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Len [333]
3 years ago
11

The frame of a bridge is constructed of triangles, as shown below.

Mathematics
2 answers:
aleksandrvk [35]3 years ago
6 0

Answer:

1, 4

Step-by-step explanation:

Artemon [7]3 years ago
3 0

Answer:

UV = 14 ft and m∠TUV = 45°

ST = 20 ft, UV = 14 ft, and m∠UST = 98°

Step-by-step explanation:

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Solve the Differential equation (x^2 + y^2) dx + (x^2 - xy) dy = 0
natita [175]

Answer:

\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C

Step-by-step explanation:

Given differential equation,

(x^2 + y^2) dx + (x^2 - xy) dy = 0

\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)

Let y = vx

Differentiating with respect to x,

\frac{dy}{dx}=v+x\frac{dv}{dx}

From equation (1),

v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}

v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}

v+x\frac{dv}{dx}=-\frac{1 + v^2}{1 - v}

v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}

x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v

x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}

x\frac{dv}{dx}=\frac{v+1}{v-1}

\frac{v-1}{v+1}dv=\frac{1}{x}dx

Integrating both sides,

\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx

\int{\frac{v-1+1-1}{v+1}}dv=lnx + C

\int{1-\frac{2}{v+1}}dv=lnx + C

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Now, y = vx ⇒ v = y/x

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