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Readme [11.4K]
3 years ago
9

Evaluate the numerical expression [18 Divided by (2 x 3)] x 4

Mathematics
1 answer:
Nastasia [14]3 years ago
6 0
P: parenthesis
E: exponents
MD: multiplication or division (whichever comes first left to right)
AS: addition or subtraction (whichever comes first left to right)

This is the order of operations. We will use this to solve the equation correctly.
We will start with the parenthesis. 2x3=6.
[18/6]x4
Next, we will do the rest of the parenthesis.
18/6=3.
This gets rid of the parenthesis (or brackets.) We will now do the rest of the problem, which is multiplying 3 and 4.
3x4=12.
12 is your final answer.
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two fractions with different denominators have a sum of 7/12 what are two possible addends that results in this sum
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15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then find<br>dy/dx at =22/7*4<br>​
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By the chain rule,

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}

It looks like we're given

\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}

where <em>a</em> and <em>b</em> are presumably constant.

Recall that

\cos^2t=\dfrac{1+\cos(2t)}2

\sin^2t=\dfrac{1-\cos(2t)}2

so that

\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}

Then we have

\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t

\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}

\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}

where the last reduction follows from dividing through everything by \cos(2t)\cos^2t and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

8 0
3 years ago
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