Answer:
The correct answer is C. 8.15%.
Step-by-step explanation:
Given that Natasha is a bank teller, and she received a 5% raise last year and a subsequent merit raise of 3% this year, to determine what is the accumulative or compound effect of these two raises as a percentage, the following calculation must be performed, assuming, as an example, that her starting salary was $ 2,000:
(2,000 x 1.05) x 1.03 = X
2,100 x 1.03 = X
2,163 = X
2,000 = 100
2,163 = X
2,163 x 100 / 2,000 = X
216,300 / 2,000 = X
108.15 = X
108.15 - 100 = 8.15
Thus, the compound effect of both salary increases is a salary increase of 8.15%.
(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)
Use the shell method. Each shell has a height of 3 - 3/4 <em>y</em> ², radius <em>y</em>, and thickness ∆<em>y</em>, thus contributing an area of 2<em>π</em> <em>y</em> (3 - 3/4 <em>y</em> ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ <em>y</em> ≤ 2, thus given by the integral
![\displaystyle 2\pi \int_0^2 y \left(3-\frac34 y^2\right) \,\mathrm dy = 2\pi \left(\frac32 y^2 - \frac3{16} y^4\right)\bigg|_0^2 = 6\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E2%20y%20%5Cleft%283-%5Cfrac34%20y%5E2%5Cright%29%20%5C%2C%5Cmathrm%20dy%20%3D%202%5Cpi%20%5Cleft%28%5Cfrac32%20y%5E2%20-%20%5Cfrac3%7B16%7D%20y%5E4%5Cright%29%5Cbigg%7C_0%5E2%20%3D%206%5Cpi)
Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 <em>x</em>), thus contributing an area of <em>π</em> (√(4/3 <em>x</em>))² = 4<em>π</em>/3 <em>x</em>. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ <em>x</em> ≤ 3, or by the integral
![\displaystyle \pi \int_0^3 \left(\sqrt{\frac43x}\right)^2 \,\mathrm dx = \frac{2\pi}3 x^2\bigg|_0^3 = 6\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cpi%20%5Cint_0%5E3%20%5Cleft%28%5Csqrt%7B%5Cfrac43x%7D%5Cright%29%5E2%20%5C%2C%5Cmathrm%20dx%20%3D%20%5Cfrac%7B2%5Cpi%7D3%20x%5E2%5Cbigg%7C_0%5E3%20%3D%206%5Cpi)
Using either method, the volume is 6<em>π</em> ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...
When a line is perpendicular, the slope is the negative reciprocal. Therefore, since the slope is 4, the slope of a line perpendicular is -1/4