Choice 1. He did not square 40, he just multiplied by 2.
Step-by-step explanation:
Step 1:
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The hypotenuse measures c cm while the other sides are 40 cm and 9 cm each.
Step 2:
According to the Pythagorean theorem,
![9^{2} +40^{2} = c^{2}.](https://tex.z-dn.net/?f=9%5E%7B2%7D%20%2B40%5E%7B2%7D%20%3D%20c%5E%7B2%7D.)
![81 + 1600 = c^{2} .](https://tex.z-dn.net/?f=81%20%2B%201600%20%3D%20c%5E%7B2%7D%20.)
![1681 = c^{2} .](https://tex.z-dn.net/?f=1681%20%3D%20c%5E%7B2%7D%20.)
![\sqrt{1681} = c.](https://tex.z-dn.net/?f=%5Csqrt%7B1681%7D%20%3D%20c.)
This is the correct solution to the given problem. Hans did not square 40, he just multiplied by 2. Which is the first option.
Transmission must be in third gear as both are running at the same speed ! so third gear !!!
Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
![A=\frac{\sqrt{3} }{4} a^{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%20a%5E%7B2%7D)
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
![A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}](https://tex.z-dn.net/?f=A_%7B1%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%281.2a%29%5E%7B2%7D)
![A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}](https://tex.z-dn.net/?f=A_%7B1%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D1.44a%5E%7B2%7D)
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
![A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}](https://tex.z-dn.net/?f=A_%7B2%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%20%280.8a%29%5E%7B2%7D)
![A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}](https://tex.z-dn.net/?f=A_%7B2%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%200.64a%5E%7B2%7D)
Now, comparing areas:
![\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )](https://tex.z-dn.net/?f=%5Cfrac%7BA_%7B1%7D%7D%7BA_%7B2%7D%7D%3D%20%28%5Cfrac%7B%5Csqrt%7B3%7D.1.44a%5E%7B2%7D%20%7D%7B4%7D%29%28%5Cfrac%7B4%7D%7B%5Csqrt%7B3%7D.0.64a%5E%7B2%7D%20%7D%20%29)
2.25
<u>The area of ΔABC is </u><u>2.25x</u><u> greater than the area of ΔDEF.</u>
In 8 weeks the reef grows 13 m, or 104 m.
Converting 104 m into mm:
104 m 1000 mm
--------- * ------------- = 104,000 mm
1 1 m