Describe how you would factor x^2 - 10x + 24. Be specific.
2 answers:
<h2>Problem:</h2>
Describe how you would factor.
To factorize we split
into two factors, whose sum is b. In polynomial
, the product is 24 and hence such factors would be -6 and -4. Hence splitting middle term this way.
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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
Answer:
Step-by-step explanation:
I'm assuming you meant to type in
because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to
and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.
The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!