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Kay [80]
3 years ago
12

A forecast is defined as a(n) a. set of observations on a variable measured at successive points in time. b. prediction of futur

e values of a time series. c. outcome of a random experiment. d. quantitative method used when historical data on the variable of interest are either unavailable or not applicable.
Mathematics
1 answer:
marshall27 [118]3 years ago
8 0

Answer:

D

Step-by-step explanation:

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D.) 57

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1 \frac{7}{15}

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1)a chord of length 18cm midway the radius of a circle. calculate the radius of the circle correct to 1d.p. 2)if two parallel ch
kykrilka [37]
Part 1:

Given that the length of the chord is 18 cm and the chord is midway the radius of the circle. 

Thus, half the angle formed by the chord at the centre of the circle is given by:

\cos\theta=\frac{\left( \frac{1}{2} r\right)}{r}= \frac{1}{2}  \\  \\ \Rightarrow\theta=\cos^{-1}\left( \frac{1}{2} \right)=60^o

Now, 

\sin60^o= \frac{9}{r}  \\  \\ \Rightarrow r= \frac{9}{\sin60^o} =10.392

Therefore, the radius of the circle is 10.4 cm to 1 d.p.


Part 2I:

Given that the radius of the circle is 10 cm and the length of chord AB is 8 cm. Thus, half the length of the chord is 4cm. Let the distance of the mid-point O to /AB/ be x and half the angle formed by the chord at the centre of the circle be θ, then

\sin\theta= \frac{4}{10} = \frac{2}{5} \\ \\ \theta=\sin^{-1}\left( \frac{2}{5} \right)=23.6^o

Now, 

\cos23.6^o= \frac{x}{10} \\ \\ \Rightarrow x=10\cos23.6^o=9.165\approx9.2cm


Part 2II:

Given that the radius of the circle is 10cm and the angle distended is 80 degrees. Let half the length of chord CD be y, then:

\sin40^o= \frac{y}{10}  \\  \\  \\ \Rightarrow y=10\sin40^o=6.428

Thus, the length of chord CD = 2(6.428) = 12.856 which is approximately 12.9 cm.
3 0
3 years ago
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