4 years ago

The product of a number and 4 is 69. What is the number?

Mathematics

1 answer:

ICE Princess25 [194]4 years ago

6 0

Answer:

The number that you can multiply by 4 to get 69 is 17.25

Step-by-step explanation:

For this problem, we will divide 69 by 4.

69 ÷ 4 = 17.25

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How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160

Marina CMI [18]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=3\\
S_n=160
\end{cases}$

$\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
\\\\\\
160=2(3^n-1)\implies \cfrac{160}{2}=3^n-1\implies 80=3^n-1
\\\\\\
81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^4=3^n\implies 4=n$

3 0

3 years ago

The company is building a scale model of the theater's main show tank for an investor's presentation. Each dimension will be mad

Ede4ka [16]

Answer:

This means the mock-up tank has a volume 216 times smaller than the initial tank.

Step-by-step explanation:

The ratio between volume is given by

$\frac{V_2}{V_1}=\frac{(1/6)L^{3} }{L^{3}} =\frac{1}{216}$