For this case as MNOP is a square then the angles of each vertex are equal to 90 degrees.
Therefore, we have the following equations:
![4t + 20 = 90\\7f + 6 = 90](https://tex.z-dn.net/?f=%204t%20%2B%2020%20%3D%2090%5C%5C7f%20%2B%206%20%3D%2090%20%20)
From these equations, we can clear the values of the unknowns.
For equation 1 we have:
![4t + 20 = 90\\4t = 90 - 20\\4t = 70](https://tex.z-dn.net/?f=%204t%20%2B%2020%20%3D%2090%5C%5C4t%20%3D%2090%20-%2020%5C%5C4t%20%3D%2070%20%20)
![t = \frac{70}{4}\\t = 17.5](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cfrac%7B70%7D%7B4%7D%5C%5Ct%20%3D%2017.5%20%20%20)
For equation 2 we have:
![7f + 6 = 90\\7f = 90 - 6\\7f = 84](https://tex.z-dn.net/?f=%207f%20%2B%206%20%3D%2090%5C%5C7f%20%3D%2090%20-%206%5C%5C7f%20%3D%2084%20%20)
![f = \frac{84}{7}\\f = 12](https://tex.z-dn.net/?f=%20f%20%3D%20%5Cfrac%7B84%7D%7B7%7D%5C%5Cf%20%3D%2012%20%20%20)
Answer:
The values of t and f are given by:
![t = 17.5\\f = 12](https://tex.z-dn.net/?f=%20t%20%3D%2017.5%5C%5Cf%20%3D%2012%20)
Density = Mass / Volume = 2000/0.5
Density = 4000 Kg/m^3
Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
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ANSWER
True
EXPLANATION
The given trigonometric equation is:
![{ \tan}^{2} x + 1 = { \sec}^{2} x](https://tex.z-dn.net/?f=%20%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%7B%20%5Csec%7D%5E%7B2%7D%20x)
We take the LHS and simplify to arrive at the RHS.
![{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x}{{ \cos}^{2} x} + 1](https://tex.z-dn.net/?f=%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%20%5Cfrac%7B%7B%20%5Csin%7D%5E%7B2%7D%20x%7D%7B%7B%20%5Ccos%7D%5E%7B2%7D%20x%7D%20%20%2B%201)
Collect LCM on the right hand side to get;
![{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x + {\cos}^{2} x}{{ \cos}^{2} x}](https://tex.z-dn.net/?f=%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%20%5Cfrac%7B%7B%20%5Csin%7D%5E%7B2%7D%20x%20%2B%20%7B%5Ccos%7D%5E%7B2%7D%20x%7D%7B%7B%20%5Ccos%7D%5E%7B2%7D%20x%7D%20)
This implies that
![{ \tan}^{2} x + 1 = \frac{1}{{ \cos}^{2} x} .](https://tex.z-dn.net/?f=%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%20%5Cfrac%7B1%7D%7B%7B%20%5Ccos%7D%5E%7B2%7D%20x%7D%20.)
![{ \tan}^{2} x + 1 = {( \frac{1}{ \cos(x) }) }^{2}](https://tex.z-dn.net/?f=%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%20%7B%28%20%5Cfrac%7B1%7D%7B%20%5Ccos%28x%29%20%7D%29%20%7D%5E%7B2%7D%20)
![{ \tan}^{2} x + 1 = { \sec}^{2} x](https://tex.z-dn.net/?f=%7B%20%5Ctan%7D%5E%7B2%7D%20x%20%2B%201%20%3D%20%20%7B%20%5Csec%7D%5E%7B2%7D%20x)
This identity has been verified .Therefore the correct answer is true.