Answer:
<u>It</u><u> </u><u>is</u><u> </u><u>c</u><u>:</u><u> </u><u>1</u><u>5</u><u>.</u><u>6</u><u>2</u><u>5</u><u> </u><u>cm³</u>
Step-by-step explanation:
Formular for cube volumes:
![{ \tt{volume = (side \times side \times side)}} \\ { \tt{v = (s_{1} \times s_{2} \times s_{3}) }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bvolume%20%3D%20%28side%20%5Ctimes%20side%20%5Ctimes%20side%29%7D%7D%20%5C%5C%20%7B%20%5Ctt%7Bv%20%3D%20%28s_%7B1%7D%20%5Ctimes%20s_%7B2%7D%20%5Ctimes%20s_%7B3%7D%29%20%7D%7D)
since sides of a cube are identical:
![{ \sf{s_{1} = {s_{2} = {s_{3}}}}}](https://tex.z-dn.net/?f=%7B%20%5Csf%7Bs_%7B1%7D%20%3D%20%7Bs_%7B2%7D%20%3D%20%20%7Bs_%7B3%7D%7D%7D%7D%7D)
Therefore:
![{ \sf{volume = (250 \times 250 \times 250) \: mm {}^{3} }} \\ { \sf{v =15,625,000 \: {mm}^{3} }}](https://tex.z-dn.net/?f=%7B%20%5Csf%7Bvolume%20%3D%20%28250%20%5Ctimes%20250%20%5Ctimes%20250%29%20%5C%3A%20mm%20%7B%7D%5E%7B3%7D%20%7D%7D%20%5C%5C%20%20%7B%20%5Csf%7Bv%20%3D15%2C625%2C000%20%5C%3A%20%20%7Bmm%7D%5E%7B3%7D%20%20%7D%7D)
but 1 mm³ = 0.000001 cm³
![{ \sf{v = (15,625,000 \times \{1 \times {10}^{ - 6} \} ) \: cm}} \\ { \sf{v = 15.625 \: {cm}^{3} }}](https://tex.z-dn.net/?f=%7B%20%5Csf%7Bv%20%3D%20%2815%2C625%2C000%20%5Ctimes%20%20%5C%7B1%20%5Ctimes%20%20%7B10%7D%5E%7B%20-%206%7D%20%5C%7D%20%29%20%5C%3A%20cm%7D%7D%20%5C%5C%20%7B%20%5Csf%7Bv%20%3D%2015.625%20%5C%3A%20%20%7Bcm%7D%5E%7B3%7D%20%7D%7D)
L.C.D least common demoninator of 2,4,8 is 8 because you can multiply all of them by something to get 8 and that is the lowest number you can get. now just change all of them into 8ths
4/8, 6/8, 3/8
![\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Bhypotenuse%7D%0A%5Cqquad%0Acos%28%5Ctheta%29%3D%5Ccfrac%7Badjacent%7D%7Bhypotenuse%7D%0A%5Cquad%20%0A%25%20tangent%0Atan%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Badjacent%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
![\bf sin(\theta )=\cfrac{2}{7}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{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} \\\\\\ \pm\sqrt{7^2-2^2}=a\implies \pm\sqrt{45}=a\implies \pm 3\sqrt{5}=a](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%20%29%3D%5Ccfrac%7B2%7D%7B7%7D%5Ccfrac%7B%5Cleftarrow%20opposite%7D%7B%5Cleftarrow%20hypotenuse%7D%5Cqquad%20%5Ctextit%7Blet%27s%20find%20the%20adjacent%20side%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%5C%5C%5C%5C%0Ac%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Cpm%5Csqrt%7Bc%5E2-b%5E2%7D%3Da%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ac%3Dhypotenuse%5C%5C%0Aa%3Dadjacent%5C%5C%0Ab%3Dopposite%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cpm%5Csqrt%7B7%5E2-2%5E2%7D%3Da%5Cimplies%20%5Cpm%5Csqrt%7B45%7D%3Da%5Cimplies%20%5Cpm%203%5Csqrt%7B5%7D%3Da)
but.... which is it? the + or the -? well, we know that tan(θ) > 0, is another way to say that the tangent of the angle is positive, now, for the tangent to be positive, since it's opposite/adjacent both opposite and adjacent have to be the same exact sign, now, we know the opposite is +2, so that means the adjacent has to be the same sign, thus is the positive version 3√(5)
thus
Answer:
its 20 2/3
Step-by-step explanation:
bc 4 * 5 which equals 20 and then just add a 2/3
Answer:
2 pints: 0.25 gallons
16 pints: 2 gallons
Step-by-step explanation:
1 gallon = 0.125 pints