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Anettt [7]
3 years ago
10

Chelsea writes the expression (n + 1)(n + 2) + 2n for the number of circles used to make the nth figure in the pattern shown.

Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

Answer:

Step-by-step explanation:

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Integrate Sec (4x - 1) Tan (4x - 1) Dx ​
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\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill

\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C

5 0
3 years ago
A relation is a function if _____.
valentina_108 [34]
... <span>exactly one output for each input

This is an important concept; be certain that you understand it.

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8 0
3 years ago
Translate into an equation or inequality to solve: Two more than twice the sum of a number and 12 is greater than the difference
tamaranim1 [39]
Let say the number is 0.5
Then, sum of this number will be 0.5+0.5=1
Now two is twice of 1.
Hence, it proved to be correct.
And difference between 5 and 1 is 4 which is less than 12. It also match the question condition.

Answer: The number is 1.
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2 years ago
Find the arc length of the semicircle?
myrzilka [38]

Answer:

The length of the semicircle arc is 6π

Step-by-step explanation:

To solve this problem we need to use the circumferenc formula of a circle:

c = circumference

r = radius = 12

π = pi

c = π * d

we replace with the known values

c = π * 12

c = 12π

The length of the circumference is 12π

N ow we divide the circumference by 2 and we will obtain the length of the arc of the semicircle

12π / 2 = 6π

The length of the semicircle arc is 6π

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