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3 years ago

what is the value of c? enter your answer in the box. round only your final answer to the nearest whole number.

Mathematics

1 answer:

muminat3 years ago

4 0

Answer:

c ≈ 21

Step-by-step explanation:

By applying cosine rule in the given triangle ABC,

c² = a² + b² - 2abcos(C)

c² = (17)² + (10)² - 2(17)(10)cos(98.8°)

c² = 289 + 100 - 340(-0.1530)

c² = 441.015

c = 21

c ≈ 21

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What kind of shift does the graph have? y = -sin (x-1) from y = sin(x)

Mademuasel [1]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}}
\\\\
f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\
f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}}
\end{array}
\\\\
-------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{ A}}|\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{function period or frequency}\\
\left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
\left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)$

now, with that template in mind, let's see

$\bf \begin{array}{lllll}
y=&-1sin(&1x&-1)&+0\\
&A&B&C&D
\end{array}
\\\\\\
\textit{horizontal shift of }\cfrac{C}{B}\implies \cfrac{-1}{1}\implies -1
\\\\\\
\textit{A is negative, so is flipped upside-down}$

8 0

3 years ago

A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he

mina [271]

Answer:

Step-by-step explanation:

<u>Concentration of Liquids </u>

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

$\displaystyle C=\frac{x}{y}$

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

$\displaystyle \frac{x-1}{x}$

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

$\displaystyle x-1-\frac{x-1}{x}$ cups of juice.

Simplifying, the cups of juice are

$\displaystyle \frac{\left (x-1\right)^2}{x}$

The new concentration is

$\displaystyle \frac{\left (x-1\right)^2}{x^2}$

For the third time, we now have

$\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}$ cups of juice.

Simplifying, the final amount of juice is

$\displaystyle \frac{\left (x-1\right)^3}{x^2}$

And the final concentration is

$\displaystyle \frac{\left (x-1\right)^3}{x^3}$

According to the conditions of the question, this must be equal to 50% (0.5)

$\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5$

Taking cubic roots

$\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}$

$\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}$

Operating and joining like terms

$\displaystyle x-\sqrt[3]{0.5}\ x=1$

Solving for x

$\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}$

$x=4.8473\ cups$

Let's test our result

Final concentration:

$\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5$

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3 years ago

Francine uses 2/3 cup of pineapple juice for every 1/3 cup of orange juice to make a smoothie. Enter the number of cups of pinea

Oksanka [162]

$\bf \begin{array}{ccllll}
pineapple&orange\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
\frac{2}{3}&\frac{1}{3}\\\\
x&1
\end{array}\implies \cfrac{\frac{2}{3}}{x}=\cfrac{\frac{1}{3}}{1}\implies \cfrac{\frac{2}{3}}{\frac{x}{1}}=\cfrac{\frac{1}{3}}{\frac{1}{1}}\\\\
-----------------------------\\\\$

$\bf \textit{now recall that }\qquad \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\
-----------------------------\\\\
\cfrac{2}{3}\cdot \cfrac{1}{x}=\cfrac{1}{3}\cdot \cfrac{1}{1}\implies \cfrac{2}{3x}=\cfrac{1}{3}\implies 2\cdot 3=1\cdot 3x\implies 6=3x
\\\\\\
\cfrac{6}{3}=x$

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Answer:

Step-by-step explanation:

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