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Scilla [17]
2 years ago
12

Calculus - need work shown

Mathematics
2 answers:
Trava [24]2 years ago
7 0

\frac{ - 1}{2} [\cos(8x(x + 3))]+ c

Cloud [144]2 years ago
7 0

Answer:

\large \text{$ -\dfrac{1}{2}\cos (8x^2+24x) + C $}

Step-by-step explanation:

\large \displaystyle\begin{aligned}\textsf{let }\:u & =8x^2+24x\\\\\implies \dfrac{du}{dx} & =16x+24\\ & =2(8x+12)\\\\\implies dx & =\dfrac{1}{2(8x+12)}\: du\\\end{aligned}

\large\displaystyle\begin{aligned}\int (8x+12) \sin (8x^2+24x)\:dx & = \int (8x+12) \sin (u) \cdot \dfrac{1}{2(8x+12)}\:du\\\\& = \int \dfrac{(8x+12)\sin (u)}{2(8x+12)}\:du\\\\& = \int \dfrac{1}{2}\sin (u)\:du\\\\& = -\dfrac{1}{2}\cos (u) + C\\\\& = -\dfrac{1}{2}\cos (8x^2+24x) + C\\\\\end{aligned}

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Find the slope of the line containing the points (7,5) and (9,5).
svet-max [94.6K]

Answer:

\frac{2}{4}

Step-by-step explanation:

Remember that in order to find the slope of two points you need to substitute the variables and subtract making sure you keep the 2's and the 1's together.

m=\frac{y2-y1}{x2-x1}

Plugin your numbers:

=\frac{7-5}{9-5}

7-5=2

9-5=4

=\frac{2}{4}

Hope this helps.

5 0
3 years ago
Read 2 more answers
You were assigned 225 pages to read. You finished ¼ of them. How many pages do you have left to read?
DENIUS [597]

Answer: 169 pages

Step-by-step explanation:

225-[1/4(225)]

225-56.25          ROUND DOWN

225-56

169 pages

7 0
3 years ago
Read 2 more answers
The quotient of 4 and the difference of an integer and 3 is the same as two-thirds. Find the integer.
quester [9]
To find the integer, you must cross multiply, group the same terms, then divide both side by 2:

Solution:
4/(x-3)= 2/3
12 = 2x-6
18=2x
x= 9

7 0
3 years ago
A senior paid $3.47, $9.50 and $2.50 for lunch during a basketball tournament. What was the average amount he paid over three da
cestrela7 [59]

Answer:

The average amount he paid over 3 days is $15.47.

Step-by-step explanation:

4 0
3 years ago
in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference​
allsm [11]

I believe there is no such AP...

Recursively, this sequence is supposed to be given by

\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}

so that

a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d

a_n=a_1+(n-1)d

33=8+(n-1)d

21=(n-1)d

n has to be an integer, which means there are 4 possible cases.

Case 1: n-1=1 and d=21. But

\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123

Case 2: n-1=21 and d=1. But

\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123

Case 3: n-1=3 and d=7. But

\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123

Case 4: n-1=7 and d=3. But

\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123

8 0
3 years ago
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