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allochka39001 [22]
2 years ago
9

What is the area of this figure? Please help.

Mathematics
1 answer:
Ad libitum [116K]2 years ago
8 0

The area of the composite figure can be found by summing the whole area that made up the figure. Therefore, the area of the figure is 213.5m²

<h3>Area of a composite figure</h3>

The area of the composite figure is the sum of the area of the whole figure.

Therefore, the composite figure can be divided into 2 triangles and two rectangles.

Hence,

area of triangle1 = 1 / 2 × 10 × 13 = 65 m²

area of the triangle2 = 1 / 2 × 15 × 7 = 52.5 m²

area of the rectangle1 = 8 × 3 = 24 m²

area of rectangle2 = 7 × 6 = 42 m²

area of rectangle3 = 5 × 6 = 30 m²

Therefore,

area of the composite figure = 65 + 52.5 + 24 + 42 + 30 = 213.5 meters squared

learn more on area here: brainly.com/question/27744042

#SPJ1

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A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo
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Answer:

a) y(t)=50000-49990e^{\frac{-2t}{25}}

b) 31690.7 g/L

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is \frac{dy}{dt}=R_{i}-R_{o}, where R_{i} is the rate of salt entering and R_{o} is the rate of salt going outside.

Then we have, R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}, and

R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}

So we obtain.  \frac{dy}{dt}=4000-\frac{2y}{25}, then

\frac{dy}{dt}+\frac{2y}{25}=4000, and using the integrating factor e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}, therefore  (\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}, we get   \frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}, after integrating both sides y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C, therefore y(t)= 50000 +Ce^{\frac{-2t}{25}}, to find C we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions y(0)=10, so 10= 50000+Ce^{\frac{-0*2}{25}}

10=50000+C\\C=10-50000=-49990

Finally we can write an expression for the amount of salt in the tank at any time t, it is y(t)=50000-49990e^{\frac{-2t}{25}}

b) The tank will overflow due Rin>Rout, at a rate of 80 L/min-40L/min=40L/min, due we have 500 L to overflow \frac{500L}{40L/min} =\frac{25}{2} min=t, so we can evualuate the expression of a) y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7, is the salt concentration when the tank overflows

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