Answer:
TU=86.5 feet
Step-by-step explanation:
We are given with <U is 90 degrees. It means it is a right triangle.
So, we can use trigonometric ratio to solve.
There are 50 millimeters in 5 centimeters.
Checking answer A:
distance from U to V = -2-(-11)=9
distance from U to W =7-(-2)=9 -> same distance !
checking answer B:
distance U-V : -2-(-8)=6
U-W : -2-(-6)=4 -> not the same distance
answer C :
U-V : -2-(-6)=4
U-W : 6-(-2)=8 -> not the same distance
answer D :
U-V : 0-(-2)=2
U-W : 2-(-2)=4 -> not the same distance
Conclusion : answer A
Answer:
4
Step-by-step explanation:
Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have
population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as
(original population)*1.011ˣ
Therefore, to get from 7 billion to 7.31 billion, we have
7 billion * 1.011ˣ = 7.31 billion
divide both sides by 7 billion to relatively isolate the x
1.011ˣ = 7.31/7
Another way of writing this is
log (base 1.011) (7.31/7) = x
≈ 3.96
Rounding to the nearest whole number, we get 4 as our answer
Answer:
See answer below
Step-by-step explanation:
Define the intervals:
for n≥1.
The intervals are nested, in the sense that 
To see this, use the fact that for all n≥1, -1/n≤-1/(n+1) and 1/n≥1/(n+1) (intuitively, the intervals are "shrinking" in size, and are centered around √2).
The only point common to all intervals is √2, in the sense that 
The idea for this construction is to center the intervals around √2 and shrink their size with the summand 1/n. As n goes to infinity, 1/n tends to zero and the intervals became closer and closer to √2, but they NEVER degenerate to the point √2, in contrast to their intersection.
