commutative for addition
<span>22+(m+8)=(m+8)+22</span> then associative
<span>(m+8)+22=m+(8+22)</span>
<span>=m+30</span>
SA= 72cm
SA = 2(LW+LH+WH)
L-length
W-width
H-height
This is the application of trigonometry. The distance of the ladder from from the wall will be given by:
cos θ=(adjacent)/(hypotenuse)
θ=72°
adjacent=base (distance the ladder to base of the wall)= xft
hypotenuse=length of the ladder.
Therefore plugging our values in the formula we get:
cos 72=x/15
x=15 cos 72
x=4.635 ft
Hence we conclude that the foot of the ladder is 4.635 ft away from the base of the wall.
Hi there!
A.) Begin by verifying that both endpoints have the same y-value:
g(-1) = 2(-1)² - 4(-1) + 3
Simplify:
g(-1) = 2 + 4 + 3 = 9
g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3
Since the endpoints are not the same, Rolle's theorem does NOT apply.
B.)
Begin by ensuring that the function is continuous.
The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:
Begin by finding the average rate of change over the interval:
Now, Find the derivative of the function:
g(x) = 2x² - 4x + 3
Apply power rule:
g'(x) = 4x - 4
Find the x value in which the derivative equals the AROC:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2