Answer:
x = 7
Step-by-step explanation:
When 2 secants are drawn from an external point to a circle.
The product of the external part and the entire secant of one secant is equal to the product of the external part and the entire secant of the other secant, that is
5(5 + x) = 6(6 + 4) ← distribute and simplify both sides
25 + 5x = 6 × 10
25 + 5x = 60 ( subtract 25 from both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Answer:
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The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
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