<span>3down votefavorite1Find minimum and maximum value of function <span>f(x,y)=3x+4y+|x−y|</span> on circle<span>{(x,y):<span>x2</span>+<span>y2</span>=1}</span>I used polar coordinate system. So I have <span>x=cost</span> and <span>y=sint</span> where <span>t∈[0,2π)</span>.Then i exploited definition of absolute function and i got:<span>h(t)=<span>{<span><span>4cost+3sintt∈[0,<span>π4</span>]∪[<span>54</span>π,2π)</span><span>2cost+5sintt∈(<span>π4</span>,<span>54</span>π)</span></span></span></span>Hence i received following critical points (earlier i computed first derivative):<span>cost=±<span>45</span>∨cost=±<span>2<span>√29</span></span></span>Then i computed second derivative and after all i received that in <span>(<span>2<span>√29</span></span>,<span>5<span>√29</span></span>)</span> is maximum equal <span>√29</span> and in <span>(−<span>45</span>,−<span>35</span>)</span> is minimum equal <span>−<span>235</span></span><span>
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Answer:
f(8) = -9
Step-by-step explanation:
Substitute 8 in for x.
f(8) = -2(8) + 7
f(8) = -16 + 7
f(8) = -9
Slope = (y2 - y1)/(x2 - x1) = (10 - 70)/(5 - (-15)) = -60/(5 + 15) = -60/20 = -3
Cylinders are 3D figures, as they are solids with volume and take up space.
2D figures are flat figures that you can draw, like a square or circle.
1D figures are actually just a line, a segment, or a point, etc.
Answer:
1,2,4,29,58,116
Step-by-step explanation:
Prime factorization 116=2x2x29
