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3 years ago

How would i work out the inequality 3x - 3 < 9?

Mathematics

1 answer:

ehidna [41]3 years ago

5 0

Answer:

$x$

Step-by-step explanation:

$3x-3$

$+3$ $+3$

$3x$

$/3$ $/3$

$x$

Hope this helps!

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You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

How to solve this problem

rodikova [14]

$\bf \textit{circumference of a circle}\\\\
C=2\pi r\quad 
\begin{cases}
r=radius\\
-----\\
r=10
\end{cases}\implies C=2\pi 10\implies \boxed{C=20\pi }\\\\
-------------------------------\\\\$

$\bf \textit{let's converte 1km to inches}
\\\\\\
km\cdot \cfrac{1000m}{km}\cdot \cfrac{100cm}{m}\cdot \cfrac{in}{2.54cm}\implies \cfrac{1000\cdot 100\cdot in}{2.54}\approx 39370.079\ in\\\\
-------------------------------\\\\
\textit{how many times does }20\pi \textit{ go into }39370.079?\implies \boxed{\cfrac{39370.079}{20\pi }}$

3 0

3 years ago

(31 points) Wilson County School District consists of 2,548 students. The district decided to conduct a survey regarding their n

Sauron [17]

Answer:

+ or - 0.044

Step-by-step explanation:

3 0

3 years ago

20. Find the slope of the line graphed below.

seraphim [82]

I don’t see a graph....

4 0

3 years ago

Read 2 more answers

Plz help me 1+2p+9p-4

Charra [1.4K]

-3+11p
first you add 1+2p that gets you -3 then you do 9p-4 and you get 11p from there you can either solve it, or leave it as is, depending on what your teacher wants.

8 0

3 years ago

Read 2 more answers