The average rate of change of on the interval [a,b] is:
f(b)−f(a)/ b-a
or
y1-y2/x1-x2 which is how I learned it, average ratw of change is just slope
so you would plug your numbers into x
1st the b: 6((1))^2+31((1))-12
=6+31-12 1^2=1, so it cancels
f(b) =25
2nd the a: 6((-2))^2+31((-2))-12
=6(4)+31(-2)-12
=24+-62-12
f(a) =-50
3rd plug them in: (25- -50)÷(1-(-2)
=75÷3
=25
so your average rate of change(or slope) is 25 :)
Answer:
4pi
Step-by-step explanation:
Circle circumference = 2*pi*r
2*pi*2
4*pi
Answer:
3w < 18
Step-by-step explanation:
To do 3 times if you put 3 against a variable that means to multiply. Since a number is unknown it turns into variable which is w in this case. Then less than 18 to do the less than symbol, think of them like crocodile they always eat the bigger number and since 3w is less than 18 the croc < eats 18. Thats just an easy way of remembering. Hope this helps :)
Answer:
Area = 32/3
Step-by-step explanation:
x = u
²
y = uv
z = 12v
²
0 ≤ u ≤ 2
0 ≤ v ≤ 1
Since ru = <2u, v, 0> and rv = <0, u, 24v>, we have
Where ru is the differentiation of x, y, z with respect to u and rv is the differentiation of x, y, z wit respect to v.
we find the cross product of ru and rv
ru × rv = 24v²i - 48uv²j + 2u²k
absolute value of ru × rv = 2u² + 24v²
We can now find the area
∫₀² du ∫₀¹ dv (2u² + 24v²) = ∫₀² du [2u²v + 8v³]₀¹ = 32/3
Detailed description can be found in the attachment
