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navik [9.2K]
2 years ago
14

What is the volume of a right trianular prism with the dimesions of 15 11 17

Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
3 0

Answer:

1402.5 Cubic Units

Step-by-step explanation:

Volume of a Triangular Prism: V = \frac{1}{2}bhl

b - base

h - height

l - length  

15 is the height, 17 is the length, and 11 is the width  (assuming which is the base).

V=0.5 * (11 * 15 * 17) \\V=0.5*2085\\V=1402.5

The volume of the prism should be 1402.5 cubic units.

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Find the remaining trigonometric ratios of θ if csc(θ) = -6 and cos(θ) is positive
VikaD [51]
Now, the cosecant of θ is -6, or namely -6/1.

however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.

we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

\bf csc(\theta)=-6\implies csc(\theta)=\cfrac{\stackrel{hypotenuse}{6}}{\stackrel{opposite}{-1}}\impliedby \textit{let's find the \underline{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{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{IV~quadrant}{+\sqrt{35}=a}

recall that 

\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad\qquad 
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\\\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
\qquad \qquad 
% cotangent
cot(\theta)=\cfrac{adjacent}{opposite}
\\\\\\
% cosecant
csc(\theta)=\cfrac{hypotenuse}{opposite}
\qquad \qquad 
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}

therefore, let's just plug that on the remaining ones,

\bf sin(\theta)=\cfrac{-1}{6}
\qquad\qquad 
cos(\theta)=\cfrac{\sqrt{35}}{6}
\\\\\\
% tangent
tan(\theta)=\cfrac{-1}{\sqrt{35}}
\qquad \qquad 
% cotangent
cot(\theta)=\cfrac{\sqrt{35}}{1}
\\\\\\
sec(\theta)=\cfrac{6}{\sqrt{35}}

now, let's rationalize the denominator on tangent and secant,

\bf tan(\theta)=\cfrac{-1}{\sqrt{35}}\implies \cfrac{-1}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{-\sqrt{35}}{(\sqrt{35})^2}\implies -\cfrac{\sqrt{35}}{35}
\\\\\\
sec(\theta)=\cfrac{6}{\sqrt{35}}\implies \cfrac{6}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{6\sqrt{35}}{(\sqrt{35})^2}\implies \cfrac{6\sqrt{35}}{35}
3 0
3 years ago
Answer these questions please. (All three)
viktelen [127]

Answer:

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Step-by-step explanation:

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18:3x-5=4 and 3x-3=6. For the first one add 5 to both sides to get 3x=9 then divide both side by 3 to get x=3. For the second one add 3 to both sides to get 3x=9. Again divide both sides by three to get x=3.

19: $18-$4.62=13.38 since he wants 2 models divide 13.38 by 2 to get 6.69.

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2 years ago
Solve the expression 8 x 5 − 12 x one third + 5 using PEMDAS
skelet666 [1.2K]

Answer:41

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8 0
3 years ago
About how many inches are equivalent to 3 meters? Round the number(s) needed in the table to the nearest tenth to find the appro
Burka [1]

Answer:

D

Step-by-step explanation:

three meters is 118.11 inches, so if you were to round that you would get 120 inches. That means the answer is D.

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Translate and simplify the expression the sum of fifteen and a number plus twelve
mr Goodwill [35]
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