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3 years ago

I NEED HELP PLEASE, THANKS!

Mathematics

1 answer:

Finger [1]3 years ago

3 0

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

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The line with equation −a+3b=0 coincides with the terminal side of an angle θ in standard position and sinθ<0 .

Anna11 [10]

If $a$ is the variable of the horizontal axis, then you can solve for $b$ to get the equation of the line in slope-intercept form in the $a,b$ plane:

$-a+3b=0\implies b=\dfrac a3$

i.e. a line with slope $\dfrac13$ through the origin, which means it is contained in the first and third quadrants. Since the terminal side of $\theta$ has a negative sine, the angle must lie in the third quadrant.

Because the slope of the line is $\dfrac13$ , you can choose any length along the line to make up the hypotenuse of a right triangle with reference angle $\theta$ . Any such right triangle will have $\tan\theta=\dfrac13$ , regardless of whether the angle is the first or third quadrant. But since $\theta$ is known to lie in the third quadrant, and so $\sin\theta$ and $\cos\theta$ are both negative, you have

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac13\implies \dfrac{\sin\theta}{\cos\theta}=\dfrac{-1}{-3}\implies \cos\theta=-3$

6 0

3 years ago

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The table shows the number of books donated to a library each month. Suppose the growth continues exponentially.

telo118 [61]

$\bf \begin{array}{ccll}
\stackrel{t}{months}&\stackrel{A}{books}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
0&80\\
1&100\\
2&125
\end{array}$ , we know that on Month 0, the Books were 80

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &80\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
\end{cases}
\\\\\\
80=I(1+r)^0\implies 80=I\qquad therefore\qquad \boxed{A=80(1+r)^t}$

we also know that on the first month there were 100 books,

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &100\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &1\\
\end{cases}
\\\\\\
100=80(1+r)^1\implies \cfrac{100}{80}=1+r\implies \cfrac{5}{4}=1+r
\implies 
\cfrac{5}{4}-1=r
\\\\\\
 \cfrac{1}{4}=r\implies 0.25=r\qquad therefore\qquad \boxed{A=80(1+0.25)^t}$

now, how many books when t = 8? A=80(1+0.25)⁸, or A=80(1.25)⁸.

7 0

3 years ago

Read 2 more answers

A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcoho

Rzqust [24]

Answer:

We have 8 liters of 54% alcohol.

We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.

54 * 8 + 66 x = 65 (8 + x)

432 + 66x = 520 + 65x

x = 88 liters

Step-by-step explanation:

3 0

3 years ago

One angle of a triangle measures 95°. The other two angles are in a ratio of 8:9. What are the measures of those two angles?

Luba_88 [7]

Answer:

40 degrees and 45 degrees

Step-by-step explanation:

If you subtract 95 degrees from a 180-degree triangle, you are left with 85 degrees. To proportionally split them, find two values that add to the same value. Since 40 and 45 make up 80 and they multiply by two to make 80:90, these are the two measures.

8 0

3 years ago

Aku orang Indo,Ada yang mau temenan ?

Elis [28]

Answer:

tolong tandai saya cerdas

Step-by-step explanation:

tentu aku akan senang berteman denganmu

5 0

2 years ago

Read 2 more answers