Solution
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To convert feet to centimeters, we need to know the conversion factor between these two units of length. The conversion factor is:
1 foot = 30.48 centimeters
Now, let's convert 5.8 feet to centimeters using this conversion factor.
1 foot = 30.48 centimeters
Now, let's convert 5.8 feet to centimeters using this conversion factor.
Now, let's convert 5.8 feet to centimeters using this conversion factor.
Step 1: Write down the value you want to convert (in this case, 5.8 feet).
Step 2: Multiply this value by the conversion factor to find the equivalent number of centimeters.
Step 3: Round the result to an appropriate number of significant figures if necessary. In this case, we can round the result to two decimal places:
Therefore, 5.8 feet is approximately 176.78 centimeters.
Step 1: Write down the value you want to convert (in this case, 5.8 feet).
Step 2: Multiply this value by the conversion factor to find the equivalent number of centimeters.
Step 3: Round the result to an appropriate number of significant figures if necessary. In this case, we can round the result to two decimal places:
Therefore, 5.8 feet is approximately 176.78 centimeters.
Exercise 1 part j- Compute the first order partial derivative of the function f(u,vt)=e^(uv)sin(ut)
Exercise 1- Parts b-c- How to calculate the Proportion of people taller than 190cm and exactly 173.6cm?
Exercise 2 - Conversions of units (mass, length, surface)
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Exercise 1 part j- Compute the first order partial derivative of the function f(u,vt)=e^(uv)sin(ut)
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In this exercise, we have the function f of 3 variables,
note x, y, z,
u, v, and t given as follows.
We want the first-order partial derivatives,
it's going to be 3 of them with respect to u,
which we're going to call fu.
Then with respect to v,
that will be f with respect to v and then f with respect to t.
Remember the idea is that when we differentiate with respect to 1 variable,
the others, in this case there will be 2 others,
will be treated like constants or parameters.
Let's start with the first one, with respect to u.
Actually this is the hardest of the 3,
they're all easy but this one because we have u both here and here,
I'm going to look at it as a product.
Quick reminder of product rule,
if I have a product and take its derivative the first times the derivative of the
second plus the derivative of the first times the second.
Only in our case it's going to be a partial derivative with
respect to u. I chose a variable u.
I won't spell it out because actually to avoid a name clash,
I'll use f and g. Now I've got an f here as well.
I usually write the product rule with u and v but we already have u and v here.
We're not going to use f and g. Now I have an g and h fine.
G times h derivative.
I just remembered the scheme,
derivative of the first times the second plus
the first times the derivative of the second and doesn't matter what letters.
In our case, we're going to use the partial derivative
the same thing works if I take a product,
and take its partial derivative with respect to u,
it's going to be the first with respect to u,
the other one as is,
and then the first one as is,
the second with respect to u. I'm just translating the prime as appropriate.
In our particular case of course this will be the g,
and this will be the h,
and I'm looking here and then I say,
g with respect to u.
That's going to be e to the power of something derivative,
it would be just e to the same thing,
e^uv, but I need to multiply it by the inner derivative,
which is going to be derivative of
uv is going to be v. Actually I don't need the brackets.
For example, suppose it was u times 6,
or 6u, then the derivative would be just the 6.
So far we've just done the g prime part.
Now we need the h which is the other function,
sine of ut, maybe it's best to put it in brackets.
Here you can tell its got a font that's still I would
have done it again with brackets just to make it absolutely clear.
That's the g prime h then a plus,
and then g as is which is e^uv,
and now I need the derivative.
Actually I'm looking here, derivative of h with respect to u.
Now, I first of all see a sine of something,
I start off with cosine of that same thing, cosine of ut.
I start off because again we have an inner derivative,
I need to differentiate ut with respect to u.
Once again, it's u with a constant,
this time it's t,
I need to multiply that by t which is the derivative of ut.
Other than tidying up,
this would be the answer.
I could leave this partial derivative just like
that but I'd like to just tidy it up a bit.
Optional. Bare with me.
The e^uv part appears in both,
so I'd like to take that out as a common factor in front of the brackets.
Let's start with e^uv.
Let's see what we're left with.
Here we have v times sine of ut.
In the second one I have cosine ut times t,
but it's preferable to put the t in front for
some reason this looks nicer to mathematicians at any rate.
We'll have t cosine of ut,
of course you could leave the t at the end,
no problem with that.
Maybe I'll change the square brackets.
Once again, it's just an aesthetic thing if I have already round brackets,
not to confuse the brackets I'll use square ones.
That does the first one,
2 more to go but they're easier.
If I take the partial with respect to v,
v only appears in one place and all this second bit is a constant.
In fact, you can ignore the split g, h here.
What I do is, I'm going to differentiate this with respect to
v and then just stick this thing along because it doesn't contain v. Each of the uv,
like before, e to the power of,
it's e to the power of,
then as an inner derivative,
only this time v is the variable and u is the constant and we get times u, not as before.
Then this thing is a constant,
so at sine of ut,
and there's no product here,
this is the answer.
I'll leave it as is although I would put the u in front possibly.
Next one, with respect to t. Once again,
t only appears in the second path.
There's no t here,
so this thing is a constant,
so I start off with this constant e^v.
Now I just have to differentiate this with respect to t. Sine of something,
we get cosine of the same thing,
but it wasn't just a simple t it's ut I don't know 2t,
then I would put the inner derivative of 2 or in this case u.
Once again, I would put the u upfront,
but this is fine.
That's 3 out of 3, we're done.
This video explains how to calculate the first-order partial derivatives of a function f of 3 variables, x, y, z, u, v, and t. The derivatives are fu, fv, and ft. The product rule is used to calculate the derivatives, and the derivatives of uv and ut are multiplied by the constants v and t, respectively. The result is three equations that can be used to calculate the derivatives.
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