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MaRussiya [10]
2 years ago
9

John goes from a sauna at 115 Fahrenheit to an outside temperature of -30 Fahrenheit. What is the change in temperature?

Mathematics
1 answer:
IRINA_888 [86]2 years ago
7 0

Answer: 115 - (-30) = 115 + 30 = 145 degrees change

Step-by-step explanation:

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A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an
Nataly [62]

Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

\tan\theta=\frac{perpendicular}{base}

Here \theta=45^{\circ} , perpendicular = 30 m  and base we can find.

thus,

\tan 45^{\circ}=\frac{30}{EA}

We know \tan 45^{\circ}=1

thus, EA =  30 m

Consider the Δ AEB,

Using trigonometric ratio,

\cos\theta=\frac{base}{hypotenuse}

Here \theta=60^{\circ} , hypotenuse = 80 m  and base we can find.

thus, \cos 60^{\circ}=\frac{base}{80}

We know, \cos 60^{\circ}=\frac{1}{2}

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

4 0
3 years ago
The age of the Hawaiian islands gets older as you move from east to west. If the half-life of K-40 is 1.3 billion years, approxi
Mumz [18]

Answer:

t \approx 750550.12\,yr

Step-by-step explanation:

The time constant of the isotope is:

\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}

\tau \approx 1.876 \times 10^{9}\,yr

The decay of the isotope is described by the following model:

\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }

Now, the time is cleared in the equation:

t = -\tau \cdot \ln \frac{m}{m_{o}}

t = - (1.876\times 10^{9}\,yr)\cdot \ln 0.9996

t \approx 750550.12\,yr

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3 years ago
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