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svetlana [45]
3 years ago
12

I don’t really get this question so if anyone knows it please help

Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

Answer:

116.82\:\text{square inches}

Step-by-step explanation:

The window consists of a large square and 4 smaller triangles on the outside. The side length of this square is marked as 10, and therefore the area of this square is 10^2=100\:\mathrm{in^2}.

The area of a triangle is given by \frac{1}{2}\cdot b\cdot h. Since the problem states that the overlapping squares are congruent, both legs of the triangle will be 2.9 and intersect at a 90^{\circ} angle.

Thus, the sum of all four triangles is \frac{1}{2}\cdot 2.9\cdot 2.9\cdot 4=16.82\:\mathrm{in^2}.

Therefore, the area of the window is:

100+16.82=\boxed{116.82\:\mathrm{in^2}}

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11.25 - 10.5 = 0.75

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Read 2 more answers
D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
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The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

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which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
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and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
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