The ratio of girls to boys who participated in the quiz bowl was 7:5. There were 42 girls in the competition. How many boys part
1 answer:
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Answer:
Step-by-step explanation:
The side lengths of all 30-60-90 triangles are in ratio , where
is the hypotenuse of the triangle and
is the side opposite to the 30 degree angle.
In the given diagram, the side labelled 4 is opposite to the 30 degree angle. Since is labelled as the hypotenuse of the triangle,
must be
.
Variable must then represent
for
, yielding
Let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3
Then the equation is (x-x₁)(x-x₂) = 0
If you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.
You can see that a=1 (there is just an x²)
b = (-5 -2√7 + 2√7 - 5)/3 = -10/3
c = ((-5-2√7)/3 ) * (-5+2√7)/3) = -1/3
So the equation you're looking for is:
Then the equation is (x-x₁)(x-x₂) = 0
If you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.
You can see that a=1 (there is just an x²)
b = (-5 -2√7 + 2√7 - 5)/3 = -10/3
c = ((-5-2√7)/3 ) * (-5+2√7)/3) = -1/3
So the equation you're looking for is:
Answer:
1. Along a diagonal, and then along an edge.
2. 48.28 cm.
Step-by-step explanation:
Assume points A and B are at diagonally opposite corners, as in the diagram below.
1. Shortest path
The shortest path is to go along the diagonal AC and continue along the edge CB.
2. Distance
The distance travelled is
d = AC + CB
According to Pythagoras,
AC² = AD² + CD² = 20² + 20² = 400 + 400 = 800
AC = √800 = 20√2
d = AC + CB = 20√ 2+ 20 ≈ 2 × 1.414 + 20 = 48.28 cm
The ant travels 48.28 cm.
