You are not logged in.
Pages: 1
For the arithmetic progression problem, let's call the three terms a-d, a, and a+d (where 'd' is the common difference). We know their sum is -6, so we have: (a-d) + a + (a+d) = -6. Simplifying gives us 3a = -6, and therefore, a = -2. Now, let's find the common difference 'd': (-2) + a + (-2+d) = -6. Solving this gives us d = -2. Now we can find the three terms: -2-(-2) = -4, -2, -2+(-2) = -4. So the three terms are -4, -2, and -4.
For the cylindrical jar and leadshots problem, first, let's find the volume of the jar when it's half-full of water. The volume of a cylinder is V = π * r^2 * h, where 'r' is the radius and 'h' is the depth. The radius is half of the diameter, so r = 14 cm / 2 = 7 cm. When half-full, the water level is 20 cm / 2 = 10 cm. So, the volume of water in the jar is V_water = π * 7^2 * 10 = 490π cm³.
After dropping the 300 leadshots, the water level rises by 2.8 cm, so the new depth is 20 cm + 2.8 cm = 22.8 cm. Let's call the diameter of each leadshot 'd'. The volume of one leadshot is V_leadshot = (π * d^3) / 6. The total volume added by the 300 leadshots is 300 * V_leadshot. Since the total volume added equals the increase in water volume (490π cm³), we can set up the equation: 300 * (π * d^3) / 6 = 490π.
Now, we can solve for 'd': 300 * d^3 = 2940. Dividing both sides by 300 gives d^3 = 9.8. Finally, taking the cube root of both sides, we get d ≈ 2.15 cm (rounded to two decimal places).
So, the diameter of each leadshot is approximately 2.15 centimeters.
This thread is fun!
To calculate this, we need to consider the percentages each agent earns individually. Since Agent 1 takes 70% and Agent 2 takes 50%, we have a total of 120% accounted for. This means there's a remaining 80% to divide among the three agents.
To split it fairly, one way you could do it is by allocating a percentage of that remaining 80% to each agent. For example, Agent 1 could get 40%, Agent 2 could get 30%, and the third agent could get 10%. This way, everyone gets a share based on their individual commission splits, plus an additional portion from the remaining percentage.
Of course, the exact split would depend on the specific circumstances and the agreement between the agents. But I hope this gives you a good starting point to work with.
The brackets around 1/3 indicate that the fraction applies only to the x and y^2 terms, not to any additional terms that might appear in the expression. If the brackets were not there, it would imply multiplication of the entire expression by 1/3.
In this context, there is no difference between (1/3)xy^2 and 1/3xy^2. The parentheses are optional and only serve to make it clear that the 1/3 applies to the x and y^2 terms.
To simplify (1/3)xy^2 - 2xy^2 + 6xy^2, we combine the like terms (terms with the same variables and exponents).
(1/3)xy^2 - 2xy^2 + 6xy^2 = (1/3)xy^2 + 4xy^2
We cannot add the 1/3 and the 4 because they are not like terms. The expression is already in its simplest form, so we cannot simplify it any further.
Pages: 1