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user100 [1]
3 years ago
12

Log(base10)(6/5)^6 expand

Mathematics
1 answer:
aev [14]3 years ago
7 0
Log10 (6/5)^6
= 6 log10 (6/5)
= 6 (log10 6 - log10 5) Answer
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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
2 years ago
Read 2 more answers
Please help meeeeeeee​
Tomtit [17]

Answer:

  • y = -1/2x + 1

Step-by-step explanation:

<u>Slope-intercept form: </u>

  • y = mx + b

<u>Use two of the ordered pairs and find the slope:</u>

  • m = (1-2)/(0-(-2)) = -1/2

<u>y-intercept is 1 as point (0, 1) is given in the table:</u>

  • b = 1

<u>The line is:</u>

  • y = -1/2x + 1
8 0
3 years ago
Jen scored 80 on a test. 16 of the questions she answered were correct. How many questions did the test have?
Dmitry [639]
16 questions right = 80%
So that means Jen missed 4 questions.
Hope this helped.
8 0
3 years ago
Find the equation of a line that passes through (-2,4) and (1,-2)
Basile [38]

\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x

8 0
3 years ago
If a man making $22 an hour gets a 20% raise, she will make an additional 1/10 of her salary an hour.
MariettaO [177]

Answer:

True

Step-by-step explanation:

If this is a true or false question it is true.

22 x 20% = 2.2

22 ÷ 10 = 2.2

Hope this helps!

3 0
3 years ago
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