Answer:The trip would be about 13.75 inches on the map
Step-by-step explanation:
<u><em>Answer:</em></u>
<em>276,108 < x < 271,680</em>
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<u><em>Step-by-step explanation:</em></u>
<em>*Hope this helped*</em>
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Answer:
(5,0)(3,0)
Step-by-step explanation:
x^2 - 8x + 15 = 0
(x - 5)(x - 3) = 0
x - 5 = 0
x = 5
x - 3 = 0
x = 3
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.