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2 years ago

Which equation is equivalent to the equation x^2+y^2= 25?

Mathematics

1 answer:

satela [25.4K]2 years ago

3 0

9514 1404 393

Answer:

D. y = ±√(25 -x²)

Step-by-step explanation:

Subtract x² and take the square root to solve for y.

x² +y² = 25 . . . . . . . given

y² = 25 -x² . . . . . . . . subtract x²

y = ±√(25 -x²) . . . . . take the square root

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Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

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Camera 2nd has to cover the maximum angle, i.e. $78.70^\circ$ .

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As per Law of cosine:

$cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}$

Putting the values of a,b and c to find out angles $\angle A, \angle B, \angle C$ .

$cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ$

$cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ$

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