The distance between the points C(-3,1) and D(5,6) is 10.3 units.
<u>Step-by-step explanation:</u>
Let us consider CD is a line segment.
The point C is (-3,1) and D is (5,6).
The Cartesian formula for line is used to find the length between the CD.
Distance between two points =
.
The points are (-3,1) and (5,6).
=
.
=![\sqrt{(6+3)^2+(6-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%286%2B3%29%5E2%2B%286-1%29%5E2%7D)
=
.
=
.
=
.
=10.295 ≈ 10.3.
Distance between two points 10.3 units.
<u>Question</u> :-
- Seven times the opposite of a number is 50 less than 3 times the number. What is the number?
<u>Explanation</u> :-
According to the question, it's given –
Seven times the opposite of a number is 50 less than 3 times the number.
We've assumed that the number is x. So, opposite of the number will be -x.
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\pink{ \bf \longrightarrow 7(-x) = 3x-50}](https://tex.z-dn.net/?f=%5Cpink%7B%20%5Cbf%20%20%5Clongrightarrow%207%28-x%29%20%3D%203x-50%7D%20)
Now, let's solve this equation –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\bf \longrightarrow 7(-x) = 3x-50](https://tex.z-dn.net/?f=%20%5Cbf%20%20%5Clongrightarrow%207%28-x%29%20%3D%203x-50%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow -7x = 3x -50](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20-7x%20%3D%203x%20-50)
Subtract 3x from both side –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow -7x -3x = 3x -50-3x](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20-7x%20-3x%20%3D%203x%20-50-3x%20)
Cancel 3x from right side –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow -7x -3x =\cancel{ 3x} -50-\cancel{3x }](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20-7x%20-3x%20%3D%5Ccancel%7B%203x%7D%20-50-%5Ccancel%7B3x%20%7D)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow -10x = -50](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20-10x%20%3D%20-50)
Now, cancel (-) sign from both side –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow \cancel{-}10x = \cancel{-}50](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20%5Ccancel%7B-%7D10x%20%3D%20%5Ccancel%7B-%7D50)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow 10 x = 50](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%2010%20x%20%3D%2050)
Then, divide both sides by 10 –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow \dfrac{10x}{10} = \dfrac{50}{10}](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20%5Cdfrac%7B10x%7D%7B10%7D%20%3D%20%5Cdfrac%7B50%7D%7B10%7D)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \longrightarrow \dfrac{\cancel{10}x}{\cancel{10}} = \cancel{\dfrac{50}{10}}](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clongrightarrow%20%5Cdfrac%7B%5Ccancel%7B10%7Dx%7D%7B%5Ccancel%7B10%7D%7D%20%3D%20%5Ccancel%7B%5Cdfrac%7B50%7D%7B10%7D%7D)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\pink{ \bf \longrightarrow x = 5 }](https://tex.z-dn.net/?f=%5Cpink%7B%20%5Cbf%20%20%5Clongrightarrow%20x%20%3D%205%20%7D)
- Henceforth, the number will be 5.
Answer:
The taylor's series for f(x) = ln x centered at c = 1 is:
![ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }](https://tex.z-dn.net/?f=ln%20%28x%29%20%3D%20%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%20%3D%201%7D%20%7B%5Cfrac%7B%28-1%29%5E%7Bn%2B1%7D%28x-1%29%5En%7D%7Bn%7D%20%7D)
Step-by-step explanation:
The calculations are handwritten for clarity and easiness of expression.
However, the following steps were taken in arriving at the result:
1) Write the general formula for Taylor series expansion
2) Since the function is centered at c = 1, find f(1)
3) Get up to four derivatives of f(x) (i.e. f'(x), f''(x), f'''(x),
)
4) Find the values of these derivatives at x =1
5) Substitute all these values into the general Taylor series formula
6) The resulting equation is the Taylor series
![ln (x) = \sum\limits^{\infty}_{n = 1} {\frac{(-1)^{n+1}(x-1)^n}{n} }](https://tex.z-dn.net/?f=ln%20%28x%29%20%3D%20%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%20%3D%201%7D%20%7B%5Cfrac%7B%28-1%29%5E%7Bn%2B1%7D%28x-1%29%5En%7D%7Bn%7D%20%7D)
Answer:
True.
Step-by-step explanation:
2.5*6 = 15
Answer:option D is m best guess
Step-by-step explanation:
correct me if im rong