Answer:
60th caller.
the 12th caller would hit a number divisible by 20 at 60.
12,24,35,48,60
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
Answer:
45 = (one third)x + 15
Step-by-step explanation:
If x represents the number of minutes Tom commutes, then (1/3)x is "one-third as many minutes as Tom's commute." 15 minutes more than that is ...
(1/3)x + 15
We are told this is the length of Paul's commute, and that it is 45 minutes. So, the appropriate equation is ...
45 = (1/3)x +15
Answer:
The arc measure, x, that the satellite can see is 160°
Step-by-step explanation:
Given that the two tangents intersect at a point outside the with circle center O
The angle formed between between the two tangent = 20°
The first arc formed is measured as x°, which is the arc opposite the point where the two tangents meet = The arc the satellite can see
The angle x is given by the relationship;
x = 2 × (90 - v/2)
Where;
v = The angle formed at the point where the two tangent meet = 20°
Therefore;
x = 2 × (90 - 20/2) = 2 × (90 - 10) = 2 × 80 = 160°
The arc measure, x, that the satellite can see = 160°.
Answer: 3/5
Step-by-step explanation: simplified completely
