Let the smaller number be x.
Given, the larger number is 7 times the smaller number.
So, the larger number = 7x.
Given, 3 times the larger number is 7 more than 4 times the smaller number.
So we can write the equation as,
Now we have to move 4x to the left side by subtracting 4x from both sides.
To get x, we will divide both sides by 17. We will get,
So the smaller number =
The larger number = =
So we have got the required numbers.
Smaller number = and larger number =
.
Answer:
V (max) = 2 ft³
and x side of the base is x = 0,5 feet
Step-by-step explanation: See annex ( two different cubes)
We have a square piece of cardboard of 3 inches wide
Let x be lenght of side to cut in each corner
Then the base of the (future cube) is 3 - 2x, and the area is
( 3 - 2x )²
And the height is x Then volume of the cube as a function of x is:
V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x
V(x) = 4x³ - 12x² + 9x
Taking derivatives on both sides of the equation
V´(x) = 12x² - 24x + 9
V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0
Second degree equation solving for x
x₁,₂ = [ 24 ± √( 576) - 432 /24
x₁,₂ = [24 ±√144 ]/24
x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet
Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )
Then we take x = 0,5 feet
And
V (max) = (2)²*0,5 = 4*0,5
V (max) = 2 ft³
