That point will be where the perpendicular line through the origin intersects the given line.
.. (-1/4)x = 4x +3
.. -3 = (17/4)x
.. -12/17 = x
The point on the given line that is closest to the origin is (-12/17, 3/17).
9514 1404 393
Answer:
The pool is being filled
Step-by-step explanation:
The function definition tells you ...
f(5) = the volume of water in the pool 5 minutes after they start
f(10) = the volume of water in the pool 10 minutes after they start
So, the inequality ...
f(5) < f(10)
means the volume of water in the pool 10 minutes after they start is greater than it is 5 minutes after they start. In short, <em>they are filling the pool</em>.
Answer:
47.8
Step-by-step explanation:
8^2+3.8-10*2
64+3.8-20
47.8
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
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The solution to x + 8.5 = 64.5 is 56.
x + 8.5 = 64.5
- 8.5 - 8.5
---------------------------
x = 56
