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2 years ago

Help me solve these equations

Mathematics

1 answer:

boyakko [2]2 years ago

6 0

$\left\{\begin{array}{ccc}3x-7y=20&|\cdot10\\11x+10y=5&|\cdot7\end{array}\right\\\underline{+\left\{\begin{array}{ccc}30x-70y=200\\77x+70y=35\end{array}\right}\ \ \ \ |\text{add both sides of the equations}\\\\.\ \ \ \ \ 107x=235\ \ \ \ |:107\\.\ \ \ \ \ \ \ \ \ \ x=\dfrac{235}{107}\\\\\text{substitute the value of x to the second equation}\\\\11\cdot\dfrac{235}{107}+10y=5\\\\\dfrac{2585}{107}+10y=\dfrac{535}{107}\ \ \ \ |-\dfrac{2585}{107}\\\\10y=-\dfrac{2050}{107}\ \ \ \ |:10\\\\y=-\dfrac{205}{107}$

$Answer:\ x=\dfrac{235}{107},\ y=-\dfrac{205}{107}$

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Lateral: 560

Surface Area: $560 + 96\sqrt{3}$

Step-by-step explanation:

Well, we know that the lateral area is just the surface area subtracted by the hexagon base of the figure. Thus, if we (1) find the area of one of the triangular faces and multiply by 6, we get the lateral area. And then, if we (2) add the area of the hexagonal base, we get the surface area.

Let's do (1) first to get the lateral area

They mention that the base of one of the triangular faces is 8 and its height (which is the slant height) is 20. So the area is simply 20 * 8/2 = 80

Then, we multiply by 6 because there are 6 of these triangles and get 560

So the lateral area is 560

Let's do (2) next to find the surface area

If we add the area of the hexagonal base to 560, we obtain the surface area

The hexagon is a regular hexagon with a length of 8. Now, the area of a hexagon $3\sqrt{3} * s^2 /2$ where $s$ is the side. We can obtain this formula if we separate the hexagon into 6 equilateral triangles.

Plugging in 8 for $s$ we get $96\sqrt{3}$

So the surface area is $560 + 96\sqrt{3}$

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