X, Y and Z are three points on a map. Y is 75km and on a bearing of 200° from X. Z is on a bearing of 150°, from Y. Z is due sou
1 answer:
Answer:
The distance between X and Z is approximately 114.9 km
Step-by-step explanation:
The given parameters are;
The distance of Y from X = 75 km
The bearing of Y from X = 200°
The bearing of Z from Y = 150°
The bearing of Z from X = 180°
In triangle XYZ, we have;
∠YZX = 180° - (130° + 20°) = 30°
By sine rule, we have;
(75 km)/sin(30°) = XZ/(sin(130°))
XZ = sin(130°) × (75 km)/sin(30°) ≈ 114.9 km
The distance between X and Z ≈ 114.9 km. to one decimal place.
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This equation uses two properties of logarithms:
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15
Answer:
V = 1385.44
Step-by-step explanation:
The equation for volume is V = π r 2 h! Where V = volume, r = radius <em>(half the diameter)</em>, and h = height. Now lets substitute what we know into this equation!
<em>Since we are giving the diameter (14) we must divide by 2 to find the radius.</em>
14 ÷ 2 = 7
Radius = 7
Height = 9
V = ?
Time to plug these values in!
V = π (9)
<em>We have to distribute </em><em>pi to 7 square that term </em><em>and then </em><em>multiply the value by 9</em><em>. </em>
<em />
V = 1385.44
Hope this Helps! :)
<em>Have any questions? Ask below in the comments and I will try my best to answer.</em>
-SGO