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Molodets [167]
4 years ago
8

What is the common ratio, r, for the sequence represented by the formula a∨n= 3(2)ˆ-n

Mathematics
1 answer:
fgiga [73]4 years ago
6 0
\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}
\end{cases}\\\\
-------------------------------\\\\
a_n=3(2)^{-n}\implies a_n=3(2^{-1})n\implies a_n=3\left( \stackrel{r}{\cfrac{1}{2}} \right)^n
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The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and
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Answer:

3.2 feet


Step-by-step explanation:

The equation  f(x)=-0.3x^{2}+2x  shows the height of water [f(x)] and horizontal distance [x].

<em>Given the </em><em>horizontal distance is 4 feet</em><em>, they want to know the height.</em>


<em>Simply put 4 in x of the equation and solve for f(x). So,</em>

<em>f(x)=-0.3(4)^{2}+2(4)\\f(x)=3.2</em>

So, the height of the water was 3.2 feet above the ground.

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The base, b, has a length of 12 centimeters. The height, h, is 8 centimeters.
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b=12

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solmaris [256]

Answer:

x =  \frac{25}{13}

Step-by-step explanation:

Given:

\frac{2}{5} x -  \frac{1}{2}  =  \frac{1}{3}  +  \frac{5}{6} x

Combine like terms:

\frac{2}{5} x -  \frac{5}{6} x =  \frac{1}{3}  +  \frac{1}{2}

Find GCF :

\frac{12}{30} x -  \frac{25}{30}  =  \frac{2}{6}  +  \frac{3}{6}

Subtraction and Addition :

\frac{13}{30} x =  \frac{5}{6}

Divide both sides by 13/30 :

\frac{ \frac{13}{30} }{ \frac{13}{30} } x =  \frac{ \frac{5}{6} }{ \frac{13}{30} }

Simplify :

Multiplication (Reciprocal) :

x =  \frac{5}{6}  \times  \frac{30}{13}

x =   \frac{150}{78}

x =  \frac{25}{13}

Answer :

x =  \frac{25}{13}

Hope it helps

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2 years ago
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