What is (3x+8) + (6x+2) in simplest form
2 answers:
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Answer:
x = 0.53 cm
Maximum volume = 1.75 cm³
Step-by-step explanation:
Refer to the attached diagram:
The volume of the box is given by
Let x denote the length of the sides of the square as shown in the diagram.
The width of the shaded region is given by
The length of the shaded region is given by
So, the volume of the box becomes,
In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.
We are left with a quadratic equation.
We may solve the quadratic equation using quadratic formula.
The quadratic formula is given by
Where
Volume of the box at x= 1.59:
Volume of the box at x= 0.53:
The volume of the box is maximized when x = 0.53 cm
Therefore,
x = 0.53 cm
Maximum volume = 1.75 cm³
Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.
Here is how much the worker earned each year:
In the year 1985 the worker earned <span>$10,500.
</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:
$10,500(1+0.06).
In the year 1987 the worker earned
$10,500(1+0.06) + 0.06[$10,500(1+0.06)].
Now we can factorize $10,500(1+0.06) and write the earnings as:
$10,500(1+0.06) [1+0.06]=
.
Similarly we can check that in the year 1987 the worker earned
, which makes the pattern clear.
We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:
.
Factorizing, we have
![=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]](https://tex.z-dn.net/?f=%3D10%2C500%5B1%2B1.06%2B%281.06%29%5E2%2B%281.06%29%5E3%2B...%2B%281.06%29%5E%7B26%7D%5D%3D10%2C500%5Ccdot%5B1%2B1.06%2B%281.06%29%5E2%2B%281.06%29%5E3%2B...%2B%281.06%29%5E%7B26%7D%5D)
We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula
(where a is the first term and r is the common ratio) we have:
.
Finally, multiplying 10,500 by 59.17 we have 621.285 ($).
The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating
.
Answer: D
Here is how much the worker earned each year:
In the year 1985 the worker earned <span>$10,500.
</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:
$10,500(1+0.06).
In the year 1987 the worker earned
$10,500(1+0.06) + 0.06[$10,500(1+0.06)].
Now we can factorize $10,500(1+0.06) and write the earnings as:
$10,500(1+0.06) [1+0.06]=
Similarly we can check that in the year 1987 the worker earned
We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:
Factorizing, we have
We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula
Finally, multiplying 10,500 by 59.17 we have 621.285 ($).
The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating
Answer: D