Admission to the movies is $10 for adults and $7 for children. Find the

Mathematics

1 answer:

nevsk [136]3 years ago

6 0

Answer:

$96

Step-by-step explanation:

4 times 10 is 40. 7 times 8 is 56. 40 + 56 = 96

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Ex 4.8 14) integrate 3^(2x-1)

sesenic [268]

Take the integral:

$\large\begin{array}{l} \mathsf{\displaystyle\int\!3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\int\!\frac{1}{2}\cdot 2\cdot 3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^{2x-1}\cdot 2\,dx\qquad(i)} \end{array}$

$\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}$

$\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope it helps. :-)}$


Tags: integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

4 0

3 years ago

Travis has a savings account that his parents opened for him. It pays 6% annual interest. His uncle also opened an account for h

mezya [45]

So let's say the amounts are "a" and "b", at 6% and 8% respectively.

how much is 6% of a? well (6/100) * a, or 0.06a.
how much is 8% of b? well (8/100) * b, or 0.08b.

so hmm whatever "a" and "b" amounts are, we know that their yield is $100, thus 0.06a + 0.08b = 100.

now, there's more money in "a" than in "b", 500 bucks more, so whatever "b" is, we know that a = b + 500.

$\bf \begin{cases}
0.06a+0.08b=100\\
\boxed{a}=b+500\\
----------\\
0.06\left( \boxed{b+500} \right)+0.08b=100
\end{cases}
\\\\\\
0.06b+0.08b+30=100\implies 0.02b=70\implies b=\cfrac{70}{0.02}
\\\\\\
b=3500$

how much was deposited in the 6% one? well, a = b + 500.

8 0

3 years ago

Find the solution set for this inequality. SHOW YOUR WORK OR NO CREDIT -2x+4>-4x+8

Digiron [165]

Answer:

x<2 is your answer

Step-by-step explanation:

-2x+4>-4x+8

subtract each term by 8

-2x+4-8>-4x+8-8

add both side by 2x

-2x+2x-4>-4x+2x