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True [87]
3 years ago
15

Math test questions Find the measurement of the unknown angle​

Mathematics
2 answers:
Evgen [1.6K]3 years ago
6 0
The correct answer is 65°
crimeas [40]3 years ago
4 0

Answer:

The unknown angle is 65°

Step-by-step explanation:

Let the unknown angle be y

40°+75°+y = 180°

y = 180°-115°

y = 65°

Therefore, the unknown angle is 65°

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
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Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = xyz

with subject to x+2y+3z=9

So, let z=\dfrac{9-x-2y}{3}

So, Volume becomes,

V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}

Partially derivative wrt x and y we get that

9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9

By solving these two equations, we get that

x=3,y=\dfrac{3}{2}

So, z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1

So, Volume of largest rectangular box would be

xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5

Hence, the volume of largest rectangular box is 4.5 units.

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