Answer:
L ≈ 1023.0562
Step-by-step explanation:
We are given;
x = t² - 2t
dx/dt = 2t - 2
Also, y = t^(5)
dy/dt = 5t⁴
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt
L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt
L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt
Using online integral calculator, we have;
L ≈ 1023.0562
Answer:
1. 617.5 cm³
2. 335.6 in³
3. 151.6 m³
4. 3479.1 ft³
Step-by-step explanation:
1.
B1: 19.5 × 9 = 175.5
B2: 6 × 13 = 78
sqrt(B1 ×B2) = 117
h = 5
Volume = ⅓ × 5 × [175.5 + 78 + 117]
617.5
2.
B1: 3.14 × 4.5² = 63.585
B2: 3.14 × 3² = 28.26
sqrt(B1 ×B2) = 42.39
h = 7.5
Volume = ⅓ × 7.5 × [63.585 + 28.26 + 42.39]
335.5875
3.
B1: ½(8+12) × 6 = 60
B2: ½(3+4.5) × 2.25 = 8.4375
sqrt(B1 ×B2) = 22.5
h = 5
Volume = ⅓ × 5 × [60 + 8.4364 + 22.5]
151.5625
4.
B1: 3.14 × 12² = 452.16
B2: 3.14 × 7² = 153.86
sqrt(B1 ×B2) = 263.76
h² = 13² - (12-7)²
h² = 13² - 5²
h² = 144
h = 12
Volume = ⅓ × 12 × [452.16 + 153.86 + 263.76]
3479.12
Error: they divided both sides by three.
correct: they should’ve first subtracted both sides by two then divided both sides by three.
Answer:
x > 2
Step-by-step explanation:
2(x+5) = 2x + 10 -> 2x + 10 < 4+5x
Subtract 4 from each side.
2x +6 < 5x
Subtract 2x from each side
6 < 3x
2<x
So, x must be > 2
Answer:
Take deep breaths and focus, don't be afraid to ask for help.
Good luck!
