Answer:
2n + 7
Step-by-step explanation:
b) Determine x so that the volume of the box is at least 450 cubic inches.
c) Determine x so that the volume of the box is maximum.
The volume of the box as a function of x V(x) = x ( 60 -2x )( 15-2x )
The volume of the box as a function of x inches 0.55 inches ≤ x ≤ 6.79
The volume of the box is maximum x ≥ 6.79 inches
Given ,
The box with no top that is to be made by removing squares of width x
The corners of a 15-in by 60-in piece of cardboard.
V(x) = x ( 60 -2x )( 15-2x )
Where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width
The volume of the box as a function of x is V(x) = x ( 60 -2x )( 15-2x )
The volume of the box ≥ 450 inches
V(x) = x ( 60 -2x )( 15-2x )
The volume of the box is at least 450 cubic inches.0.55 inches ≤ x ≤ 6.79 inches
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Answer:
a) V(x) = x ( 60 -2x )( 15-2x )
b) 0.55 inches ≤ x ≤ 6.79 inches
c) x ≥ 6.79 inches
Step-by-step explanation:
Given data:
No top, cardboard dimensions ; 15-in by 60-in
a) A function for the volume of the box as a function of x the Volume can be represented by this function below
= V(x) = x ( 60 -2x )( 15-2x )
where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width
b) determine x so that the volume of the box ≥ 450 inches
450 = x( 60 - 2x ) ( 15 -2x ) ( solving the equation )
0.55 inches ≤ x ≤ 6.79 inches
c ) The value of x for which volume of the box is maximum
will be x ≥ 6.79 inches
Answer:
Eric's father work 5 hours each afternoon
Step-by-step explanation:
Let x be the no. of hours Eric's father work each afternoon
He works for hours in morning each day = 3
He works for total hours in morning in 5 days=
He works for total hours in afternoon in 5 days=5x
We are given that he works a total of 40 hours each 5-day workweek.
ATQ
15+5x=40
5x=25
x=5
Hence Eric's father work 5 hours each afternoon
The product of two consecutive integers is 420 is 20 and 21.
Consider x one the two number
Then the successor of x = x + 1
Then x and x+1 are the consecutive numbers
Now according to the question,
The product of two consecutive integers is 420,
Then, multiply x and x+1 and equate it to 420
Therefore,
⇒ x(x+1) = 420
⇒ x² + x = 420
⇒ x² + x - 420 = 0
This is a quadratic equation
Now solve it to find the value of x
We can write it as,
⇒ x² + 21x - 20x - 420 = 0
⇒ x(x + 21) - 20(x + 21) = 0
⇒ (x+21)(x-20) = 0
⇒ x = 20 or x = -21
Since number should be an integer so - 21 is absurd.
Hence, consecutive numbers are,
20 and 21
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