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3 years ago

Find the value of X. Show your work.

Mathematics

2 answers:

den301095 [7]3 years ago

6 0

Answer:

x = 3

Step-by-step explanation:

The triangle in the left is dilated 3 times bigger than the triangle in the right

that means that the left triangle is 3 times larger. In order to solve for x, you must compare one side from the left triangle to the other side of the right triangle.

so…

since the hypotenuse of the left triangle is 18, the hypotenuse of the right triangle is 3. 18 to 3 is 6 because 18 divided by 6 is 3.
And from 15 to 2 1/2 is 6 as well. (Use your calculator if you need to). so with all that information, x = 3 because…

4x > 2

and since the right triangle is 3 times larger…

4(3) > 2

12 > 2

and that means that 12 to 2 is 6

Therefore, the value of x is 3

Wittaler [7]3 years ago

4 0

Answer:

x = 3

Step-by-step explanation:

The traingels are similar so we can conpare sides.

3 is to 18 as 2 is to 4x or

3/18 = 2/4x

1/6 = 1/2x

6 = 2x

3 = x

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dolphi86 [110]

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Fiesta28 [93]

Newton's Law of Cooling:

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}$

$T(t) =$ Temperature given at a time

$t =$ Time

$T_{s} =$ Surrounding temperature

$T_{o}=$ Initial temperature

$e =$ Constant (Euler's number) ≈ 2.72

$k =$ Constant

Using this information, find the value of $k$ , to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.

First, plug in the given values in the equation and solve for $k$ :

$T(t) =$ 197°, $t =$ 1.5 minutes, $T_{s} =$ 70° and $T_{o}=$ 210°

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k$

$k$ ≈ $0.065$

Let the temperature of the water cup after $t = 4$ minutes be $T(t) = x$

Now, let's plug the new time and $k$ constant in the equation and solve for $x$ :

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\$

$x=70+(140})e^{-\frac{13}{50}}\\\\$

$x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\$

$x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\$

$x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\$

$x = 70 +\frac{140}{1.3} \\x=70+107.947\\$

$x=177.95$ ≈ $178$

Temperature of water after 4 minutes is 178°

sorry if there's any misspelling or wrong step but I hope my answer is correct ':3

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