Discrete Math - Find X
1 answer:
Answer:
x = 70°
Step-by-step explanation:
Clockwise from top, call the three tangent points A, B, and C. Central angle AXC is the supplement of the marked external angle, so is 140°. Arc AB is bisected by the upper ray of angle x; and arc BC is bisected by the lower ray of angle x. That is to say x is half the measure of arc AC, so is 70°.
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Attached is the output of a geometry program. The angle at lower left is 40° as in the given figure. The central angle α (70°) remains the same as tangent point C is moved around, which is to say that the measure of the angle α does not depend on the dimensions of the triangle containing α. It just depends on the fact that the triangle is tangent to the circle.
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Answer:
There will be one person on 1 square yard of land after 1,892,147.588 years.
Step-by-step explanation:
Continuous exponential growth formula:
P(t)= Population after t years.
P= Initial population
r=rate of growth.
t= time in year
Given that,
Growth rate of country A (r)= 4.9% per year=0.049 per year.
Initial population (P)= 151,000.
Land area of country area= 14,000,000,000 square yards.
There will be one person on one square yard of land.
So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.
P(t)=14,000,000,000 person
Taking ln both sides
years
There will be one person for every square yard of land after 1,892,147.588 years.