Answer:
2
Step-by-step explanation:
Answer: Choice C. 107.9 degrees (approximate)
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Explanation:
Draw a line segment from A to B. Mark point E as the intersection between this new line segment and the arc CD.
We can see that AE = 4000 because it's another radius of the same circle. The diagram shows that EB = 2800.
So,
AB = AE+EB = 4000+2800 = 6800
Because point D is a tangent point, this means radius AD is perpendicular to tangent segment BD. We have a 90 degree angle at point D, or we can write angle BDA = 90.
With triangle BDA being a right triangle, we can use a trig ratio to compute angle DAB. I'll call this angle A for short.
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Apply the cosine ratio. Focus entirely on triangle BDA.
cos(angle) = adjacent/hypotenuse
cos(A) = AD/AB
cos(A) = 4000/6800
cos(A) = 10/17
A = arccos(10/17)
A = 53.9681209275294 ... make sure your calc is in degree mode
A = 53.968
Angle DAB = 53.968 degrees approximately
This represents exactly half of central angle CAD, so we'll double the value to get 2*53.968 = 107.936 which rounds to 107.9 degrees showing why choice C is the answer.
Central angle CAD is exactly equal to the arc it cuts off, minor arc CD. The central angle is roughly 107.9 degrees of a full 360 degree circle, and the same can be said about the outer arc edge piece of minor arc CD.
Answer:
Step-by-step explanation: the answer is 222
Answer:
56
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 17 and a₁₃ = 38, then
a₁ + 5d = 17 → (1)
a₁ + 12d = 38 → (2)
Subtract (1) from (2) term by term to eliminate a₁
7d = 21 ( divide both sides by 7 )
d = 3
Substitute d = 3 into (1) and evaluate for a₁
a₁ + 5(3) = 17
a₁ + 15 = 17 ( subtract 15 from both sides )
a₁ = 2
Thus
= 2 + (18 × 3) = 2 + 54 = 56
The correct answer is B, 8,287.