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denis23 [38]
4 years ago
12

A rectangular prism has a volume of 864 cubic units. How many cubic unit will fill the volume of the solid if they were packed w

ithout any gaps or overlaps
Mathematics
1 answer:
Fofino [41]4 years ago
4 0

Answer: 864.

Step-by-step explanation:

The volume of a rectangular prism has a volume equal to:

V = W*L*H

W = width

L = length

H = height

We know that the volume is equal to 864 cubic units.

This means that if we want to fill the prism such that there is no gap or overlap, we should use exactly 864 unit cubes.

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(sinA-cosA+1)/(sinA+cosA-1)=2(1+cosecA)​
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Answer:

The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

Step-by-step explanation:

Given Trigonometrical function as :

\frac{sin A - cos A + 1}{sin A + cos A - 1} = 2 (1 + cosec A)

Or, \frac{sin A + ( 1 - cos A)}{sin A - (1 - cos A)} = 2 (1 + cosec A)

,<u> Now, rationalizing </u>

\frac{(sin A + ( 1 - cos A)) \times (sin A + (1 - cosA))}{(sin A - (1 - cos A))\times (sin A + (1 - cos A))} = 2 (1 + cosec A)

Or, \frac{(sin A + (1 - cos A))^{2}}{sin^{2} - (1-cos A)^{2}} = 2 ( 1 + \dfrac{1}{\textrm sinA}

Or, \frac{sin^{2}A + (1 - cosA)^{2} + 2 \times sin A \times (1 - cos A)}{sin^{2}A - (1 + cos^{2}A - 2 cos A)} = 2 ( \dfrac{1 + sin A}{sin A}

Or, \frac{sin^{2}A + 1 + cos^{2}A - 2 cos A + 2 sin A - 2 sin A cos A}{sin^{2}A - 1 - cos^{2}A +2 cos A} = 2 ( \dfrac{1 + sin A}{sin A}

Or, \frac{sin^{2}A + 1 + cos^{2}A - 2 cos A + 2 sin A - 2 sin A cos A}{sin^{2}A - (sin^{2}A + cos^{2}A) - cos^{2}A +2 cos A} = 2 ( \dfrac{1 + sin A}{sin A}

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Or, \frac{1-  cos A +  sin A -  sin A cos A}{- cos^{2}A + cos A} = 2 ( \dfrac{1 + sin A}{sin A}

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Or, \frac{(1 + sinA)}{(cos A)} = 2 ( \dfrac{1 + sin A}{sin A}

Or, sin A + sin² A = 2 cos A (1 + sin A)

Or,  sin A + sin² A = 2 cos A + 2 cos A × sin A

Or,   sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

So,The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0     Answer

6 0
3 years ago
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