<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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61 because it occurs the most
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Answer:
Length of arc = 5 cm (Approx)
Step-by-step explanation:
Given:
Radius of circle = 20 cm
Angle = 1/4 radian
Find:
Length of arc
Computation:
Angle in degree = 1/4 radian × 180°π
Angle in degree = 1/4 × 180° / 22/7
Angle in degree = 14.31° Approx
Length of arc = (Ф / 360)2πr
Length of arc = (14.31 /360)2(22/7)(20)
Length of arc = 4.997 cm
Length of arc = 5 cm (Approx)
Answer:
Step-by-step explanation:
1. 6w*2v + 3*6w= 12vw + 18w
2. 7(-5v) - 7(8)= -35v - 56
3. 2x*(-2x) - 3(2x) = -4x^2 - 6x
4. -4*v - 4(1)= -4v - 4
5. 2n*6n + 2n + 2*6n + 2= 12n^2 + 14n + 2
6. 4n(2n) + 4n(6) + 2n + 6= 8n^2 + 26n + 6
7. x(6x) - 2x - 18x + 6 = 6x^2 - 20x + 6
8. 8p(6p) + 8p(2) - 2(6p) - 4 = 48p^2 + 16p - 12p - 4= 48p^2 + 4p - 4
9. 6p(5p) - 6p(8) + 8(5p) - 40= 30p^2 - 48p + 40p - 40= 30p^2 - 8p - 40
10. 3m(8m) + 3m(7) - 8m - 7 = 24m^2 + 21m - 8m - 7= 24m^2 + 13m - 7
11. 2a(8a) - 2a(5) - 8a + 5 = 16a^2 - 10a - 8a + 5 = 16a^2 - 18a + 5
12. 5n(5n) - 5n(5) + 6(5n) - 6(5)= 25n^2 - 25n + 30n - 30= 25n^2 + 5n - 30
13. 4p(4p) - 4p - 4p + 1 = 16p^2 - 8p +
14. 7x(5x) + 7x(6) -6(5x) - 6(6)= 35x^2 + 42x - 30x - 36= 35x^2 + 12x - 36
Answer:
Step-by-step explanation:
