Use the Rational Zeros Theorem to write a list of all potential rational zeros f(x) = 14x^3 + 56x^2 + 2x - 7
1 answer:
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To solve a system of inequalities we graph both of them.
The inequality representing their combined pay would be
. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
, since they do not want their combined hours to be over 65. In both of these inequalities, <em>x</em> represents the number of hours Jane works and <em>y</em> represent the number of hours Jack works.
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
The inequality representing their combined pay would be
The inequality representing their combined hours working would be
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
z = 6
Step-by-step explanation:
We know that ...
sin(x) = cos(90 -x)
Substituting (9z-1) for x, this is ...
sin(9z -1) = cos(90 -(9z -1))
But we also are given ...
sin(9z -1) = cos(6z +1)
Equating the arguments of the cosine function, we have ...
90 -(9z -1) = 6z +1
90 = 15z . . . . . . . . . add (9z-1) to both sides
6 = z . . . . . . . . . . . . divide by 15
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<em>Comment on the graph</em>
The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...
sin(x) = cos(90 +360k -x) . . . . . for any integer k
Then the above equation becomes ...
90 +360k = 15z
6 +24k = z . . . . . . . . . for any integer k
The sine and cosine functions also enjoy the relation ...
sin(x) = cos(x -90)
sin(9z -1) = cos(9z -1 -90) = cos(6z +1)
3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z
z = 30 2/3
Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
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<h3>setup</h3>The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
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<h3>solution</h3>Dividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
