Answer:
the angle is changing at a rate of 0.0375 rad/s when the time is t=8 seconds
Step-by-step explanation:
since the line D that starts from the spectator and follows the plane has the following equation
D² = x² + H² , where H= altitude of the plane , x= horizontal distance
then for x=v*t , where v=speed of the plane and t=time since the plane has passed overhead , we have for the elevation angle
tan θ = x/y = v*t /H
θ = tan⁻¹ ( v*t /H)
the rate of change in the angle of the spectator's sight θ with the time is
dθ/dt = 1/1+(v*t /H)² * (v/H) = (v/H)/[1+ (v/H)²*t²]
for t=8 seconds
dθ/dt = (875 ft/s/21000 ft)/[1+ (875 ft/s/21000 ft)²*(8 s)²] = 0.0375 rad/s
therefore the angle is changing at a rate of 0.0375 rad/s when the time is t=8 seconds
Answer:
x = 8
Step-by-step explanation:
Using the sine or cosine ratio in the right triangle and the exact value
sin30° = 
, then
sin30° = 
= 
= ( cross- multiply )
x = 8
Answer:
divide the equation by 5
Step-by-step explanation:
all the components are factors of 5 so if we divide by 5, then we get as x² - 2x = -1
Solve the following system:
{-3 + 2 x + y = 0 | (equation 1)
{-1 + x + y = 0 | (equation 2)
Express the system in standard form:
{2 x + y = 3 | (equation 1)
{x + y = 1 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + y = 3 | (equation 1)
{0 x+y/2 = (-1)/2 | (equation 2)
Multiply equation 2 by 2:
{2 x + y = 3 | (equation 1)
{0 x+y = -1 | (equation 2)
Subtract equation 2 from equation 1:
{2 x+0 y = 4 | (equation 1)
{0 x+y = -1 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 2 | (equation 1)
{0 x+y = -1 | (equation 2)
Collect results:
Answer: {x =2 , y = -1
