Answer:
It will still be a frame
Step-by-step explanation:
F(x + 1) = (5/2)*f(x)
f(x + 1) = 2.5*f(x), f(1) = 3.2
f(2) = 2.5f(1) = 2.5*3.2 = 8
<span>f(3) = 2.5f(2) = 2.5*8 = 20
</span>
f(4) = 2.5f(3) = 2.5*20 = 50
<span>f(5) = 2.5f(4) = 2.5*50 = 125</span>
Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
When the car is moving, it has Kinetic Energy. As soon as the car entercount with the spring, its Kinetic Energy will transfer to Elastic Potential Energy.
<span>KE = EPE </span>
<span>1/2mv^2 = 1/2kx^2 </span>
<span>change the speed into m/s </span>
<span>50 km/hr = 13.9 m/s </span>
<span>1/2(1200)(13.9)^2 = 1/2k(2.2)^2 </span>
<span>now you do the math to solve for k.
k= 115926/2.42
K= 47903.30</span>
