Below is a table showing the different sales prices of a bicycle that Juan wants to purchase. Juan wants to get the best deal. W
hich store offers the bike at the lowest price after the discount?
Pls show your work as you find the price of the bike at each store.
Pls show your work as you find the price of the bike at each store.
1 answer:
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The function
f(x) is even
g(x) is neither even nor odd
h(x) is odd
Steps:
for an even function it holds that f(-x) = f(x):
f(-x) = (-1)^6 x^6 - (-1)^4 x^ 4 = x^6 - x^4 = f(x) => f is even
for an odd h(x) it holds that h(-x) = -h(x):
It is easy to show that g(x) does not match any of the two possibilities above.
Answer:
The volume of the largest rectangular box (V) = 81/4
Step-by-step explanation:
<u>Step 1</u>:-
Given volume of the largest rectangular box in the first octant
V = l b h
let (x ,y, z) be the one vertex in the given plane
V = f(x, y, z) = x y z
given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)
<u>Step( ii):</u>
By using Lagrange multipliers
Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0
Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers
F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)
Obtain the equations are δ F / δ x = 0
δ f / δ x +λ δ Ф / δ x =0
⇒ y z + λ ( 1) = 0
⇒ y z = - λ ......(a)
Obtain the equations are δ F / δ y = 0
δ f / δ x +λ δ Ф / δ x =0
⇒ x z + λ ( 9) = 0
⇒ = - λ .......(b)
Obtain the equations are δ F / δ z = 0
δ f / δ x +λ δ Ф / δ z =0
x y + λ ( 4) = 0
⇒ = - λ .......(c)
<u>Step (iii):-</u>
Equating (a) and (b) equations
we get
cancel 'z' value we get x = 9y .......(d)
Equating (b) and (c) equations
we get
cancel 'x' value on both sides , we get
4z =9y ......(e)
substitute (d) (e) values in equation (1) we get
x + 9y + 4z -27 = 0
9y + 9y + 9y -27 =0
27y -27 =0
<u> y = 1</u>
substitute y =1 in x = 9y
<u>x = 9</u>
substitute y =1 in 4z =9y
<u>z = 9 /4</u>
therefore the dimensions are x =9 , y=1 and z = 9 /4
<u>Conclusion</u>:-
The largest volume of the rectangular box V = x y z
substitute x =9 , y=1 and z = 9 /4
V = 9(1)(9/4) =81/4
The largest volume of the rectangular box (V) = 81/4
Verification :-
Given plane x + 9y + 4z = 27
substitute x =9 , y=1 and z = 9 /4
9 + 9 + 4(9/4) = 27
27 =27
so satisfied equation