P(t)=500(1+4t/(50+t^2 ))
P'(t) = 500 [(50+t^2).4 - 4t.2t]/(50+t^2)^2
by the quotient rule
500 (-4t^2 + 200)/(t^2 + 50)^2
Hence
P'(2) = 500 . (-16 + 200)/54^2 ~= 31.6
To convert 180 degrees to its equivalent radian measure, multiply it with π/180.
180 (π/180)
The result is π radians.
This is also how the other angles in degrees are converted to radians. Simply multiply with π/180 and express the result in terms of pi.<span />
Answer: Yes, the point (3,4) is a solution to the system.
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Proof of this:
Replace x with 3 and y with 4 in the first equation
x+y = 7
3+4 = 7
7 = 7
This confirms the first equation. Repeat for the second equation
x-2y = -5
3-2(4) = -5
3 - 8 = -5
-5 = -5
We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).
You haven't provided any value, but I can tell you the solution set for the inequality.
First of all, expand both sides:
Add 3x to both sides:
Add 6 to both sides:
Which is of course equivalent to
Divide both sides by 9
So, every number smaller than 2 is part of the solution of this inequality.
Answer:
Step-by-step explanation:
