Which is the prime factorization of 84?
1 answer:
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Answer:
f(x) =
Step-by-step explanation:
The given options are,
a) f(x) =
b) f(x) =
c) f(x) =
d) f(x) =
Now, among the given options only option (a) satisfies the criteria stated in the question i. e.,
1. f(x) → 0 as x → - ∞ and
2 f(0) = 1
so, the correct answer is,
f(x) =
Step-by-step explanation:
The upstream speed is S / t₁, and the downstream speed is S / t₂.
If we say f is the speed of the fish in calm water, and r is the speed of the river, then:
f − r = S / t₁
f + r = S / t₂
If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.
Using Pythagorean theorem:
f² = (ℓ/T)² + r²
f² − r² = (ℓ/T)²
(f − r) (f + r) = (ℓ/T)²
(S / t₁) (S / t₂) = (ℓ/T)²
S² / (t₁ t₂) = (ℓ/T)²
(t₁ t₂) / S² = (T/ℓ)²
√(t₁ t₂) / S = T/ℓ
T = ℓ√(t₁ t₂) / S
