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3 years ago

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The states C and D spend a total of $56.6 million for tourism. The state C spends $2.6 million more than the state D. Find the

amount that each state spends on tourism.

1 answer:

igomit [66]3 years ago

5 0

Answer:

State C : $30.9 Million State D : $25.7 Million

Step-by-step explanation:

It may help to just forget about the word "million" and focus on the decimal number part,so one you get the deciaml number you can just put the word million after it as your answer.

First do 56.6 divided by 2, which equals 28.3. Since it said that State C spends 2.6 million more, you hvae to add 28.3 and 2.6 together, which also equals 30.9. So now you know State C spends $30.9 million total. In order to find out how much money State D sends, you have to do 56.6 - 30.9,which comes up to 25.7. So finnaly you know that State C spends 30.9 million dollars and State D spends 25.7 million dollars.

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Evaluate the integral, show all steps please!

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Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

<u>Integration by substitution</u>

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<u /> $\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

<u>Substitute</u> everything into the original integral:

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Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

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$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

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$\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Learn more about integration by substitution here:

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3 years ago

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OverLord2011 [107]

Easy, take:

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3 years ago

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Anettt [7]

Answer:

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and the volume of a cone is given by:

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since both have the same height and radius, we can solve each equation for $r^2h$ (because this quantity is the same in both figures) and then match the expressions we find:

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