Answer:
-9
Step-by-step explanation:
-2x + 3 = -x + 12
move -x over by adding
-x + 3 = 12
move the 3 over by subtracting
-x = 9
divide by - to get the x positive
x = -9
Answer:
x = 4
, y = 6
Step-by-step explanation:
Solve the following system:
{x + 3 y = 22 | (equation 1)
2 x - y = 2 | (equation 2)
Swap equation 1 with equation 2:
{2 x - y = 2 | (equation 1)
x + 3 y = 22 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x - y = 2 | (equation 1)
0 x+(7 y)/2 = 21 | (equation 2)
Multiply equation 2 by 2/7:
{2 x - y = 2 | (equation 1)
0 x+y = 6 | (equation 2)
Add equation 2 to equation 1:
{2 x+0 y = 8 | (equation 1)
0 x+y = 6 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 4 | (equation 1)
0 x+y = 6 | (equation 2)
Collect results:
Answer: {x = 4
, y = 6
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)
