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abruzzese [7]
3 years ago
8

Solve the equation 144x²-1=0

Mathematics
1 answer:
ratelena [41]3 years ago
8 0
<span><span>x=0.083333</span>,<span>−0.083333</span></span><span>
</span>
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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

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Step-by-step explanation: 3% of $70 is $2.10.

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Divide the number that you want to turn into a percentage by the whole. In this example, you would divide 2 by 5. 2 divided by 5 = 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.

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