The ladder, the ground and the wall form a right triangle; the ladder length (L) is the longest side of this triangle. L^2 = h^2 + x^2, where h represents the height of the point on the wall where the ladder touches the wall, and x represents the distance of the base of the ladder from the wall.
We need dh/dt, which will be negative because the top of the ladder is sliding down the wall.
Starting with h^2 + x^2 = L^2, we differentiate (and subst. known values such as x = 5 feet and 4 ft/sec to find dh/dt. Note that since the ladder length does not change, dL/dt = 0. This leaves us with
dh dx
2h ---- + 2x ----- = 0.
dt dt
Since x^2 + h^2 = 15^2 = 225, h^2 = 225 - (5 ft)^2 = 200, or
200 ft^2 = h^2. Then h = + sqrt(200 ft^2)
Substituting this into the differential equation, above:
2[sqrt(200)] (dh/dt) + 2 (5) (4 ft/sec) = 0. Solve this for the desired quantity, dh/dt:
[sqrt(200)] (dh/dt) + (5)(4) = 0, or
dh/dt = -20 / sqrt(200) = (-1.41 ft / sec) (answer)
This result is negative because the top of the ladder is moving downward.
Answer:
f(x)= 1.8x + 1
Step-by-step explanation:
Just got it right on edge :)
The formula for simple interest is <em>I</em> = <em>prt</em>, where <em>I</em> is the amount of interest, <em>p</em> is the principal borrowed, <em>r</em> is the interest rate written as a decimal number, and <em>t</em> is the amount of time in years. First we find the amount of interest. He borrowed $35000 but paid back $46375. That means he paid 46375-35000 = $11375 in interest. We can now substitute our information into our interest formula:
11375=35000(<em>r</em>)(5)
11375=35000(5)(<em>r</em>) ----- remember that multiplication is commutative
11375=175000<em>r</em>
Divide both sides by 175000 to cancel it:
11375/175000 = 175000<em>r</em>/175000
0.065 = <em>r</em>
To convert this to a percentage, we multiply by 100:
0.065(100) = 6.5%
Answer:
the answer is 6
Step-by-step explanation:
2x + 9 = 21
2x = 21 - 9
2x = 12
x = 6
Answer:
16 km !
Step-by-step explanation:
all the others are FAR too small.. they wouldnt even be one story up ! and 16m isnt 5 stories either... km would be right !
i hope this helps !!
