My Notes A spring has a natural length of 22 cm. If a 29-N force is required to keep it stretched to a length of 30 cm, how much work W is required to stretch it from 22 cm to 26 cm

W = 0.058 J

Step-by-step explanation:

given data

natural length = 22 cm

force = 29 N

length = 30 cm

stretch = 22 cm to 26 cm

solution

force F = K x  .....................1

K is spring constant and x is length

Δx = 30 - 26

Δx = 4 cm = 0.4 m

and

F = Kx   ..............2

29 = K(0.4)

K =

K = 72.5

so here

required work to stretch spring

W = 0.5 × K  × Δx²   ...................3

but here

Δx = 26-22 = 4 m = 0.04

and

W = 0.5 × 72.5  × 0.04²

W = 0.058 J

the answer would be the last one (constat) she stays at the same rat every two mintues it goes up by 0.4

step-by-step explanation:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!