If the 2 lines are parallel, their slopes are the same.
The slope of both is
3+3
m = ---------- = 3
2 - 0
If the new line <span>passes through the point (−1, −1), then the equation in point slope form is:
y+1 = 3(x+1).</span>
We know, that the <span>area of the surface generated by revolving the curve y about the x-axis is given by:
In this case a = 0, b = 15,
and:
So there will be:
![\left(\star\right)=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\dfrac{2\pi}{15}\cdot\dfrac{25}{6}\cdot\left[\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}\right]_0^{15}=\\\\\\= \dfrac{5\pi}{9}\left[\left(1+\dfrac{15^4}{25}\right)^\frac{3}{2}-\left(1+\dfrac{0^4}{25}\right)^\frac{3}{2}\right]=\dfrac{5\pi}{9}\left[2026^\frac{3}{2}-1^\frac{3}{2}\right]=\\\\\\= \boxed{\dfrac{5\Big(2026^\frac{3}{2}-1\Big)}{9}\pi}](https://tex.z-dn.net/?f=%5Cleft%28%5Cstar%5Cright%29%3D%5Cdfrac%7B2%5Cpi%7D%7B15%7D%5Ccdot%5Cint%5Climits_0%5E%7B15%7Dx%5E3%5Ccdot%5Csqrt%7B1%2B%5Cdfrac%7Bx%5E4%7D%7B25%7D%7D%5C%2C%5C%2C%20dx%3D%5Cdfrac%7B2%5Cpi%7D%7B15%7D%5Ccdot%5Cdfrac%7B25%7D%7B6%7D%5Ccdot%5Cleft%5B%5Cleft%281%2B%5Cdfrac%7Bx%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D_0%5E%7B15%7D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Cdfrac%7B5%5Cpi%7D%7B9%7D%5Cleft%5B%5Cleft%281%2B%5Cdfrac%7B15%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D-%5Cleft%281%2B%5Cdfrac%7B0%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5Cdfrac%7B5%5Cpi%7D%7B9%7D%5Cleft%5B2026%5E%5Cfrac%7B3%7D%7B2%7D-1%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Cboxed%7B%5Cdfrac%7B5%5CBig%282026%5E%5Cfrac%7B3%7D%7B2%7D-1%5CBig%29%7D%7B9%7D%5Cpi%7D)
Answer C.
</span>
In order to use the simple interest formula, we first define the variables. The interest would be equal to Samuel's desired amount $ 2,488 minus the principal amount of $ 1,800 which is then equal to $ 688. The rate must be in decimal form which is equal to 0.12 while t is expressed in years. Substituting the values, t is equal to 3. Thus, it will take 36 <span>months for Samuel's account balance to reach $2,448. </span>
Answer: D
Step-by-step explanation:
D is the correct answer because first of all, there are 13 balls total. So the denominator would have to be 13. Also, white is the second largest number of balls in the set, so it is pretty likely that you will pick it. Although the most common picked would be green since it has the most balls.
