If no number can be used more than once, how many different 2-digit numbers can be formed from the digits 4, 6, and 8?
1 answer:
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Answer:
NK = 14.4
Step-by-step explanation:
Given the following question:
We know that the two sides are similar
JI = 3, NM = 7.2
<u>The scale factor is 2.4 since....</u>
Knowing the two sides are similar and if we multiply JI by 2.4, we get NM we can easily do the same for JG and NK.
JG = 6
NK = 14.4
Hope this helps.
Answer:
(i) see first attached diagram
(ii) QR = 22.67 km (2 dp)
(iii) 243°
Step-by-step explanation:
A bearing is the angle in degrees measured clockwise from north.
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<u>Part (i)</u>
see first attached diagram
<u>Part (ii)</u>
The angles marked in blue on the second attached diagram are Consecutive Interior Angles. In this case they add to 180° as the North lines are parallel.
The sum of angles around a point is 360°
⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°
To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.
⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)
⇒ QR² = 32² + 24² - 2(32)(24)cos(45)
⇒ QR² = 513.8839841...
⇒ QR = √513.8839841...
⇒ QR = 22.67 km (2 dp)
<u>Part (iii)</u>
We need to find the angle marked in green on the third attached diagram.
To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°
Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)
Orange angle (o) using the sine rule:
⇒ sin(o)/32 = sin(45)/QR
⇒ sin(o) = 32sin(45)/22.67
⇒ sin(o) = 0.9981652337...
⇒ o = 86.52868176...°
Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)
