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The maximum compression of the spring is 0.276 m
Step-by-step explanation:
First of all, we calculate the spring constant of the spring, by using Hooke's law:

where
F = 10 kN = 10,000 N is the force applied
x = 1.25 cm = 0.0125 m is the corresponding compression of the spring
k is the spring constant
Solving for k,

When the truck impacts with the spring, all the kinetic energy of the truck is converted into elastic potential energy of the spring, so we can write
(1)
where
m is the mass of the truck
v = 2 m/s is the initial speed of the truck
is the spring constant
x is the compression of the spring
The mass of the truck can be found from its weight:

So now we can re-arrange eq.(1) to find the compression, x:

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Answer:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Step-by-step explanation:
The area of a sphere is given by the following formula:

In which A is the area, measured in cm², and r is the radius, measured in cm.
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.
This means that 
Determine the rate of change in surface area when r = 20 cm.
This is
when
. So

Applying implicit differentiation.
We have two variables, A and r, so:



The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Answer:
x = -26
Step-by-step explanation:
Multiply both sides by the lowest common multiple of 4 and 3, which is 12.
3(x+2) = 4(x+8)
3x + 6 = 4x + 32 --- distribute the 4 and 3
6 = x + 32 --- subtract 3x from both sides
-26 = x --- subtract 32 from both sides
x = -26
Answer:
75
Step-by-step explanation:
did it 5 mins ago