We know that a dog, a goat, and a bag of tin cans are to be transported across a river in a ferry that can carry only one of these three items at once (along with a ferry driver).

The driver will first transport the goat to the other shore and then return empty. Then they will take a bag of tin and transport it to the other shore, and then they will return with the goat to their original place.

Then he will leave the goat there and take a dog and carry it to the other shore and then return empty.

And eventually they will take the goat and transport it to the other shore.

4 0

2 years ago

Find the exact value of cos(sin^-1(-5/13))

son4ous [18]

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

$\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}$

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}$

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

8 0

2 years ago

17.5 how to make this into a fraction

BARSIC [14]

Take the .5 of the 17.5 and convert it to a fractin.
we know .5 is equal to 50% or 1/2

now we have a mixed number $17 \frac{1}{2}$

in order to convert it into an improper fraction you need to multiply the whole number by the denominator and then add the numerator all while keeping the denominator constant.

$W \frac{N}{D} = \frac{(W*D)+N}{D}$

so $17 \frac{1}{2}= \frac{(17*2)+1}{2}= \frac{35}{2}$

5 0

3 years ago

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