P' (8,5)
Q' (3,14)
R' (10, 11)
Why: Anything that is translated left or right you will be changing the x axis, if the translation is right, you add, if its left, you subtract. If the translation is up or down, its going to change the y axis. Down means you subtract from the y axis, up means you add to the y axis.
We are given the parametric equations:
x = 6 cos θ
y = 6 sin θ
We know that the derivative of cos a = - sin a and the
derivative of sin a = cos a, therefore taking the 1st and 2nd
derivates of x and y:
d x = 6 (-sin θ) = - 6 sin θ
d^2 x = -6 (cos θ) = - 6 cos θ
d y = 6 (cos θ) = 6 cos θ
d^2 y = 6 (-sin θ) = - 6 sin θ
Therefore the values we are asked to find are:
dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ
d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ =
tan θ
We can find the value of the slope at θ = π/4 by using
the dy/dx:
dy/dx = slope = - cot θ
dy/dx = - cot (π/4) = - 1 / tan (π/4)
dy/dx = -1 = slope
We can find the concavity at θ = π/4 by using the d^2 y/d^2
x:
d^2 y / d^2 x = tan θ
d^2 y / d^2 x = tan (π/4)
d^2 y / d^2 x = 1
Since the value of the 2nd derivative is
positive, hence the concavity is going up or the function is concaved upward.
Summary of Answers:
dy/dx = - cot θ
d^2 y/d^2 x = tan θ
slope = -1
concaved upward
Answer:
m∠R = 60° and AB ≅ MQ
m∠Q = 56° and CB ≅ RQ
Step-by-step explanation:
Given data :
Prove ΔABC ≅ ΔMQR using SAS
The missing information to prove ΔABC ≅ ΔMQR using SAS
Answer:
C 56,000
Step-by-step explanation:
Answer:
Austin is correct.
Step-by-step explanation:
19.5 has a tens, ones, and tenths place. 8.21 has a ones, tenths, and hundredths place.
