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Genrish500 [490]
3 years ago
9

exFormula1" title=" \int\limits {3 ^{ \frac{x}{2} } } \, dx " alt=" \int\limits {3 ^{ \frac{x}{2} } } \, dx " align="absmiddle" class="latex-formula">=
Mathematics
2 answers:
Kryger [21]3 years ago
7 0
\int 3^{\tfrac{x}{2}}\, dx=(*)\\
t=\dfrac{x}{2}\\
dt=\dfrac{x}{2}\, dx\\
dx=2\, dt\\
(*)=\int 3^t\cdot2\, dt=\\
2\int 3^t \, dt=\\
2\cdot\dfrac{3^t}{\ln 3}+C=\\
\boxed{\dfrac{2\cdot3^{\tfrac{x}{2}}}{\ln 3}+C}

jekas [21]3 years ago
7 0
\int { { 3 }^{ \frac { x }{ 2 }  } } dx\\ \\ =\int { { \left( { 3 }^{ x } \right)  }^{ \frac { 1 }{ 2 }  } } dx

However:

u={ 3 }^{ x }\\ \\ \therefore \quad \frac { du }{ dx } ={ 3 }^{ x }\cdot \ln { 3 } \\ \\ \therefore \quad du={ 3 }^{ x }\cdot \ln { 3 } dx\\ \\ \therefore \quad dx=\frac { 1 }{ { 3 }^{ x }\cdot \ln { 3 }  } du=\frac { 1 }{ u\cdot \ln { 3 }  } du

So let's use:

\int { { u }^{ \frac { 1 }{ 2 }  } } \cdot \frac { 1 }{ u\cdot \ln { 3 }  } du\\ \\ =\int { \frac { 1 }{ \ln { 3 }  }  } \cdot { u }^{ -\frac { 1 }{ 2 }  }du

But you need to know that:

\int { k{ u }^{ n } } du\\ \\ =\frac { k{ u }^{ n+1 } }{ n+1 } +C

Therefore:

\int { \frac { 1 }{ \ln { 3 }  }  } \cdot { u }^{ -\frac { 1 }{ 2 }  }du\\ \\ =\frac { \frac { 1 }{ \ln { 3 }  } \cdot { u }^{ \frac { 1 }{ 2 }  } }{ \frac { 1 }{ 2 }  } +C

\\ \\ =\frac { 1 }{ \ln { 3 }  } \cdot { u }^{ \frac { 1 }{ 2 }  }\cdot 2+C\\ \\ =\frac { 1 }{ \ln { 3 }  } \cdot { 3 }^{ \frac { x }{ 2 }  }\cdot 2+C\\ \\ =\frac { 2\cdot { 3 }^{ \frac { x }{ 2 }  } }{ \ln { 3 }  } +C
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15% off the original price of $350, plus 6% sales tax
jonny [76]
Step 1. 100-15=85
Step 2. $350 *.85=$297.50
Step 3. $297.50 * .06= $17.85
Step 4. $297.50+17.85=$315.35

Answer: $315.35
7 0
3 years ago
PLS HELP ASAP FOR BRAINLIEST
rodikova [14]

Answer:

y=3

Step-by-step explanation:

it is because X=-2 had crossed the point y=3

hope this help you!!!! ;))))))

3 0
2 years ago
Katrina goes to Road Runner after school and purchases a soda for 1.50, chips for 3.50 and a candy bat for 0.50 An additional 8%
Nutka1998 [239]

<u>Answer:</u>

Sale tax paid by Katrina is 0.44 units of currency and total amount paid is 5.94 unit of currency.

<u> Solution:</u>

Given that Katrina goes to road runner after school and purchase following three products

A soda for 1.50  

Chips for 3.50

Candy for 0.50

Also she pays 8% sales tax.

Need to determine amount paid in sales tax and total amount paid by Katrina.

lets first calculate amount she paid without taxes.  

Total paid amount without taxes = 1.50 + 3.50 + 0.50 = 5.50

As she paid 8% sale tax , that is 8 % of 5.50

so sale tax paid = \frac{8}{100} \times 5.50 = 0.44

<em>Total amount paid = Total amount paid without taxes + tax paid </em>

= 5.50 + 0.44 = 5.94

Hence sale tax paid by Katrina is 0.44 units of currency and total amount paid is 5.94 unit of currency.  

7 0
3 years ago
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galben [10]

Answer:

I say Mean.

Step-by-step explanation:

Mean (Average): 23

Mode(most common): 21

Median(Middle): 21

7 0
3 years ago
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fenix001 [56]
The answer is simplified to 15
5 0
3 years ago
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