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:
Learn more about kinetic energy:
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The final amount in the account after 25 years is $24670.42.
<h3>
How do you calculate the final Amount after 25 Years?</h3>
Given that 3400 dollars are placed in an account with an annual interest rate of 8.25% for 25 years.
The final amount in the account is calculated by the formula given below.
Where A is the final amount, P is the initial principal balance, R is the interest rate, T is the time period.
The final amount is given below.
Hence we can conclude that the final amount in the account after 25 years is $24670.42.
To know more about the compound interest, follow the link given below.
brainly.com/question/25857212.
Step-by-step explanation:
cot²x − cot x − 42
(cot x − 7) (cot x + 6)
Answer:
1300
Step-by-step explanation:
We are given
x = 35
[rate of change of price with time]
We want to find 
, which is the rate at which supply is changing.
First, we need to implicitly differentiate the equation given:
Here, we have what we need except for p. We find p when x = 35:
Now, find dx/dt:
In thousands, 1.30 * 1000 = 1300 cartons per week decrease
Answer:
10
Step-by-step explanation:
2x - 3y = 24 ------ (1)
3x + 4y = 2 ------ (2)
(1) × 4,
8x - 12y = 96 ------ (3)
(2) × 3,
9x + 12y = 6 ------ (4)
(3) + (4)
17x = 96 + 6
= 102
x = 102 ÷ 17
= 6
Sub x = 6 into (2),
3(6) + 4y = 2
18 + 4y = 2
4y = 2 - 18
= -16
y = -16 ÷ 4
= -4
Therefore,
x - y = 6 - (-4)
= 6 + 4
= 10
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