<span>The ratio of 65*3^17 to 65*3^14 can be found as follows:
(65) (3^17) 65
--------------- = ----- * 3^(17-14) = 1 * 3^3 = 27 (answer)
(65) (3^14) 65</span>
Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if ![\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_1%7D%7Bx_2%7D%3D%20%5Cdfrac%7By_1%7D%7By_2%7D%3D%20%5Cdfrac%7Bz_1%7D%7Bz_2%7D)
here;
![d_1 = (-1, \ 2, \ -3)](https://tex.z-dn.net/?f=d_1%20%3D%20%28-1%2C%20%5C%202%2C%20%5C%20-3%29)
Thus;
![r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%5Cdfrac%7Bx-1%7D%7B-1%7D%20%3D%20%5Cdfrac%7By-3%7D%7B2%7D%3D%5Cdfrac%7Bz-0%7D%7B-3%7D%20%3D%20t)
![d_2 =(2, \ -4, \ +6)](https://tex.z-dn.net/?f=d_2%20%3D%282%2C%20%5C%20-4%2C%20%5C%20%20%2B6%29)
![s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cdfrac%7Bx-0%7D%7B2%7D%20%3D%20%5Cdfrac%7By%2B5%7D%7B-4%7D%3D%5Cdfrac%7Bz-3%7D%7B6%7D%20%3D%20t)
∴
![\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_1%7D%7Bd_2%7D%3D%20%5Cdfrac%7B-1%7D%7B2%7D%20%3D%20%5Cdfrac%7B2%7D%7B-4%7D%3D%20%5Cdfrac%7B-3%7D%7B-6%7D)
Hence, we can conclude that r(t) and s(t) are parallel.
For a question like this you need to find the surface area
The formula is :
b x w x h (base x width x height)
So you multiply 3 1/2 x 6 x 5 1/2 = 22.5
Answers 22.5
Answer:
35.786
12(3) - 3(1/2)/4(3) - 5
This is then further simplified to:
36 - 1.5/7
And when you divide 1.5 by 7, the number (rounded) is .214.
Thus, subtract, and gain the final answer of 35.786.
Hope this helps!
Step-by-step explanation:
Can you please mark me brainliest