<span>y = sqrt(25-x^2) at point (3,4)
The derivative gives us the slope at 3 to be:
-2x
------------ at x=3: -3/4
2sqrt(25-x^2)
</span><span>so we have a vector that is parallel to the slope of the tangent line is: <4,-3>
</span>
<span>the mag = 5 so; unit tangent = <4/5 , -3/5>
</span>
<span>since perpendicular lines have a -1 product between slopes we get the normal to be...
<3/5,4/5>
</span>
<span>It is <4,-3> because it is rise over run. Rise is y component of vector and run is x component of vector.</span>
Answer:
209.22cm²
Step-by-step explanation:
A=πrl+πr2
l=r2+h2
Solving forA
A=πr(r+h2+r2)=π·4·(4+122+42)≈209.21889cm²
He worked 36 hours (9.57), and anything over that was over pay (14.36)
36 * 9.57 = 344.52
So, working his normal hours he got $344.52.
416.32 - 344.52 = 71.80
71.80/14.36 = 5
Therefore, he worked 5 hours of overtime.
Answer:
2 3/4 in.
Step-by-step explanation:
66/6 = 11
11(1/4) = 11/4
11/4 = 2 3/4
Full Question
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
Answer:
Spring Constant = 1000Nm^-1
Step-by-step explanation:
Given
Mass = 10kg
Spring Extension = 9.8cm
Spring Constant K = Force/Extension
Force = Mass * Acceleration
Force = 10 * 9.8 = 9.8N
Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m
Spring constant = 98 / 0.098
Spring Constant = 1000Nm^-1
