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AveGali [126]
3 years ago
14

What is the slope of the line?

Mathematics
1 answer:
il63 [147K]3 years ago
4 0

Answer:

i think its 4

Step-by-step explanation:

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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
$12 meal; 4.5% tax find total cost to the nearest cent
Lemur [1.5K]

Answer:

12.54

Step-by-step explanation:

just multiply 12×0.045 and add the 12.

I hope and this helps.

Have a good day.

Good luck

8 0
3 years ago
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1/a+2/b+3/c; Express as a single fraction.
Anika [276]
Answer: (bc+2ac+3ab)/(abc)
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3 years ago
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i think my my mom figured out i was bi and she is gonna be mad what do i do i think she is gonna whip me HELP ME PLS
Eva8 [605]
If you can you should go to a friends house for a while until you feel like it’s safe to go back
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3 years ago
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HELP I NEED HELP ASAP
tatiyna

Answer:

D) 8x²-172x+120

Step-by-step explanation:

Length=2(-2x+20)+6

Width=-2x+20

(-4x+40+6)(-2x+20)

(-4x+46)(-2x+20)

8x²-80x-92x+920

8x²-172x+920

5 0
3 years ago
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