Special Triangles Theorem
leg1=leg2=a
hypotenuse=a√2=10
Both Legs are 5√2 inches
In
order to solve for a nth term in an arithmetic sequence, we use the formula
written as:<span>
an = a1 + (n-1)d
where an is the nth term, a1 is the first value
in the sequence, n is the term position and d is the common difference.
</span><span>THIRD
</span><span>A3=4+(3-1)(-5)
A3 = -6
A(3)=-2(3-1)(-5)
A3 = 20
</span><span>
FIFTH
</span>A5=4+(5-1)(-5)
A5 = -16
A(5)=-2(5-1)(-5)
A5 = 40<span>
TENTH
</span>A10=4+(10-1)(-5)
A10 = -41
A(10)=-2(10-1)(-5)
A10 = 90
I) f(2)=1.5
ii) f(x)=0 ⇒ x=1.2
iii) k=-1
iv) x=1 ⇒ f(x)=1
Answer:
100.9 yards
Step-by-step explanation:
One circuit of the track is a distance of ...
C = 2πr = 2π(60 yd) = 120π yd.
At Alex's running rate, the distance covered in 20 minutes is ...
(4 yd/s)(20 min)(60 s/min) = 4800 yd
The number of circuits will be ...
(4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits
The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,
That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd
The shortest distance along the track to Alex's starting point is about 100.9 yards.
_____
<em>Additional comment</em>
The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.
