Answer:
33/16
Step-by-step explanation:
x = y⁴/8 + 1/(4y²), 1 ≤ y ≤ 2
dx/dy = y³/2 − 1/(2y³)
Arc length is:
s = ∫ ds
s = ∫ √(1 + (dx/dy)²) dy
s = ∫₁² √(1 + (y³/2 − 1/(2y³))²) dy
s = ∫₁² √(1 + y⁶/4 − ½ + 1/(4y⁶)) dy
s = ∫₁² √(½ + y⁶/4 + 1/(4y⁶)) dy
s = ∫₁² ½ √(2 + y⁶ + 1/y⁶) dy
s = ∫₁² ½ √(y³ + 1/y³)² dy
s = ∫₁² ½ (y³ + 1/y³) dy
s = ½ (y⁴/4 − 1/(2y²)) |₁²
s = ½ (16/4 − 1/8) − ½ (1/4 − 1/2)
s = 33/16
Answer (x is the money Harper found):
- Equation: (35 + x) = (41 - 2x)
- Solution: x = 2
I hope this helps!
1. 92 x 43 = 3,956
2. 524 x 51 = 26,724
3. 294 x 32 = 9,408
4. 828 x 24 = 19,872
Answer:
20 feet
Step-by-step explanation:
In this case, you'd use pythagoras's theorem (a^2 + b^2 = c^2)
The hypotenuse is always = c, so you'd set up the equation like this:
16^2 + 12^2 = c^2, where you're solving for c (to find out the length of the kite string)
This equation simplifies to 256 + 144 = c^2
which further simplifies to 400 = c^2
to solve for c, we square root both sides so the c is isolated:

20 = c
so the length of the kite string is 20 feet
{(3, 9), (4, 8), (–7, 4), (0, 4), (2, 4), (3, 5), (–3, 8)}
LekaFEV [45]
<span>d. No, there is an x-value paired with more than one y-value.</span>