Well, for 4 I believe you must divide 2/4 by 100 to make it a decimal, then divide the decimal by the 5. :) Hopefully that is correct!
Answer:
1st: 3*root6 + 5
2nd: 35*root2 + 115
3rd: 24*root2 - 20*root6 + 15*root3 - 18
4th: 17*root6 - 38
5th: 13*root10 - 42
Step-by-step explanation:
To simplify these expressions we need to use the distributive property:
(a + b) * (c + d) = ac + ad + bc + bd
So simplifying each expression, we have:
1st.
(2 root 2 + root 3 ) ( 2 root 3 - root 2)
= 4*root6 - 2*2 + 2*3 - root6
= 3*root6 - 4 + 9
= 3*root6 + 5
2nd.
(root 5 + 2 root 10) (3 root 5 + root 10)
= 3 * 5 + root50 + 6*root50 + 2*10
= 15 + 5*root2 + 30*root2 + 100
= 35*root2 + 115
3rd.
(4 root 6 - 3 root 3) (2 root 3 - 5)
= 8*root18 - 20*root6 - 6*3 + 15root3
= 24*root2 - 20*root6 + 15*root3 - 18
4rd.
(6 root 3 - 5 root 2 ) (2 root 2 - root 3)
= 12*root6 - 6*3 - 10*2 + 5*root6
= 17*root6 - 18 - 20
= 17*root6 - 38
5th.
(root 10 - 3 ) ( 4 - 3 root 10)
= 4*root10 - 3*10 - 12 + 9*root10
= 13*root10 - 30 - 12
= 13*root10 - 42
Answer:
No, the absolute value of a number is different from the opposite.
Step-by-step explanation:
For example, the absolute value of 4 is 4.
l4l = 4
But the opposite of 4 is -4.
Absolute value is ALWAYS positive, but the opposite of a positive number is a negative number.
Step-by-step explanation:
y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1
dy/dx = 12√x
Arc length is:
s = ∫ ds
s = ∫₀¹ √(1 + (dy/dx)²) dx
s = ∫₀¹ √(1 + (12√x)²) dx
s = ∫₀¹ √(1 + 144x) dx
If u = 1 + 144x, then du = 144 dx.
s = 1/144 ∫ √u du
s = 1/144 (⅔ u^(³/₂))
s = 1/216 u^(³/₂)
Substitute back:
s = 1/216 (1 + 144x)^(³/₂)
Evaluate between x=0 and x=1.
s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]
s = 1/216 (145)^(³/₂) − 1/216
s = (145√145 − 1) / 216
