<span>Inflection points are where the function changes concavity. Since concave up corresponds to a positive second derivative and concave down corresponds to a negative second derivative, then when the function changes from concave up to concave down (or vise versa) the second derivative must equal zero at that point. So the second derivative must equal zero to be an inflection point. But don't get excited yet. You have to make sure that the concavity actually changes at that point.</span>
Answer:
The equation for the line of reflection will be x = y.
Step-by-step explanation:
On a coordinate plane, triangle Δ ABC has points (6, 3.7), (5.4, 2), (1, 3). Triangle Δ A'B'C' has points (3.7, 6), (2, 5.4), (3, 1).
And we have to find the equation of the line of reflection of the points.
Now, it is clear from the coordinates of vertices of Δ ABC and Δ A'B'C' that after reflection the x and y-values of the respective coordinates interchange and there is no change in signs.
Therefore, the equation for the line of reflection will be x = y. (Answer)
.07×1.22 = ?
first take away the decimals in the question, 7×122 =854.
now add the decimals back to the answer, we had 4 decimal places in the questions so add 4 decimal places to 854 = 0.0854
answer= 0.0854
Answer: 16a^12 b^16
Step-by-step explanation:
Everything in the parenthesis to the 4th power.
2a^4= 16a
3*4=12
b^4*4=b^16
Answer:
Step-by-step explanation:
Let's use the definition of the Laplace transform and the identity given:![\mathcal{L}[t \cos 5t]=(-1)F'(s)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bt%20%5Ccos%205t%5D%3D%28-1%29F%27%28s%29)
with ![F(s)=\mathcal{L}[\cos 5t]](https://tex.z-dn.net/?f=F%28s%29%3D%5Cmathcal%7BL%7D%5B%5Ccos%205t%5D)
.
Now, 
. Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that 
.
Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that
.
Solving for F(s) on the last equation, 
, then the Laplace transform we were searching is 
