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Vladimir [108]
3 years ago
15

Please help me with this one I don’t understand. I need help with #20 thank you!

Mathematics
1 answer:
dimaraw [331]3 years ago
8 0

part A)

we know that for every 1000 ft the temperature drops by 1.3.

so after 1000ft up it went down by 1.3(1)

2000ft up it went down by 1.3(2) or 2.6

3000ft up it went down by 1.3(3) or 3.9

after 10000 up it went down by 1.3(10) or 13.

part B)

well, the current temperature on the ground where the plane is sitting is -2.8°F, after 10000ft it dropped by 13°, so the temperature will just be -2.8 - 13 = -15.8°F.

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Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m

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Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o

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cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4  \,\,m

Now fro the new position of the bottom of the ladder relative to the wall:

cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

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