Marco solves the equation 4sin(3x) + 0.25 ≤ 2sin(3x) − 0.3 by graphing y = 2sin(3x) and y = −0.55. he then locates the intervals
2 answers:
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Assignment:
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Answer:
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Explanation:
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[ Step One ] Remove Parenthesis (a) = a
[ Step Two ] Simplify Equations
[ Step Three ] Rewrite Equation
[ Step Four ] Add Similar Elements
[ Step Five ] Rewrite Equation
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Check the picture below.
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line <span>y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike </span>⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line <span>y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike </span>⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.