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klio [65]
3 years ago
10

The following system of equations lacks solutions when b ≠ - c

Mathematics
1 answer:
Naddik [55]3 years ago
8 0

Answer:

These lines have the same slope and will never intersect unless the y offset is identical.  This will only happen when b is equal to -c.

Step-by-step explanation:

Let's reformat these to match, starting with the first one:

2ax - y + b = 0\\-y = -2ax - b\\y = 2ax + b

And the second one:

2y - 4ax+2c = 0\\2y = 4ax - 2c\\y = 2ax - c

It now shows clearly that these are both lines with same slope and differ only by the y position, depending on the values of b and c.  If b is equal to negative c, then both lines are identical, otherwise they are parallel and never intersect.

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The region in the first quadrant bounded by the x-axis, the line x = In(pi), and the curve y = sin(ex) is rotated about the x-ax
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D

Step-by-step explanation:

Please refer to the graph below.

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\displaystyle V=\pi\int_a^bR(x)^2\, dx

Where R(x) is the radius or height of the representative rectangle.

We are integrating from <em>x</em> = 0 to <em>x</em> = ln(π). The height of a representative rectangle is given by <em>y. </em>Therefore, the volume is:

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(Courtesy of WolframAlpha.)

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