Topic
Q:
Evaluate the integral
\[ \int x^{5}\left(x^{6}-8\right)^{21} d x, \]
by making the appropriate substitution: \( u=\square \)
Q:
На автомашине планировали перевезти сначала \( 3 \frac{8}{9} \) т груза, а г
том ещё \( 2 \frac{11}{18} \) т. Однако перевезли на \( 1 \frac{1}{4} \) т меньше, чем предпол
гали. Сколько всего тонн груза перевезли на автомашине?
Q:
Evaluate \( a-b \) if \( a=-2.5 \) and \( b=\frac{2}{5} \). Write your answer as a decimal to the nearest tenth.
Q:
You have \( \$ 400,000 \) saved for retirement. Your account earns \( 9 \% \) interest. How much will you be able to pull
out each month, if you want to be able to take withdrawals for 20 years?
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Q:
\( x-y \) if \( x=-5 \frac{1}{4} \) and \( y=-6.8 \). Write your answer as a decimal to the nearest hundredth.
Q:
Solve for \( x \) and \( y \) simultaneously:
\( y=2+5 x \) and \( 2 x y-7=-x^{2} \)
Q:
Consider the indefinite integral \( \int \frac{x^{4}}{\left(x^{5}+3\right)^{5}} d x \) :
This can be transformed into a basic integral by letting
\( u=\square \) and
\( d u=\square \)
Q:
3.3 \( \begin{array}{l}\text { The general term of a quadratic number pattern is } T_{n}=n^{2}+2 n-15 \text {. } \\ \text { Determine which term has a value of } 20 .\end{array} \)
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
You deposit \( \$ 400 \) each month into an account earning \( 7 \% \) interest compounded monthly. Round to the
nearest cent as needed.
a) How much will you have in the account in 20 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
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