Answer:
500
Step-by-step explanation:
It's a box with a square base, so let's say the width and length are x and the height is y.
The surface area of the box without the top is:
A = x² + 4xy
300 = x² + 4xy
The volume of the box is:
V = x²y
Solve for y in the first equation and substitute into the second:
y = (300 − x²) / 4x
V = x² (300 − x²) / 4x
V = x (300 − x²) / 4
V = 75x − ¼ x³
To optimize V, find dV/dx and set to 0:
dV/dx = 75 − ¾ x²
0 = 75 − ¾ x²
x = 10
So the volume of the box is:
V = 75x − ¼ x³
V = 500
The maximum volume is 500 cm³.
96÷120 =0.8 ⇒0.8 ×100 =80 % :))
Answer:
£13496.80
Step-by-step explanation:
We can ignore the £ sign for now, that is just units.
If we decrease a number by 4.5%, we will have to find 
% of 14132.77.
We can easily do this by setting up a proportion.
Multiply 14132.77 by 95.5:
Divide by 100:
Rounding this to two decimal places, it simplifies to 13496.80.
Hope this helped!
Answer: 333.33m²
Step-by-step explanation:
Since we are informed that 15 litres of paint covers an area of 250 m2, the the area that 1 liter of paint will cover will be:
= 250m²/15
= 16.666667m²
Therefore, the area that 20 litres of paint will cover will be:
= 16.666667m² × 20
= 333.33m²
X^4 + 2x^2 - 24
= (x^2 + 6)(x^2 - 4)
= (x^2 + 6)(x - 2)(x + 2)
x^4 - 9x^2 + 18
= (x^2 - 6)(x^2 - 3)
