A ball is pushed down a hill with an initial velocity of 2.5 m/s. As it rolls it accelerates at a rate of 6m/s/s. What will be it’s velocity 1.5 minutes later?

Step-by-step explanation:

This is more physics than math because you need to know the equations for one-dimensional motion to get this done. The equation we need is

where v is the final velocity, v0 is the initial velocity, a is the acceleration and t is the time in seconds. That means that since our time is given in minutes we have to convert it to seconds. I'm not sure how much importance your teacher gives to significant digits, but if you use them here, the answer you get is way off, so we will disregard them here. 1.5 minutes is 90 seconds. Now that have the time in seconds and the equation we need, we will fill it in accordingly:

Note immediately that the seconds on the time cancels out one of the seconds in the denominator of the acceleration so we're left with m/sec + m/sec which is what we need to add those 2 terms. Multiply 6 by 90 to get 540 m/sec. then add that to 2.5 m/sec to get 542.5 m/sec. That must be really long hill!!!

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

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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

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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!

70.30

step-by-step explanation: