$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=6
\end{cases}
\\\\\\
S_n=4\left( \cfrac{1-6^n}{1-6} \right)\implies S_n=4\left( \cfrac{1-6^n}{-5} \right)$

6 0

2 years ago

A staff gauge measures the height of the water level in a river compared to the average water level. At one gauge the river is 1

Juli2301 [7.4K]

The river will not reach a level of 7 ft. after 5 hours.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the height of the water level after x hours.

Since the river is 1 ft below its average water level and begins to rise by a constant rate of 1.5 ft per hour. Hence:

b = -1, m = 1.5. The equation becomes:

y = 1.5x - 1

To reach a level of 7 ft. That is y = 7:

7 = 1.5x - 1

1.5x = 8

x = 5.3 hours

The river will not reach a level of 7 ft. after 5 hours.

Find out more at: brainly.com/question/13911928

5 0

1 year ago

Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!

Licemer1 [7]

Answer:

Step-by-step explanation:

Pythagorean theorem. 24^2+b^2=25^2

Simplify

576+b^2=625

b^2=49

b=7

4 0

2 years ago