answer:The area of the circle can be calculated using the formula A = πr², where r is the radius. Given the diameter is 4 units, the radius is half of that, which is 2 units. So, the area is: A = π(2)² A = π × 4 A = 4π Using 3.14 as an approximation for π, the area becomes: A ≈ 4 × 3.14 A ≈ 12.56 units²

answer:To solve the system, we can use the method of substitution or elimination. Here, we'll use elimination by multiplying the first equation by 51 and the second equation by 98 to make the coefficients of y equal and opposite. First equation: -99x + 98y = 40 Second equation: -56x + 51y = 52 Multiply the first equation by 51: -5049x + 5098y = 2050 Multiply the second equation by 98: -5512x + 4998y = 5096 Now, subtract the second equation from the first: begin{align*} (-5049x + 5098y) - (-5512x + 4998y) &= 2050 - 5096 -5049x + 5098y + 5512x - 4998y &= -3046 463x &= -3046 x &= -frac{3046}{463} x &= -frac{10}{1} end{align*} Substitute x into one of the original equations to find y. Let's use the second equation: begin{align*} -frac{28}{5}x + frac{51}{5}y &= frac{52}{5} -frac{28}{5}(-frac{10}{1}) + frac{51}{5}y &= frac{52}{5} 56 + frac{51}{5}y &= frac{52}{5} frac{51}{5}y &= frac{52}{5} - 56 frac{51}{5}y &= frac{52}{5} - frac{280}{5} frac{51}{5}y &= -frac{228}{5} y &= -frac{228}{51} y &= -frac{4}{1} end{align*} Therefore, the solution is x = -frac{10}{1} and y = -frac{4}{1}, or in simplified form, x = -10 and y = -4.

answer:To find the real solutions to the given equation, we can equate the logarithms' arguments since their bases are the same: log (x-24) + log (4x+7) = log (9x-5) Using the logarithmic property log a + log b = log (ab), we combine the terms: log ((x-24)(4x+7)) = log (9x-5) This implies that: (x-24)(4x+7) = 9x-5 Expanding and simplifying the equation, we get: 4x^2 - 7x - 96x - 168 = 9x - 5 4x^2 - 102x - 168 + 5 = 0 4x^2 - 102x - 163 = 0 Now, we can solve the quadratic equation using the quadratic formula: x = frac{-b pm sqrt{b^2 - 4ac}}{2a} x = frac{102 pm sqrt{102^2 - 4 cdot 4 cdot (-163)}}{2 cdot 4} x = frac{102 pm sqrt{10404 + 2572}}{8} x = frac{102 pm sqrt{12976}}{8} x = frac{102 pm 4sqrt{811}}{8} x = frac{51 pm 2sqrt{811}}{4} Thus, the real solutions are: x = frac{51 - 2sqrt{811}}{4} quad text{and} quad x = frac{51 + 2sqrt{811}}{4} However, since the original logarithmic arguments should be positive, we need to ensure that: x - 24 > 0 4x + 7 > 0 9x - 5 > 0 After checking these inequalities, we find that both solutions satisfy these conditions, so the final real solutions are: x = frac{1}{4} left(51 - 2sqrt{811}right) quad text{and} quad x = frac{1}{4} left(51 + 2sqrt{811}right)

answer:After researching, I found a software solution called Parts-in-place that seems to meet most of the requirements for managing a small electronic components inventory. Here's a breakdown of how it aligns with your wishlist: 1. (Yes) Free or low-cost software - Parts-in-place offers a free account. 2. (Yes) Not too complicated - The system is user-friendly and easy to navigate. 3. (Yes) Locations feature - You can indicate the storage location of each component. 4. (Yes) Stock/shopping history - It tracks purchase history and updates stock upon arrival. 5. (No) Categories with tree structure - While it lacks a hierarchical category structure, you can use part number prefixes as a workaround. 6. (Yes) Functionality to assign parts to projects - Bills of Materials (BOMs) serve this purpose. 7. (Yes) Client-server architecture - It is an online service but can also be set up on your servers, although this may be costly. 8. (Yes) Shopping list preparation - You can create shopping lists based on BOMs and planned production. Parts-in-place integrates well with Excel for importing and exporting data. The free account includes one user, three BOMs, and about 100 parts per BOM. However, the software doesn't meet the following requirements: 1. (No) Open-source 2. (No) On-premise hosting without additional cost Please note that I am not affiliated with Parts-in-place. Other alternatives to consider, though they may not fully meet your criteria, include zParts, PartKeepr, and Ciiva.