<span><span><span>y2</span>(<span>y2</span>−4)=<span>x2</span>(<span>x2</span>−5)</span><span><span>y2</span>(<span>y2</span>−4)=<span>x2</span>(<span>x2</span>−5)</span></span><span> Multiplying the polynomials gets us to </span><span><span><span>y4</span>−4<span>y2</span>=<span>x4</span>−5<span>x2</span></span><span><span>y4</span>−4<span>y2</span>=<span>x4</span>−5<span>x2</span></span></span><span>. Taking the derivative with respect to </span><span>xx</span><span> gets us: </span><span><span>4<span>y3</span><span>y′</span>−>!8y<span>y′</span>=4<span>x3</span>−10x</span><span>4<span>y3</span><span>y′</span>−>!8y<span>y′</span>=4<span>x3</span>−10x</span></span><span>. Factoring to get </span><span><span>y′</span><span>y′</span></span><span> by itself: </span><span><span><span>y′</span>(4<span>y3</span>−8y)=4<span>x3</span>−10)</span><span><span>y′</span>(4<span>y3</span>−8y)=4<span>x3</span>−10)</span></span><span>. Divide through to get </span><span><span>y′</span><span>y′</span></span><span> by itself: </span><span><span><span>y′</span>=<span><span>4<span>x3</span>−10x</span><span>4<span>y3</span>−8y</span></span></span><span><span>y′</span>=<span><span>4<span>x3</span>−10x</span><span>4<span>y3</span>−8y</span></span></span></span><span>. You could make your life a bit easier by factoring this into </span><span><span><span>y′</span>=<span><span>2x(2<span>x2</span>−5)</span><span>4y(<span>y2</span>−2)</span></span></span><span><span>y′</span>=<span><span>2x(2<span>x2</span>−5)</span><span>4y(<span>y2</span>−2)</span></span></span></span><span>. You could cancel out a factor of </span><span>22</span><span> to get </span><span><span><span>y′</span>=<span><span>x(2<span>x2</span>−5)</span><span>2y(<span>y2</span>−2)</span></span></span><span><span>y′</span>=<span><span>x(2<span>x2</span>−5)</span><span>2y(<span>y2</span>−2)</span></span></span></span><span>. To find the slope, plug in your points </span><span><span>x=0,y=−2</span><span>x=0,y=−2</span></span><span> into our equation for </span><span><span>y′</span><span>y′</span></span><span> to find the slope of the line. Note that the slope is </span><span>00</span><span>. To find the </span>equation<span> of the tangent line, use that value for </span><span>mm</span><span> you just found (</span><span><span>m=0</span><span>m=0</span></span><span>) and your given points into the point-slope formula and you find that the tangent line is </span><span><span>y=−2</span><span>y=−2</span></span><span>.
Thats what my Aunt said... Idk</span>
The formula to find slope it (y2-y1)/(x2-x1)
(2,4) is the first point
(6,2) is the second point
(2-4)/(6-2)
-2/4 which can be simplified to -1/2
Hope this helps
Jen take x hours.
Carl (x-3)hours.
Jen+carl take two hours;
This means;
In 1 hour, for they work
=
=
Working together, they take two hours;
Take reciprocal of above equation and equate to two;
=
-3x=4x-6
-x-6x+6=0
x(x-1)-6(x-1)=0
(x-6)(x-1)=0
Take the bracket x-6=0 so that Carl works positive hours
x-6=0
x=6
Answer:
the answer is 6 if we will evaluate x and y
