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Can someone please help me??? Its urgent. 15 Points.
2 answers:
Answer:
The measure of arc ABC is 180 + x ⇒ 1st answer
Step-by-step explanation:
Let us revise some notes about the arcs of a circle
- The measure of an inscribed angle is half the measure of its subtended arc
- The measure of the central angle is equal to the measure of its subtended arc
- If two tangents intersect outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs
∵ CD and AD are two tangents to the given circle
∵ They intersected at point D out side the circle
∵ The measure of ∠ADC = x°
- By using the 3rd note above
∵ The intercepted arcs are arc ABC and arc AC
∴ x° = (measure of arc ABC - measure of arc AC)
- Multiply both sides by 2
∴ 2 x = (measure of arc ABC - measure of arc AC)
- Add measure of arc AC in both sides
∴ 2 x + measure of arc AC = measure of arc ABC ⇒ (1)
∵ The measure of a circle is 360°
∵ The arcs ARC and AC is formed the circle
∴ Measure of arc ABC + measure of arc AC = 360°
- Subtract measure of arc ABC from both sides
∵ Measure of arc AC = 360 - measure of arc ABC ⇒ (2)
- Substitute (2) in (1)
∴ 2 x + 360 - measure of arc ABC = measure of arc ABC
- Add measure of arc ABC to both sides
∴ 2 x + 360 = 2 measure of arc ABC
- Divide both sides by 2
∴ x + 180 = measure of arc ABC
∴ The measure of arc ABC is 180 + x
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Answer:
2 hours
Step-by-step explanation:
Let x mph be the speed of motorboat in still water and y mph be the speed of current.
A raft and a motorboat simultaneously leave from the same point and move down the river, then speeds down the river are:
motorboat = x + y mph
raft = y mph
In two hours they will cover:
motorboat = 2(x+y) miles
raft = 2y miles
After 2 hours the motorboat turns around and starts moving towards the raft (against the current), so its speed is now x - y mph.
Let t be the time they move towards each other. In t hours, they cover
motorboat = t(x - y) miles
raft = ty miles
The distance from the starting point to the turning point is the same as the sum of the distances the raft covers and the motorboat covers after turning around, so