Answer: The value of g(x) is x+3.
Step-by-step explanation:
Since we have given that
Here,
We need to find the value of g(x):
Hence, the value of g(x) is x+3.
Simplify the following using PEMDAS: 20 / (7-2)*3
1 answer:
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I started with c, but you could’ve started with any box.
So I took the numbers in the c box (the black box in my picture) and divided to see which were multiples of two. They all were.
Then I went to a. All of a’s numbers were divisible by 7.
Then b. Two of them are divisible by 2, so that’s not the answer. None of them were divisible by 7, so there’s your answer!
Then d. Two are divisible by 7, so your rules is divisible by 2.
I hope this helps!
So I took the numbers in the c box (the black box in my picture) and divided to see which were multiples of two. They all were.
Then I went to a. All of a’s numbers were divisible by 7.
Then b. Two of them are divisible by 2, so that’s not the answer. None of them were divisible by 7, so there’s your answer!
Then d. Two are divisible by 7, so your rules is divisible by 2.
I hope this helps!
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