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2 years ago

10

the length of a rectangle is 3 meters more than twice its width what is the width of the rectangle if the area is 9 m^2. pls hel

p. solve by using applications of quadratics

1 answer:

shusha [124]2 years ago

5 0

Step-by-step explanation:

answer is shown above, that is a tricky question though.

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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.

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3 years ago

If your born August, 15, 2001 Then how old would you be now?

spin [16.1K]

Answer:

18 years old you would be

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3 years ago

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Can someone help me please

mart [117]

Your answer is D 6561 multiply each number 3 and your answer will be this

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3 years ago

(x+3)(2x-1) whats the product im sooo confused

Elodia [21]

Answer: 2x

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Step-by-step explanation:

2x

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2x

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3 years ago

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You have a mean score of 84 after taking five 100-point tests. What do you need to score on the sixth 100-point test to have a m

kap26 [50]

The mean of n numbers is the sum of the numbers divided by n.

You have a mean score of 84 after taking 5 tests. Let x be the sum of scores.
$\frac{x}{5}=84 \\
x=84 \times 5 \\
x=420$
You scored a total of 420 points on five tests.

You need to have a mean score of 85 after taking 6 tests. Let y be the score you need to obtain. Your total score on 6 tests is 420+y.
$\frac{420+y}{6}=85 \\
420+y=85 \times 6 \\
420+y=510 \\
y=510-420 \\
y=90$

You need to score 90 points on the sixth test.

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3 years ago

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