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umka21 [38]
3 years ago
13

Answer both please, the topic is linear inequalities, and please explain it to me.

Mathematics
1 answer:
Bogdan [553]3 years ago
7 0
<u>Question 1 solution:</u>
You have two unknowns here:

Let the Water current speed = W

Let Rita's average speed = R

We are given <em>two </em>situations, where we can form <em>two equations</em>, and therefore solve for the <em>two unknowns, W, R</em>:

Part 1)  W→ , R←(against current, upstream) 
If Rita is paddling at 2mi/hr against the current, this means that the current is trying to slow her down. If you look at the direction of the water, it is "opposing" Rita, it is "opposite", therefore, our equation must have a negative sign for water<span>:  

</span>R–W=2  - equation 1

Part 2)  W→ , R<span>→</span>(with current)
Therefore, R+W=3  - equation 2

From equation 1, W=R-2, 
Substitute into equation 2.
R+(R–2)=3
2R=5
R=5/2mi/hr

So when W=0 (still), R=5/2mi/hr

Finding the water speed using the same rearranging and substituting process:

1...               R=2+W
2...  (2+W)+W=3
                 2W=1
                   W=1/2mi/hr
 
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The function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily

<h3>How to rewrite the function?</h3>

The function is given as:

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There are 7 days in a week.

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Substitute x/7 for x in

f(x) = 86(1.08)^(x/7)

Rewrite as:

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What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-
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The sum of the infinite geometric series is -288.

<h2>Given that</h2>

A finite geometric series with n = 4, a₁ = -144, and r = ½.

<h3>We have to determine</h3>

What is the sum of the infinite geometric series?

<h3>According to the question</h3>

The sum of the infinite is determined by the following formula;

\rm S\infty = \dfrac{a_1(1-r^n)}{1-r}\\\\

A finite geometric series with n = 4, a₁ = -144, and r = ½.

Substitute all the values in the formula;

\rm S\infty = \dfrac{a_1(1-r^n)}{1-r}\\\\S\infty = \dfrac{-144 (1- \dfrac{1}{2}^4)}{1-\dfrac{1}{2}}\\\\S \infty = \dfrac{-144 \times \dfrac{15}{16}}{\dfrac{1}{2}}\\\\S \infty = -270

Therefore,

The sum of the infinite geometric series is,

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