It is not a rational number it is irrational because the decimal doesn't terminate.
Answer:
9600400000000000 is in standard form
Answer: q = 40
Step-by-step explanation:
Given the quadratic formula as
x = [-b +/-√(b^2 -4ac)]/2a
b = -14
a = 1
c = q
Difference d between the two roots.
d = [-b + √(b^2 -4ac)]/2a - [-b -√(b^2 -4ac)]/2a
d = 2√(b^2 -4ac)/2a
d = √(b^2 -4ac)/a
And d = 6
Substituting the values of a,b and c. We have;
6 = √[(-14^2) - (4×1×q)]
Square both sides
6^2 = 196 - 4q
4q = 196 - 36
q = 160/4
q = 40
The equation becomes
x^2 - 14x + 40 = 0
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
