Aspelunker is surveying a cave. she follows a passage 180 m straight west, then 290 m in a direction 45∘ east of south, and then 280 m at 30∘ east of north. after a fourth unmeasured displacement, she finds herself back where she started. determine the direction of the fourth displacement? (degrees) (south of west)

The direction of the fourth displacement is θ = 12.775  ( south of west)

Explanation:

write down the values in the question,

The passage is 180m west, 290m in the direction 45° east of south, 280m at 30° east of north.

x = 290 × cos 45° + 280 × sin 30° -180

x=165.06 m

y= 280 cos ( 30° - 290 × sin (45°)

y= 37.426°

θ = tan ^-1 (y/x) = tan^-1 (37.426 / 165.06)

θ= 12.775° ( south of west)

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.