Answer:
the circumference of a circle with a radius is 5000
Answer:
- MN = (21 -6√3)/37 ≈ 0.286694
- RK = (14√3 -12)/37 ≈ 0.331046
Step-by-step explanation:
In the attached figure, we have defined LM to be length x. Then the other lengths on side AC are ...
AM = LR = x/√3
RC = (2/√3)RK = (2/√3)(2/√3)x = 4/3x
Then the sum of lengths along AC is ...
AC = AM +ML +LR +RC
1 = x(1/√3 +1 +1/√3 +4/3) = x(7/3 +2/√3) = x(7√3 +6)/(3√3)
Then the value of x is ...
![x=\dfrac{3\sqrt{3}}{7\sqrt{3}+6}=\dfrac{3\sqrt{3}(7\sqrt{3}-6)}{(7\sqrt{3})^2-6^2}=\dfrac{3(21-6\sqrt{3})}{3(49-12)}\\\\\boxed{MN=\dfrac{21-6\sqrt{3}}{37}}\\\\RK=\dfrac{2\sqrt{3}}{3}MN\\\\\boxed{RK=\dfrac{14\sqrt{3}-12}{37}}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%5Csqrt%7B3%7D%7D%7B7%5Csqrt%7B3%7D%2B6%7D%3D%5Cdfrac%7B3%5Csqrt%7B3%7D%287%5Csqrt%7B3%7D-6%29%7D%7B%287%5Csqrt%7B3%7D%29%5E2-6%5E2%7D%3D%5Cdfrac%7B3%2821-6%5Csqrt%7B3%7D%29%7D%7B3%2849-12%29%7D%5C%5C%5C%5C%5Cboxed%7BMN%3D%5Cdfrac%7B21-6%5Csqrt%7B3%7D%7D%7B37%7D%7D%5C%5C%5C%5CRK%3D%5Cdfrac%7B2%5Csqrt%7B3%7D%7D%7B3%7DMN%5C%5C%5C%5C%5Cboxed%7BRK%3D%5Cdfrac%7B14%5Csqrt%7B3%7D-12%7D%7B37%7D%7D)
Answer:
Don caught 3.6 kg and Dan caught 0.6 kg.
Step-by-step explanation:
Set up a system of equations:
Don's fish is the variable a and Dan's fish is the variable b.
a + b = 4.2 (1)
a=6b (2)
We can substitute a in the first equation using the second equation, so:
6b + b = 4.2
7b = 4.2
b = 0.6 kg
Dan caught 0.6 kg. Then, we can use equation 2 to find how much Don caught.
a = 6 x 0.6
a = 3.6
Don caught 3.6 kg.