6, 7) is

densk [106]

Answer:

$(x-2)^{2}+(y-4)^{2}=25$

Step-by-step explanation:

step 1

Find the diameter of the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-2,1)\\B(6,7)$

substitute the values

$d=\sqrt{(7-1)^{2}+(6+2)^{2}}$

$d=\sqrt{(6)^{2}+(8)^{2}}$

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$d=10\ units$

The radius is half the diameter

so

$r=10/2=5\ units$

step 2

Find the center of the circle

the center of the circle is the midpoint between the endpoints of the diameter

so

The center is

$(\frac{-2+6}{2},\frac{1+7}{2})$

$(2,4)$

step 3

Find the equation of the circle

The equation of the circle is

$(x-h)^{2}+(y-k)^{2}=r^{2}$

substitute the values

$(x-2)^{2}+(y-4)^{2}=5^{2}$

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