I) if the triangles are similar then the corresponding angles are congruent. this means that the angles are of the same size.
ii) If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
thus, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, thus to get m∠C;
180- (52+65)
= 63 , therefore; m∠C= 63
iii) if two figures are similar they have the same shape and not necessarily the same size while if two figures are congruent then they have the same shape and size
y = 9ln(x)
<span>y' = 9x^-1 =9/x</span>
y'' = -9x^-2 =-9/x^2
curvature k = |y''| / (1 + (y')^2)^(3/2)
<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2)
= (9/x^2) / (1 + 81/x^2)^(3/2)
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)]
= 9x(x^2 + 81)^(-3/2).
To maximize the curvature, </span>
we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2)
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2]
...= 9(81 - 2x^2)/(x^2 + 81)^(5/2)
Setting k' = 0 yields x = ±9/√2.
Since k' < 0 for x < -9/√2 and k' > 0 for x >
-9/√2 (and less than 9/√2),
we have a minimum at x = -9/√2.
Since k' > 0 for x < 9/√2 (and greater than 9/√2) and
k' < 0 for x > 9/√2,
we have a maximum at x = 9/√2. </span>
x=9/√2=6.36
<span>y=9 ln(x)=9ln(6.36)=16.66</span>
the
answer is
(x,y)=(6.36,16.66)
Answer:
Step-by-step explanation:
Question 1: C
1 multiplied by 5 = 5
1 plus 5 = 6
So you get: (x+5)(x+1) which means x = -5 or -1
Question 2: B
2 multiplied by -4 = - 8
2 plus -4 = -2
So you get: (x-4)(x+2) which means x = 4 or -2
The image of p is (-1, 1)
Because the rule for 270 counterclockwise is (y,-x)
Step-by-step explanation:
6.5r - 7.4= 12.1
6.5r = 19.5
r = 3
