<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
Formula: s = r<span>θ
With r = 24 cm, </span>θ = (2/3)*<span>3.14 radians
s = 24*(2/3)*3.14 = 50.24 cm</span>
Answer:
182
Step-by-step explanation:
The correct answer is 182 because to figure out the total we needed to multiply the 2 sides, a quicker way instead of counting. To do this you needed to multiply 13 times 14 and you would get 182!
Hope this helped!
Please mark as best answer if right!
If the face is a square, then (l*l)
If the face is a triangle, then (b*h)(1/2)
If the face is a rectangle, then (l*w)
If the face is a circle, then (r²)(3.14)
You can then add all these faces up to get the total surface area of the prism.
Answer: 58/9 exact form, decimal form is 6.4the four is repeated, mixed number is 6 4/9
Step-by-step explanation: