What is the inequality of n+8<

Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.

Hitman42 [59]

$\bf sin^{-1}(some\ value)=\theta \impliedby \textit{this simply means}
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sin(\theta )=some\ value\qquad \textit{now, also bear in mind that}
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sin(\theta)=\cfrac{opposite}{hypotenuse}\qquad 
\qquad 
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\\\\
-------------------------------\\\\$

$\bf sin^{-1}\left( \frac{2}{5} \right)=\theta \impliedby \textit{this simply means that}
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sin(\theta )=\cfrac{2}{5}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{now let's find the adjacent side}
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\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm \sqrt{5^2-2^2}=a\implies \pm\sqrt{21}=a
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\textit{we don't know if it's +/-, so we'll assume is the + one}\quad \sqrt{21}=a\\\\
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tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad tan(\theta)=\cfrac{2}{\sqrt{21}}
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\textit{and now, let's rationalize the denominator}
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\cfrac{2}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies \cfrac{2\sqrt{21}}{(\sqrt{21})^2}\implies \cfrac{2\sqrt{21}}{21}
$

7 0

3 years ago

Brett works at a local pet store. When he works 4 hours he earns $36. When he works 9 hours he earns $81. What is the rate per h

Kitty [74]

The answer is 9 Dollars per hour because 36 divided by 9 is 4 and 9 times 9 is 81.

4 0

3 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

AleksandrR [38]

2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 <== slope intercept form
=================
y = -2/3x + 490
slope = -2/3
y int = (0,490)
=================
description of graphing : Plot ur point at (0,490). Since the slope is -2/3, starting at (0,490)...go down 2 and to the right 3,then down 2 and to the right 3 and you will eventually cross the x axis at the x intercept.

The x intercept can be found by subbing in 0 for y and solving for x
y = -2/3x + 490
0 = -2/3x + 490
2/3x = 490
x = 490 * 3/2
x = 1470/2 = 735...so ur x intercept is (735,0)

therefore, your line will cross the x axis at (735,0)
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function notation is : f(x) = -2/3x + 490
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suppose his profit is 1593....
2x + 3y = 1593
3y = -2x + 1593
y = -2/3x + 531

the graphs for the two months :
similarities : they both have the same slope of -2/3
differences : they have different x and y intercepts
By the way, these are parallel lines
===================
sorry about the last one....can't see the 3rd month graph

7 0

3 years ago

when camping alone , mr adam uses all of the water in 12 days, then when mrs adams and mr adams camp together they use all of th

professor190 [17]

Using the together rate, it is found that if Mrs Adams camps alone, she will use all the water in 24 hours.

<h3>What is the together rate?</h3>

The together rate is the sum of each separate rate.

In this problem, the rates are: