A) suppose {u,v,w} spans the vectore space V.
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Answer: The length of the hypotenuse is 26 cm
Step-by-step explanation: Please refer to the attached diagram
The triangle ABC is drawn as described such that the right angle is at point C and line AB is the hypotenuse which is yet unknown.
Since we have a right angled triangle with two sides known and one unknown, we can apply the Pythagoras theorem which states that
AC² = AB² + BC² where AC is the hypotenuse and AB and BC are the other two sides
In this question the hypotenuse is AB, so we now have;
AB² = AC² + CB²
AB² 24² + 10²
AB² = 576 + 100
AB² = 676
Add the square root sign to both sides of the equation
√AB² = √676
AB = 26
Therefore the length of the hypotenuse is 26 cm
A passenger flies on a heading of N40W with an airspeed of 240 km/h. His actual ground velocity is 250 km/h at a bearing of N60E. the speed and direction of the wind are V=245.15kw/h at N83.46E. This is further explained below.
<h3>What is the speed and direction of the wind.?</h3>Generally, the equation for the cosine rule is mathematically given as
a2 = b2 + c2 – 2bc cos ∠x.
Therefore
V^2 = (240^2 + 250^2) – (2(240*250)* cos 100)
V^2=140937.7813
V=375.42kw/h
In conclusion, the sine rule is mathematically given as
Sin x/240=sin60/375.42kw/h
Therefore
sin x=sin100*250/375.42kw/h
x=40.981
Hence
Direction N83.46E
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