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
Answer:
3 pounds
Step-by-step explanation:
12/4=3 (because we need to see how much bryant ate first)
12-3=9 (original - what bryant ate)
9/3=3 (what was left after bryant finish and what 1/3 of 9 is)
Picture cards are Jacks, queens and Kings. There are 4 of each for a total of 12 picture cards.
52-12 = 40 non picture cards.
Probability of being dealt a non picture card would be 40/52
The probability of not being dealt a non picture card would be 1 - 40/52 = 12/52 = 3/13
Answer: 3/13
The area of the rectangular part = 14 x 20 = 280 sq. cm
The area of the half circle = 1/2 (3.14 x 7^2) = 76.9 sq. cm.
Total area = 280 + 76.93 = 356.9 cm^2
Answer:
2590
Step-by-step explanation:
30+2000+400+60+100
