Which values are solutions to the inequality below? Check all that apply
1 answer:
Given inequality:
To find:
Which values are solutions to the inequality.
Solution:
Substitute the values in the x place.
Option A: 48
6.9 ≤ 7
Therefore 48 is one solution of the inequality.
It is true.
Option B: -5
We cannot compare a complex number and a real number.
Therefore -5 is not a solution of the inequality.
it is not true.
Option C: 50
7.07 > 7
Therefore 50 is not a solution of the inequality.
It is not true.
Option D: 49
7 ≤ 7
Therefore 49 is one solution of the inequality.
It is true.
Option E: 44
6.6 ≤ 7
Therefore 44 is one solution of the inequality.
It is true.
Option F: 2401
49 > 7
Therefore 2401 is not a solution of the inequality.
It is not true.
Therefore 48, 49 and 44 are solutions to the inequality.
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Answer:
D) 3.8 cm
Step-by-step explanation:
There are several ways this problem can be solved. Maybe the easiest is to use the Law of Cosines to find angle BAC. Then trig functions can be used to find the length of the chord.
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In triangle BAC, the Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
A = arccos((b² +c² -a²)/(2bc)) = arccos((8² +6² -3²)/(2·8·6)) = arccos(91/96)
A ≈ 18.573°
The measure of half the chord is AB times the sine of this angle:
BD = 2(AB·sin(A)) ≈ 3.82222
The length of the common chord is about 3.8 cm.
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<em>Additional comment</em>
Another solution can be found using Heron's formula to find the area of triangle ABC. From that, its altitude can be found.
Area ABC = √(s(s-a)(s-b)(s-c)) . . . . where s=(a+b+c)/2
s=(3+8+6)/2 = 8.5
A = √(8.5(8.5 -3)(8.5 -8)(8.5 -6)) = √54.4375 ≈ 7.64444
The altitude of triangle ABC to segment AC is given by ...
A = 1/2bh
h = 2A/b = 2(7.64444)/8 = 1.911111
BD = 2h = 3.822222
