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ki77a [65]
2 years ago
5

What was the purpose of the townshend program

Mathematics
1 answer:
kykrilka [37]2 years ago
4 0

This was to raise revenue for the British Empire by taxing the North American colonies.

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Find dy/dx for y= x^3 ln (cot x)
ICE Princess25 [194]
<h3>Answer</h3>

  \dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)

<h3>Explanation</h3>

By the product rule (d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x), we have

  \begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}

By the chain rule:

  \begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}

By the power rule:

  (x^3)' = 3x^2

thus

  \begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}

Nothing to do to simplify any further, other than factoring out x^2.

4 0
3 years ago
Describe a real-word example of when it is necessary that line segments are parallel
Alex_Xolod [135]
If you are drawing a map, you may need to draw two parallel line segments.
8 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE PLEASE HELP!! even if it's only one! actually answer it!
Alex
So for number 2 i am 100% on which the area of the triangle is 6.
and then 1 i think not 100% sure is an acute angle again not 100% 
then 3. it don't make sense to me so idk about that 1 srry.
~Good Luck~ 
6 0
3 years ago
I need help with this I got -10 is it right??
Dahasolnce [82]

Answer:

-14

Step-by-step explanation:

difference between -20 and -5 = 15

15 x 2/5 = 30/5 = 6

-20 + 6 = -14

7 0
3 years ago
5 questions plz answer all of them if you do you will get points, thanks, Brainliest answer,
babunello [35]
1. 1/6

2. 1/8

3. 80%

4. 1/5

5. 2/8 or 25%
5 0
3 years ago
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