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3 years ago

3. Determine whether the triangles are similar. If so, write a similarity statement and name the

Mathematics

1 answer:

Elanso [62]3 years ago

5 0

They are both similar.
tri cba ~ tri rqp
AA theorem
tri bac ~ tri edf
SSS theorem

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Given that P = xy.<br> Find P when:<br> x = -5 and y = -9

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Answer: 6/8 + 12/8 + 12/8 + 10/8 = 5

Step-by-step explanation: The answer is five.

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For a cost of $6, you can have a carnival worker draw a random number from 1 to 20. If the number is even, you win $11. If the n

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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

Solve the following equation

Gnoma [55]

40x+8x^2=0 can be solved for x (there are two solutions):

Divide all 3 terms by the greatest common multiple (which is 8x):

40x+8x^2=0
------------- -----
8x 8x

5 + x = 0 produces the root x = - 5.

Setting 8x = 0 and solving for x produces the root x = 0.

Be certain to check these results. substitute x = -5 into 40x+8x^2=0. Is the resulting equation true or false? Next, subs. x=-5 into 40x+8x^2=0. Is the resulting equation true or false?

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