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.
You line the segments up in order from the first quad to the second.
The only one that lines up is AG and NP the first option.
Answer:
6 and 4
Step-by-step explanation:
Let one number be x.
Then another will be : 4x - 20
In accordance with the question;
x + 4x - 20 = 10
5x = 10 + 20
x = 30/5
= 6
x = 6
4x - 20 = 4×6 - 20 = 4
So, the numbers are 6 and 4.
Answer:
Answer:
3.14159
Step-by-step explanation:
This number is pi. Pi goes on for millions of digits on end.
Step-by-step explanation:
Answer:
65 feet and 2 inches
Step-by-step explanation:
to find the area of a rectangle you need to multiply length times width in this case 17" times 3'10". But first you must convert everything into the same form(in this case feet) so first you can convert everything to inches by multiplying 3 times 12 which gives you 36 then add the 10, so it is now 46 inches then multiply that by 17 and altogether it is 782 inches, then divide by 12 (to convert it back to feet) and the answer is 65.1666666667. After you can round and get 65 feet and 2 inches.
