Answer:
The work will be finished in 10 days.
Step-by-step explanation:
Rashid can do a piece of work in 8 days
This means that each day he works, Rashid does 
of the work.
Tipu can finish in 12 days.
This means that each day he works, Tipu does 
of the work.
Each 2 days:
Each 2 days they work, the amount done is given by:
Each 2 days, 5/24 of the work is done:
The number of periods of 2 days that is needed to finish the work(100% = 1 completed), is given by:
2*4.8 = 9.6
Rounding up
The work will be finished in 10 days.
![\bf 2[x^2+y^2]^2=25(x^2-y^2)\qquad \qquad \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 3}}\quad ,&{{ 1}})\quad \end{array}\\\\ -----------------------------\\\\ 2\left[ x^4+2x^2y^2+y^4 \right]=25(x^2-y^2)\qquad thus \\\\\\ 2\left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=25\left[2x-2y\frac{dy}{dx} \right] \\\\\\ 2\left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=50\left[x-y\frac{dy}{dx} \right] \\\\\\ ](https://tex.z-dn.net/?f=%5Cbf%202%5Bx%5E2%2By%5E2%5D%5E2%3D25%28x%5E2-y%5E2%29%5Cqquad%20%5Cqquad%20%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%5C%5C%0A%25%20%20%20%28a%2Cb%29%0A%26%28%7B%7B%203%7D%7D%5Cquad%20%2C%26%7B%7B%201%7D%7D%29%5Cquad%20%0A%5Cend%7Barray%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A2%5Cleft%5B%20x%5E4%2B2x%5E2y%5E2%2By%5E4%20%5Cright%5D%3D25%28x%5E2-y%5E2%29%5Cqquad%20thus%0A%5C%5C%5C%5C%5C%5C%0A2%5Cleft%5B%204x%5E3%2B2%5Cleft%5B%202xy%5E2%2Bx%5E22y%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%2B4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%3D25%5Cleft%5B2x-2y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A2%5Cleft%5B%204x%5E3%2B2%5Cleft%5B%202xy%5E2%2Bx%5E22y%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%2B4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%3D50%5Cleft%5Bx-y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A)
![\bf \left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=25\left[x-y\frac{dy}{dx} \right] \\\\\\ 4x^3+4xy^2+4x^2y\frac{dy}{dx}+4y^3\frac{dy}{dx}+25y\frac{dy}{dx}=25x \\\\\\ \cfrac{dy}{dx}[4x^2y+4y^3+25y]=25x-4x^3+4xy^2 \\\\\\ \cfrac{dy}{dx}=\cfrac{25x-4x^3+4xy^2}{4x^2y+4y^3+25y}\impliedby m=slope](https://tex.z-dn.net/?f=%5Cbf%20%5Cleft%5B%204x%5E3%2B2%5Cleft%5B%202xy%5E2%2Bx%5E22y%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%2B4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright%5D%3D25%5Cleft%5Bx-y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A4x%5E3%2B4xy%5E2%2B4x%5E2y%5Cfrac%7Bdy%7D%7Bdx%7D%2B4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D%2B25y%5Cfrac%7Bdy%7D%7Bdx%7D%3D25x%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%5B4x%5E2y%2B4y%5E3%2B25y%5D%3D25x-4x%5E3%2B4xy%5E2%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B25x-4x%5E3%2B4xy%5E2%7D%7B4x%5E2y%2B4y%5E3%2B25y%7D%5Cimpliedby%20m%3Dslope)
notice... a derivative is just the function for the slope
now, you're given the point 3,1, namely x = 3 and y = 1
to find the "m" or slope, use that derivative, namely
that'd give you a value for the slope
to get the tangent line at that point, simply plug in the provided values
in the point-slope form
and then you solve it for "y", I gather you don't have to, but that'd be the equation of the tangent line at 3,1
Answer: my but
Step-by-step explanation:
1+1
The polynomial remainder theorem states that the remainder upon dividing a polynomial
by
is the same as the value of
, so to find
you need to find the remainder upon dividing
You have
..... | 2 ... 14 ... -58
-10 | ... -20 ... 60
--------------------------
..... | 2 ... -6 .... 2
So the quotient and remainder upon dividing is
with a remainder of 2, which means
.
