<span>a. what is the rate of change of the height of the top of the ladder?
Let y be the height
Let x be the base
dx/dt=8 ft/sec, x=6 ft, hypotenuse=10 ft
x</span>²+y²=10²
2x(dx/dt)+2y(dy/dt)=0
solving for dy/dt in terms of x,y and dx/dt:
dy/dt=(-x/y)(dx/dt)
but now x=6 and y=8
dy/dt=(-6/8)(8)=-6 ft/sec
b]<span>b. at what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
</span>Here the rate of change of the area is dA/dt
dA/dt=1/2(x*dy/dt+y*dx/dt)
but
x=6, y=8, dy/dt=-6, dx/dt=8
plugging in our values we get:
dA/dt=1/2(6×(-6)+8(8))
dA/dt=1/2(-36+64)=14 ft²/sec
c. At what rate is the angle between the ladder and the ground changing then?
The relationship that relates the angle with sides x and y of a right angle:
dθ/dt=-1/sinθ1/10dx/dt
sinθ=8/10
dx/dt=8
thus
-10/8×1/10×8
=-1 rad/sec
In the right triangle, the longest side is the hypotenuse.
Let α be the angle opposite to the side with a length of 12 units, <span>then according to the Law of sines:
</span>
In a triangle, the three interior angles always add to 180° ⇒
third angle = 180 - 90 - 67 = 23°
Answer:
67° and 23° (to the nearest degree).
Answer:
The y-intercept is (0,-3)
Step-by-step explanation:
The y-intercept is where x=0 and it intersects with the y-axis.