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Nitella [24]
3 years ago
8

a city doubles its size every 90 years if the population is currently 90,000, what will the population be in 270 years DUE IN FI

VE MINUTES
Mathematics
2 answers:
kati45 [8]3 years ago
8 0

Answer:

the world would be filled with people

we would all be dead

Step-by-step explanation:

FromTheMoon [43]3 years ago
8 0

Answer:

360,000

Step-by-step explanation:

If the population doubles every 90 years, then in 270 years, the population should become 360,000.

Good luck on your test!

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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
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Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

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