"<span>Curve passes through the point (0,8) and has the property that the slope of the curve at every point pp is four-times the y-coordinate."
Slope of tangent line at a given point = value of derivative of function at that point.
Thus, dy/dx = derivative = 4y
Thus, dy/dx = 4y. Rearrange this with all y on one side and all x on the other:
dy
--- = 4dx
y
Integrating both sides, we get ln|y| = 4x + ln C, or ln|y| - ln C = 4x
|y|
Then ln -------- =4x. This can be written as an exponential function:
C
|y|
--- = e^(4x). Thus, |y| = C*e^(4x). Given that this curve passes thru (0,8),
C
8 = C*e^0, so C = 8. Then the function question is y = 8e^(4x).</span>
Answer:
Motor 1) 7 ½ horsepower single phase, 230 volts 40 ampere) ; Motor 2) 5 ... for a 2 horsepower 115 volt motor that has a full-load current rating of 24 ampere, ... Simultaneously disconnects all conductors of the circuit.
Answer:
Step-by-step explanation:
Start by drawing out the triangle on the graph:
(See picture)
(By the drawing you can judge me that I am a really bad artist)
Theta and the side lengths are labeled, the hypotenuse has a length of √21 by Pythagora's theorem. Now, time to put everything to the trigonometric functions:
(Suppose that x is theta as I can't type it)
By some basic understanding that's all that I can do.