The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.
Answer:
x = 36.3°
using tane rule:
Here!
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( rounded to nearest tenth of a degree)
10 students (brass)=40% of band
4 students (strings)=16% of band
? students (other)=44% rest of band
14/56%=?/44%
(cross multiply to find ?){don't forget to turn percents into decimals}
?=11
There are 25 students in total in the band.
Answer:
The vertical component of the force is 1352 pounds.
Step-by-step explanation:
Given that,
Force acting on the tree trunk, F = 3200 pounds
The truck's cable makes an angle of 25 degree with the vertical. We need to find the vertical component of the force. We know that the force is a vector quantity. The vertical component is given by :
Hence, the vertical component of the force is 1352 pounds.
Answer:
Each group has 1 fiction book and 2 nonfiction book(s).
