Evaluate the integral using integration by parts with the indicated choices of u and dv. (use c for the constant of integration.
) 2x2 ln(x) dx; u = ln(x), dv = 2x2 dx
1 answer:
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Answer:
c. quarterly
Step-by-step explanation:
To start with 1 year is equal to twelve months
3months out of 12 months will be;
3/12= 1/4
Here it is compounded quarterly and n=4 where n is the number of compoundings a year.
Lets study the compound interest formula;
where;
A=The ending amount
P=Starting amount
r=rate of interest expressed as a decimal
n=number of compoundings a year
t=total number of years
The number of compoundings in any one year can be an interest compounded yearly where n=1, semi-annually with n=2, quarterly where n=4, monthly where n=12, weekly and n=52 and finaly daily with n=365.
Answer:
Step-by-step explanation:
So, we need to find the equation of a parabolic function that goes through the points (-3,67) and (-1,1) and has a stretch factor of 9.
In other words, we want to find a quadratic with a vertical stretch of 9 that goes through the points (-3,67) and (-1,1).
To do so, we first need to write some equations. Let's use the vertex form of the quadratic equation. The vertex form is:
Where a is the leading coefficient and (h,k) is the vertex.
Since a is the leading coefficient, it's also our stretch factor. Thus, let a equal 9.
Also, we have two points. We can interpret them as functions. In other words, (-3,67) means that f(-3) equals 67 and (-1,1) means that f(-1) equals 1. Write the two equations:
And:
Now, we essentially have a system of equations. Thus, to find the original equation, we just need to solve for the vertex. To do so, first isolate the k term in the second equation:
Now, substitute this value to the first equation:
And now, we just have to simplify.
First, from each of the square, factor out a negative 1:
Power of a product property:
The square of -1 is positive 1. Thus, we can ignore them:
Square them. Use the trinomial pattern:
Distribute:
Combine like terms:
The first set cancels. Simplify the second and third:
Subtract 73 from both sides. The right cancels:
Divide both sides by 36:
Therefore, h is -1/6.
Now, plug this back into the equation we isolated to solve for k:
First, remove the negative by simplifying:
Plug in -1/6 for h:
Add. Make 1 into 6/6:
Square:
Multiply. Note that 36 is 9 times 4:
Convert 1 into 4/4 and subtract:
So, the vertex is (-1/6, -21/4).
Now, plug everything back into the very original equation with 9 as a:
And this is our answer :)