Answer:
-30%
Step-by-step explanation:
The percentage change in length is given by ...
percent change = ((new length) -(original length))/(original length) × 100%
= (51.29 -73.3)/73.3 × 100%
= -22.01/73.3 × 100% = -0.30027 × 100%
= -30%
The decrease in the length of the spring was 30%.
Answer:
9.56 ft/sec
Step-by-step explanation:
We are told that a 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec.
I've attached an image showing triangle that depicts this;
Thus; dx/dt = 3.4 ft/sec
From the attached image and using principle of similar triangles, we can say that;
9/y = 5.8/(y - x)
9(y - x) = 5.8y
9y - 9x = 5.8y
9y - 5.8y = 9x
3.2y = 9x
y = 9x/3.2
dy/dx = 9/3.2
Now, to find how fast the tip of the shadow is moving away from the lamp post, it is;
dy/dt = dy/dx × dx/dt
dy/dt = (9/3.2) × 3.4
dy/dt = 9.5625 ft/s ≈ 9.56 ft/sec
The first if a twisted version of a Fibonacci sequence :P
If a1=1.2 and a2=2.3 and a(n)=a(n-1)+a(n-2)
a3=3.5, a4=5.8, a5=9.3
So the first five terms are: 1.2, 2.3, 3.5, 5.8, 9.3
The second is another modified Fibonacci sequence...
If a3=-5 and a4=3 then:
3=-5+a2, a2=8
-5=8+a1, a1=-13
a5=-5+3=-2
a6=-2+3=1
So the first six terms are -13, 8, -5, 3, -2, 1