Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marli
1 answer:
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First, let's turn all the numbers into improper fractions so that we can find the answer easier.
-2 = r -
- = r -
Now we have to isolate 'r'.
First, we have to make sure that the variable is on one side and all the numbers are on the other side.
To do this, we have to add to both sides.
In order to do this, we need to ensure that both fractions have a common denominator.
- = r -
Ensure that the denominators are the same:
= r -
+
= r
= r
Good luck!
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
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=
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:
Answer: 18000 cm cubed