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The length of the longer base is 41 ft.
<u><em>Explanation</em></u>
Lets assume, length of one base is ft.
As, another base is 19 less than five times the length of this base, so the length of another base
The trapezoid has a height of 18 ft and area of 477 ft²
Formula for Area of trapezoid, , where
= Two bases of trapezoid and
= height of the trapezoid.
Given in the question: and
We have also two bases as: and
So, according to the above formula...
So, length of one base is and another base
That means, the length of the longer base is 41 ft.
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——————————
You have y as an implicit function of x:
sin(xy) – x = 0
Use implicit differentiation. As y is a function of x, then you must apply the chain rule there:
d d
—— [ sin(xy) – x ] = —— (0)
dx dx
d d d
—— [ sin(xy) ] – —— (x) = —— (0)
dx dx dx
d
—— [ sin(xy) ] – 1 = 0
dx
d
—— [ sin(xy) ] = 1
dx
d
cos(xy) · —— (xy) = 1
dx
Now, apply the product rule for that last derivative:
![\mathsf{cos(xy)\cdot \left[\dfrac{d}{dx}(x)\cdot y+x\cdot \dfrac{dy}{dx}\right]=1}\\\\\\ \mathsf{cos(xy)\cdot \left[1\cdot y+x\cdot \dfrac{dy}{dx}\right]=1}\\\\\\ \mathsf{y\,cos(xy)+x\,cos(xy)\cdot \dfrac{dy}{dx}=1}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%28xy%29%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D1%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%28xy%29%5Ccdot%20%5Cleft%5B1%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D1%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7By%5C%2Ccos%28xy%29%2Bx%5C%2Ccos%28xy%29%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D1%7D)
dy
Isolate —— :
dx
dy
x cos(xy) · —— = 1 – y cos(xy)
dx
Assuming x cos(xy) ≠ 0,
dy 1 – y cos(xy)
—— = ———————— <——— this is the answer.
dx x cos (xy)
I hope this helps. =)
——————————
You have y as an implicit function of x:
sin(xy) – x = 0
Use implicit differentiation. As y is a function of x, then you must apply the chain rule there:
d d
—— [ sin(xy) – x ] = —— (0)
dx dx
d d d
—— [ sin(xy) ] – —— (x) = —— (0)
dx dx dx
d
—— [ sin(xy) ] – 1 = 0
dx
d
—— [ sin(xy) ] = 1
dx
d
cos(xy) · —— (xy) = 1
dx
Now, apply the product rule for that last derivative:
dy
Isolate —— :
dx
dy
x cos(xy) · —— = 1 – y cos(xy)
dx
Assuming x cos(xy) ≠ 0,
dy 1 – y cos(xy)
—— = ———————— <——— this is the answer.
dx x cos (xy)
I hope this helps. =)