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Brut [27]
3 years ago
10

How many times can 12 go into 307

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0
12 can only go into 30 about 25 whole times.
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Find the length of the hypotenuse ​
Marta_Voda [28]

Answer:

10 m

Perimeter = 24 m

Step-by-step explanation:

( Hypotenuse )² = 6² + 8²

                          = 36 + 64

                          = 100

                          = 10 x 10

( Hypotenuse )² = 10²

Hypotenuse = 10 m

Perimeter is the sum of all sides in a triangle.

Perimeter = 6 + 8 + 10 = 24 m

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2 years ago
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I hope you figure the problem out

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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
Some beads were in a box. Anne used 17 of them. Then there were 56 beads in the box. How many were in the box to begin with?
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There where 73 beads to begin with.
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Use the unit circle to find tan 30°.<br> a. 3<br> b. square root 3/2<br> c. 1/2 <br> d. 2
Montano1993 [528]
C is the answer I believe
8 0
3 years ago
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