Check the picture.
let the length of a side of each of the squares removed be x.
The box formed will have dimensions: 80-2x, 50-2x, x(the height)
So the volume can be expressed as a function of x as follows:
f(x)=(80-2x)(50-2x)x=
![[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x](https://tex.z-dn.net/?f=%5B4000-160x-100x%2B4%20x%5E%7B2%7D%20%5Dx%3D%284%20x%5E%7B2%7D-260x%2B4000%29x)
so

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions
x=10 and x=33.333
plug in f(x) these values to see which greater:

cm cubed

which is negative because (50-66.666)<0
Answer: 18000 cm cubed
Answer:
1,800, 19
Step-by-step explanation:
102,619÷57=1800 (nearest one)
102,619-1800×57=19
1 gallon of milk costs 0.50 more than 5 times a gallon of water.
From that information milk is 5x +0.50 the cost of water.
The cost of milk is $3.75, so now we have:
3.75 = 5x + 0.50
Subtract 0.50 from each side:
3.25 = 5x
Divide both sides by 5:
X = 3.25 / 5
x = 0.65
The cost of water = $0.65
Answer:
The answer to the promblem is -7
Answer:
a) 0.2
b) 0.2
c) 0.5
Step-by-step explanation:
Let
be the event "the car stops at the signal.
In the attached figure you can see a tree describing all possible scenarios.
For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

For the second one the blue path describes the situation

For the las situation the sum of the two green path will give us the answer
