Step-by-step explanation:
Use exponent property of logs.
logb(x²) = 2 logb(x) = 2(0.49) = 0.98
Answer:
The answer is 130 feet
Step-by-step explanation:
Using Pythagoras' Theorem:
120² + 50² = diagonal²
diagonal² = 16900ft
diagonal = √16900
= 130ft
(Correct me if i am wrong)
We know that
1) Sandra can run a mile in 6 minutes-------> 6*60-----> 360 sec
2) 4 laps around the track equals 1 mile
so
4 laps around the track in 360 sec
1 lap in 360/4--------> 90 sec
3) the position of Sandra for t=90 sec must be equal to the point S (0,56)
I proceed to analyze each case for t=90 sec
case a) x(t)=-140 cos(pi*t/45) y(t)=112 sin(pi*t/45)
x(t)=-140 cos(pi*90/45)------> -140
y(t)=112 sin(pi*90/45)-------> 0
the position is the point (-140,0)------> is not the point S
case b) x(t)=140 sin(pi*t/90) y(t)=-112 cos(pi*t/90)
x(t)=140 sin(pi*90/90)------> 0
y(t)=-112 cos(pi*90/90)-------> 112
the position is the point (0,112)------> is not the point S
<span>
case c) x(t)=-70 sin(pi*t/45) y(t)=56 cos(pi*t/45)
</span>x(t)=-70 sin(pi*90/45)------> 0
y(t)=56 cos(pi*90/45)
-------> 56
the position is the point (0,56)------> is equal to the point S----> is the solution
case d) x(t)=70 cos(pi*t/90) y(t)=-56 sin(pi*t/90)
x(t)=70 cos(pi*90/90)------> -70
y(t)=-56 sin(pi*90/90)-------> 0
the position is the point (-70,0)------> is not the point S
therefore
the answer is the option C
x(t)=-70 sin(pi*t/45) y(t)=56 cos(pi*t/45)
