Answer:
Step-by-step explanation:
f(x,y)=2x2+3y2−4x−1 ⇒ ∇f =⟨4x−4,6y⟩=⟨0,0⟩ ⇒ x=1, y = 0. Thus (1,0) is the only critical point of f, and it lies in the region x2+y2<16.Ontheboundary,g(x,y)=x2+y2=16 ⇒ λ∇g=⟨2λx,2λy⟩,so6y=2λy ⇒ eithery=0orλ=3. Ify=0,then x=±4;ifλ=3,then4x−4=2λx ⇒ x=−2andy=±2√3. Now f(1,0) = −3, f(4,0) = 15, f(−4,0) = 47, and f−2,±2√3 = 51. Thus the maximum value of f(x,y) on the disk x2+y2 ≤ 16 is f−2,±2√3 = 51, and the minimum value is f (1, 0) = −3.
Put that in the calculator changing the + or - sign both times tp find x
Answer:
(1)5 ft 4 in
(2)9.6 ft
Step-by-step explanation:
We are given that
AB=12 ft
BC=8 ft
All right triangles are similar
(1)Let BD=x
Triangle ABC and DBC are similar
When two triangle are similar then , the ratio of their corresponding sides are equal.
![\frac{12}{8}=\frac{8}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B8%7D%3D%5Cfrac%7B8%7D%7Bx%7D)
![x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%5Ctimes%208%7D%7B12%7D%3D%5Cfrac%7B64%7D%7B12%7D%3D5.3%20ft)
=5 ft 4in
1 feet=12 inches
(2)In triangle DBC
![CD^2=BC^2+DB^2](https://tex.z-dn.net/?f=CD%5E2%3DBC%5E2%2BDB%5E2)
Using Pythagoras theorem
![(hypotenuse)^2=(Base)^2+(perpendicular\;side)^2](https://tex.z-dn.net/?f=%28hypotenuse%29%5E2%3D%28Base%29%5E2%2B%28perpendicular%5C%3Bside%29%5E2)
![CD^2=(8)^2+(5.3)^2](https://tex.z-dn.net/?f=CD%5E2%3D%288%29%5E2%2B%285.3%29%5E2)
![CD=\sqrt{64+28.09)}=9.6 feet](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B64%2B28.09%29%7D%3D9.6%20feet)
Hence, the length of support wire=9.6 feet
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