arccos(-sqrt(2)/2). range of <span>cos − 1 ( x )=<span>[ 0 , π ]
</span></span>= arccos(0.706 )
=45 degrees
hope this helps
Answer: The required solution is
Step-by-step explanation: We are given to solve the following differential equation :
Let us consider that
be an auxiliary solution of equation (i).
Then, we have
Substituting these values in equation (i), we get
![m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmt%7D%2B10me%5E%7Bmt%7D%2B25e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2%2B10y%2B25%29e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B10m%2B25%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmt%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B2%5Ctimes%20m%5Ctimes5%2B5%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%2B5%29%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20m%3D-5%2C-5.)
So, the general solution of the given equation is
Differentiating with respect to t, we get
According to the given conditions, we have
and
Thus, the required solution is
Step-by-step explanation:
a. Given => <em>m</em>∠5 = 40°
b. Given => <em>m</em>∠2 = 140°
c. Same Side Interior Angle Theorem => The same side interior angles must add up to 180°, which in this case, it does. m∠4 and m∠2 are alternate interior angles, and so there measurements are the same. 180 - 140 = 40
d. Both angles are part of the "same-side interior angles", which means that there measurements should add up to 180°. Note that m∠5 = 40°, and m∠2 = 140° (Given). Set the equation
m∠5 + m∠2 = 180
Plug in the number for each angle
40 + 140 = 180
180 = 180 (True).
e. It is proven that the above measurements are congruent with their corresponding parts. This means that a || b through <em>Converse of Same Side Interior angle Theorem</em>.
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Answer:
18cm
Step-by-step explanation:
presents=x
14cm=7x
divide by 7
2=x
find 9x
9*2=18
