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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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A 7-kilogram bag of lollipops costs $42.14. What is the unit price?
Tanya [424]

Answer:

$6.02

Step-by-step explanation:

Divide the price of the lollipops by the weight

price/weight

42.14/7=6.02

So, the unit price is $6.02 per kilogram

Hope this helped!

8 0
3 years ago
What is an equation of the line that contains the point (3 -1) and is perpendicular to the line whose equation is y=-3x+2?
Svetach [21]
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Work in attached picture.

3 0
3 years ago
112 students are going on a field trip. If each bus can take 50 students, how many busses are needed?
MrRissso [65]

Answer:

3 buses are needed.

Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
Bailey spent $12.25 at the arcade on Saturday and $9.50 at the arcade on Sunday. How much money did Bailey spend anogether?
galben [10]

Answer:

21.75

Step-by-step explanation:

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8 0
3 years ago
Which situation can be represented by the expression -2-5−2−5minus, 2, minus, 5?
pychu [463]

The situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C

<h3>How to determine the situation?</h3>

The expression is given as:

2 - 5

When the expression illustrates change in temperature, the interpretation can be:

An initial temperature of 2°C decreases by 5°C

Hence, the situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C

Read more about expressions at:

brainly.com/question/723406

#SPJ1

6 0
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