What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If e
ither is false, give a counterexample.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
2 answers:
Answer: A
Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:
Conditional: If someone like ice cream, they have brown hair
Converse: If someone has brown hair, they like ice cream
The converse of our given conditional would be:
If two lines do not intersect, they are parallel
This eliminates Option D
Next, the converse is false.
Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they <em>could</em> be either parallel or skew.
This eliminates Option C and B, leaving us with Option A
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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
