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RoseWind [281]
3 years ago
13

What the answer and show the work ​

Mathematics
1 answer:
Rainbow [258]3 years ago
6 0

Answer: Dude i can't see what it says

Step-by-step explanation:

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Give an example of a function F(x) that is an antiderivative of f(x) = 9 cos(9x)+ 3x^2
liubo4ka [24]

We are integrating f(x) = 9cos(9x) + 3x²:    \int\ {9cos(9x)+3x^{2} } \, dx

a) Apply the sum rule

\int\9cos(9x)} \, dx +\int\ 3x^{2} } \, dx

b) Calculate each antiderivative

<u>First integral</u>

\int\ {9cos(9x)} \, dx

1. Take out the constant

9\int\ {cos(9x)} \, dx

2. Apply u-substitution, where u is 9x

9\int\ {cos(u)\frac{1}{9} }  du

3. Take out the constant (again)

9*\frac{1}{9} \int{cos(u)}  du

4. Take the common integral of cos, which is sin

9*\frac{1}{9}sin(u)}

5. Substitute the original function back in for u and simplify9*\frac{1}{9} sin(9x) = sin(9x)

6. Always remember to add an arbitrary constant, C, at the end

sin(9x) + C

<u>Second integral</u>

\int3x^{2} } \, dx

1. Take out the constant

3\int{x^{2} } \, dx

2. Apply the power rule, \int{x}^{a}  \, dx =\frac{x^{a+1} }{a+1}, where <em>a</em> is your exponent

⇒ 3*\frac{x^{2+1} }{2+1}  = x^{3}

3. Add the arbitrary constant

x^{3}  + C

c) Add the integrals

sin(9x) + C + x³ + C = sin(9x) + x³ + C

Notice the two arbitrary constants.  Since we do not know what either constant is, we can combine them into one arbitrary constant.

<h3>Answer:</h3>

F(x) = sin(9x) + x³ + C

3 0
3 years ago
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Which set of ordered pairs does NOT represent a function?
ElenaW [278]
D is not an ordered pair.

6 0
3 years ago
The two tables give the number of pints of red and blue paint that are used to make different amounts of two shades of purple pa
ValentinkaMS [17]

The two highlighted rows show that for the same amount of blue, Purple #1 uses <u>more</u> red than Purple #2.

This means that Purple #1 is <u>a redder</u> shade of purple than Purple #2.

Purple #2 is <u>a bluer</u> shade of purple than Purple #1.

Step-by-step explanation:

The two highlighted rows show that for the same amount of blue, Purple #1 uses <u>more</u> red than Purple #2.

Making blue's quantity as 3 parts for purple #1 implies red part becomes 1.5 to maintain the ratio 1:2

Purple #1 has 1/3 parts red and 2/3 parts blue. Purple #2 has 1/4th part red and 3/4th part blue.

Hence, Purple #1 is <u>a redder</u> shade of purple than Purple #2.

From the above explanation, <u>Purple #2</u> is a bluer shade of purple than Purple #1.

<em>Sure hopes this helps you :)</em>

<em></em>

<h3><em>//❀ ❀//</em></h3>
4 0
2 years ago
Which of the following statements is not correct?
NeX [460]

Answer:

The highest percentage of teenagers in the sample

listed soccer as their favorite sport.

Basketball

Lacrosse

Soccer

Football

Step-by-step explanation:

4 0
3 years ago
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How do you find the prime factorization of 504
arlik [135]
1 x 2 x 2 x 2 x 3 x 3 x 7
6 0
3 years ago
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