X=252.........................................
The potential energy, E, of the penny is given by E=mgh. The energy, Q, required to raise the temperature of an object by an amount ΔT is given by Q=mcΔT. We can equate these two to get the result but we must use proper units and include the 60%:
(0.6)mgh=mcΔT
We see we can divide out the mass from each side
0.6gh=cΔT, then 0.6gh/c=ΔT
(0.6)9.81(m/s²)50m/385(J/kg°C) = 0.7644°C
since this is the change in temperature and it started at 25°C we get
T=25.7644°C
As you can see the result does not depend on mass. The more massive the copper object the more potential energy it will have to contribute to the heat energy, but the more stuff there will be to heat up, and the effect is that the mass cancels.
Answer:
is it an echo
Step-by-step explanation:
. ................
So, we are given 5^8. It was happy and content. But then... we had to write it as a quotient of two exponential terms with the same base in four different ways and use negative or zero exponents and ahhhhhh!!!
... anyways...
We'll build a quotient of two exponential terms with the same base 5. Something like this:
5^a / 5^b
We need them to make 5^8 when we are done. I'll first use a zero exponent.
[1] Now, zero exponents are nice since they make things equal 1. Like 5^0 = 1. Well, obviously, 5^8 / 1 = 5^8. So, our first quotient can be:
5^8 / 5^0
Done.
[2] Let's try this on its head. This one's a little weird. Remember that negative exponents flip things upside down. So 5^-8 = 1/5^8 and 1/5^-8 = 5^8 for example. In fact... that's the answer!
5^0 / 5^-8 = 5^8
Done.
[3] Let's try to not use 0s or 8s. We can be clever and do something like this:
5^-1 / 5^-9
What the heck is that? Well, we just flip them and get:
5^-1 / 5^-9 = 5^9 / 5^1 = 5^8
Done.
[4] Can you come up with one last trick on your own? Try it!
Answer:
<u>The correct answer is C. 14.6 feet</u>
Step-by-step explanation:
Information given to solve the case:
Length of the ladder = 15 feet
Distance from the base of the wall = 3.5 feet
Using the Pythagorean theorem for finding the height, because this is a right triangle:
h² = Length of the ladder ² - Distance from the base of the wall ²
h² = 15 ² - 3.5 ²
h² = 225 - 12.25
h² = 212.75
h = √ 212.75
h = 14.59
<u>h = 14.6 feet (Rounding to one decimal place)</u>