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Over [174]
3 years ago
14

How many decimeters are in 3.5 dekameters? Use the metric table to help answer the question.

Mathematics
1 answer:
nataly862011 [7]3 years ago
8 0

it’s 350 or B. hope this helps! :)

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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
PLEASE HELPPPPPP
boyakko [2]

Answer:

15 if b is supposed to the side length, √15 if b is the base which is a square.

Step-by-step explanation:

8 0
3 years ago
Fill in each blank with one of the three phrases: is less than, is equal to, or is greater than.
Kazeer [188]

✧・゚: *✧・゚:*  Answer:  *:・゚✧*:・゚✧

✅ 1,742 x 1.000 > 1,742

I WOULD APPRICIATE BRAINLIEST!

~ ₕₒₚₑ ₜₕᵢₛ ₕₑₗₚₛ! :₎ ♡

~

8 0
2 years ago
Read 2 more answers
Driving 70 mph, it takes Alicia 2 hours to reach the airport to go on a vacation. It then takes her 2 hours to get to her destin
OLga [1]

She drove 2 hours at 70 miles per hour, so she drove 70 * 2 = 140 miles total.

The jet traveled 400 miles per hour for 2 hours for a total of 400 * 2 = 800 miles.

Total miles = 140 + 800 = 940 miles.

The answer is C.

4 0
3 years ago
Two people are standing in a field. One person is flying a kite with a string that is
Anastaziya [24]
Do you still need the question
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