Answer:
The smaller bottle holds 12.5 ml of perfume.
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<h2>Given</h2>
- Two bottles of similar shape;
- Larger bottle has volume of 100 ml;
- The length of larger bottle is 10 cm;
- The length of smaller bottle is 5 cm.
<h2>To find </h2>
- The volume of smaller bottle.
<h2>Solution</h2>
Find the scale factor, the ratio of corresponding dimensions:
We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:
Substitute the known values and find the volume of small bottle:
The smaller bottle holds 12.5 ml of perfume.
Answer:
A
Step-by-step explanation:
To write the equation of the line. first calculate the slope using the slope formula.
![m = \frac{y_2-y_1}{x_2-x_1} = \frac{2-2}{5--1}= \frac{0}{6} = 0](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%3D%20%5Cfrac%7B2-2%7D%7B5--1%7D%3D%20%5Cfrac%7B0%7D%7B6%7D%20%3D%200)
Since the slope of this line is 0, it is horizontal and has the form y=b where b is the y-coordinate. So y = 2 is the equation. In general form, it would be y-2 = 0
Answer:
Step-by-step explanation:
(x₁, y₁) = (-9 ,8) and (x₂ , y₂) = (-3 , -1)
![Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-1-8}{-3-[-9]}\\\\=\dfrac{-9}{-3+9}\\\\=\dfrac{-9}{6}\\\\=\dfrac{-3}{2}](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-1-8%7D%7B-3-%5B-9%5D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-9%7D%7B-3%2B9%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-9%7D%7B6%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-3%7D%7B2%7D)
Answer: 9
is the value of "x".
Answer with explanation:
The equation which we have to solve by Newton-Raphson Method is,
f(x)=log (3 x) +5 x²
![f'(x)=\frac{1}{3x}+10 x](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B1%7D%7B3x%7D%2B10%20x)
Initial Guess =0.5
Formula to find Iteration by Newton-Raphson method
![x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%3Dx_%7Bn%7D-%5Cfrac%7Bf%28x_%7Bn%7D%29%7D%7Bf%27%28x_%7Bn%7D%29%7D%5C%5C%5C%5Cx_%7B1%7D%3Dx_%7B0%7D-%5Cfrac%7Bf%28x_%7B0%7D%29%7D%7Bf%27%28x_%7B0%7D%29%7D%5C%5C%5C%5C%20x_%7B1%7D%3D0.5-%5Cfrac%7B%5Clog%281.5%29%2B1.25%7D%7B%5Cfrac%7B1%7D%7B1.5%7D%2B10%20%5Ctimes%200.5%7D%5C%5C%5C%5Cx_%7B1%7D%3D0.5-%20%5Cfrac%7B0.1760%2B1.25%7D%7B0.67%2B5%7D%5C%5C%5C%5Cx_%7B1%7D%3D0.5-%5Cfrac%7B1.426%7D%7B5.67%7D%5C%5C%5C%5Cx_%7B1%7D%3D0.5-0.25149%5C%5C%5C%5Cx_%7B1%7D%3D0.248)
![x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012](https://tex.z-dn.net/?f=x_%7B2%7D%3D0.248-%5Cfrac%7B%5Clog%280.744%29%2B0.30752%7D%7B%5Cfrac%7B1%7D%7B0.744%7D%2B10%20%5Ctimes%200.248%7D%5C%5C%5C%5Cx_%7B2%7D%3D0.248-%20%5Cfrac%7B-0.128%2B0.30752%7D%7B1.35%2B2.48%7D%5C%5C%5C%5Cx_%7B2%7D%3D0.248-%5Cfrac%7B0.17952%7D%7B3.83%7D%5C%5C%5C%5Cx_%7B2%7D%3D0.248-0.0468%5C%5C%5C%5Cx_%7B2%7D%3D0.2012)
![x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057](https://tex.z-dn.net/?f=x_%7B3%7D%3D0.2012-%5Cfrac%7B%5Clog%280.6036%29%2B0.2024072%7D%7B%5Cfrac%7B1%7D%7B0.6036%7D%2B10%20%5Ctimes%200.2012%7D%5C%5C%5C%5Cx_%7B3%7D%3D0.2012-%20%5Cfrac%7B-0.2192%2B0.2025%7D%7B1.6567%2B2.012%7D%5C%5C%5C%5Cx_%7B3%7D%3D0.2012-%5Cfrac%7B-0.0167%7D%7B3.6687%7D%5C%5C%5C%5Cx_%7B3%7D%3D0.2012%2B0.0045%5C%5C%5C%5Cx_%7B3%7D%3D0.2057)
![x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052](https://tex.z-dn.net/?f=x_%7B4%7D%3D0.2057-%5Cfrac%7B%5Clog%280.6171%29%2B0.21156%7D%7B%5Cfrac%7B1%7D%7B0.6171%7D%2B10%20%5Ctimes%200.2057%7D%5C%5C%5C%5Cx_%7B4%7D%3D0.2057-%20%5Cfrac%7B-0.2096%2B0.21156%7D%7B1.6204%2B2.057%7D%5C%5C%5C%5Cx_%7B4%7D%3D0.2057-%5Cfrac%7B0.0019%7D%7B3.6774%7D%5C%5C%5C%5Cx_%7B4%7D%3D0.2057-0.0005%5C%5C%5C%5Cx_%7B4%7D%3D0.2052)
So, root of the equation =0.205 (Approx)
Approximate relative error
![=\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7BActual%20value%7D%7D%7B%5Ctext%7BGiven%20Value%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B0.205%7D%7B0.5%7D%5C%5C%5C%5C%3D0.41)
Approximate relative error in terms of Percentage
=0.41 × 100
= 41 %