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Strike441 [17]
3 years ago
9

Pls help answer this

Mathematics
1 answer:
Paladinen [302]3 years ago
8 0

Answer: Third option

Step-by-step explanation:

For this exercise it is important to remember the following:

1. By definition, the Associative property of addition states that it does not matter how you grouped the numbers, you will always obtained the same sum.

2. The rule for the  Associative property of addition is the following (given three numbers "a", "b" and "c"):

a + (b + c) = (a + b) + c

Knowing the information shown before, you can identify in the picture attached that the option that illustrates the Associative property of addition is the third one. This is:

(11+8)+1=11+(8+1)

As you can notice that you will always get the same result:

(19)+1=11+(9)\\\\20=20

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3 years ago
Evaluate the integral following ​
alina1380 [7]

Answer:

\displaystyle{4\tan x + \sin 2x - 6x + C}

Step-by-step explanation:

We are given the integral of:

\displaystyle{\int 4(\sec x - \cos x)^2 \, dx}

First, we can use a property to separate a constant out of integrand:

\displaystyle{4 \int (\sec x - \cos x)^2 \, dx}

Next, expand the expression (integrand):

\displaystyle{4 \int \sec^2 x - 2\sec x \cos x + \cos^2 x \, dx}

Since \displaystyle{\sec x = \dfrac{1}{\cos x}} then it can be simplified to:

\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2\dfrac{1}{\cos x} \cos x + \cos^2 x \, dx}\\\\\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \cos^2 x \, dx}

Recall the formula:

\displaystyle{\int \dfrac{1}{\cos ^2 x} \, dx = \int \sec ^2 x \, dx = \tan x + C}\\\\\displaystyle{\int A \, dx = Ax + C \ \ \tt{(A \ and \ C \ are \ constant.)}

For \displaystyle{\cos ^2 x}, we need to convert to another identity since the integrand does not have a default or specific integration formula. We know that:

\displaystyle{2\cos^2 x -1 = \cos2x}

We can solve for \displaystyle{\cos ^2x} which is:

\displaystyle{2\cos^2 x = \cos2x+1}\\\\\displaystyle{\cos^2x = \dfrac{\cos 2x +1}{2}}

Therefore, we can write new integral as:

\displaystyle{4 \int \dfrac{1}{\cos^2 x} - 2 + \dfrac{\cos2x +1}{2} \, dx}

Evaluate each integral, applying the integration formula:

\displaystyle{\int \dfrac{1}{\cos^2x} \, dx = \boxed{\tan x + C}}\\\\\displaystyle{\int -2 \, dx = \boxed{-2x + C}}\\\\\displaystyle{\int \dfrac{\cos 2x +1}{2} \, dx = \dfrac{1}{2}\int \cos 2x +1 \, dx}\\\\\displaystyle{= \dfrac{1}{2}\left(\dfrac{1}{2}\sin 2x + x\right) + C}\\\\\displaystyle{= \boxed{\dfrac{1}{4}\sin 2x + \dfrac{1}{2}x + C}}

Then add all these boxed integrated together then we'll get:

\displaystyle{4\left(\tan x - 2x + \dfrac{1}{4}\sin 2x + \dfrac{1}{2} x\right) + C}

Expand 4 in the expression:

\displaystyle{4\tan x - 8x +\sin 2x + 2 x + C}\\\\\displaystyle{4\tan x + \sin 2x - 6x + C}

Therefore, the answer is:

\displaystyle{4\tan x + \sin 2x - 6x + C}

4 0
1 year ago
Chris used 45 meters of fencing to enclose a circular garden. What is the approximate radius of the garden,rounded to the neares
kobusy [5.1K]
The length of the fencing corresponds to the length of the perimeter of the garden:
p=45 m
We also know that the perimeter of a circle is given by:
p=2 \pi r
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Putting together the two equations, we have
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from which we can find r, the radius of the garden:
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3 0
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Answer:

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Step-by-step explanation:

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