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3 years ago

3x = 17 Answer Needed Very soon

Mathematics

1 answer:

mafiozo [28]3 years ago

3 0

Answer:

x=17/3

Step-by-step explanation:

divide both sides by 3 to isolate x

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A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the pro

natka813 [3]

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

Probability of passing at least one = 0.59 + 0.60 - 0.49 = 0.7 ##

3 0

3 years ago

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

<img src="https://tex.z-dn.net/?f=%5Csf%2020%3D9x-7" id="TexFormula1" title="\sf 20=9x-7" alt="\sf 20=9x-7" align="absmiddle" cl

Temka [501]

Answer:

x=3.

Add-on:

hope this helped at all.

8 0

3 years ago

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Kyleigh invested $2800 in an account paying an interest rate of 5 1/2% compounded annually Ariana invested $2800 in an account p

shutvik [7]

Answer:

Step-by-step explanation:

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3 years ago

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Irina-Kira [14]

I wish I knew this one also

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2 years ago