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2 years ago

Somebody please help math is not my thing lol

Mathematics

1 answer:

AlexFokin [52]2 years ago

3 0

What do you need help what time is 10 just put 10/1

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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

Is 83 cm greater than or less than 1 m?

o-na [289]

IT'S OBVIOUSLY LESS THAN 1 M.
1 m = 100 cm
It's LESS.

6 0

3 years ago

Point A is located at (-5, 2) on a coordinate grid. Point A is translated 4 units to the right and 2 units down to create point

HACTEHA [7]

The correct solution is A thanks

3 0

3 years ago

If a sample mean is 32, which of the following is most likely the range of

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

It is D, I did this quiz once

8 0

3 years ago

If w = 2, x = 3, y = 5, and z = 6 then evaluate the expression: z/2

galina1969 [7]

Answer:

Step-by-step explanation:

To evaluate the expression, we have to substitute the variable in the expression, z, for its stated value. Given that z = 6, substitute 6 for the z in the expression and solve:

$\frac{z}{2} \\= \frac{6}{2} \\= 3$

Thus, the answer is 3.

7 0

3 years ago