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3 years ago

For , find the value of x for which .

Mathematics

1 answer:

Mice21 [21]3 years ago

8 0

Uh what did you mean to upload a picture or somthing

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

Hitman42 [59]

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

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

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

What is the following number in decimal form? 2.93 × 10−7 =

Arisa [49]

$a^{-n}=\left(\frac{1}{a}\right)^n\\\\10^{-7}=\left(\dfrac{1}{10}\right)^7=\dfrac{1}{10,000,000}=0.0000001\\\\2.93\times10^{-7}=2.93\times0.0000001=\boxed{0.000000293}$

3 0

4 years ago

twice last month, judy carter rented a car in Fresno, California and traveled around the southwest on business. the car rentel a

mylen [45]

Create a system of 2 equations

Let x be daily fee and y the mileage charge, then

4x + 370y = 244.50...........(1)

3x + 190y = 161.50..............(2)

If we multiply (1) by 3 and (2) by -4 and add the 2 equations we eliminate x:-

12x + 1110y = 733.50

-12x - 760y = -646 Adding :-

350y = 87.5 so y = 0.25

Plugging y = 0.25 into eqation (1) we get 4x = 244.50 - 0.25 * 370

giving x = 38

Answer is daily fee = $38 and mileage charge = $0.25 per mile.

6 0

3 years ago

Read 2 more answers

I’ll give brainliest help ASAP

Ghella [55]

The answer is 3 1 2 4

3 0

3 years ago

Read 2 more answers

Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]

stealth61 [152]

$\mathbf r(t)=5\cos3t\,\mathbf i-5\sin3t\,\mathbf j+3t\,\mathbf k$
$\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt$

$\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt$
$=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt$
$=12\sqrt{26}$

4 0

4 years ago