Answer:
<u>x= 4 2/3 </u><em><u>OR</u></em><u> 14/3 </u><em><u>OR</u></em><u> 4.6... –– 4 2/3 and 4.6... are the simplest form.</u>
Step-by-step explanation:
Your original equation is -192 = -6 (6x - 4):
1. -192 = -6 (6x - 4)
Use distributive property and multiply: -6 x 6x = -36x and -6 x -4 = 24:
2. -192 = -36x + 24
We now move the +24 onto the other side of the equation, -192. Add 24 onto -192 and since we're moving the 24 on the left side of the equation, 24 will removed, so -24 on the right side of the equation:
3. -192 + 24 = -36x + 24 - 24
Divide both sides of the equations by -36 to get "x" by itself:
4. -168 / -36 = -36x / -36
Simplify the fraction of 24/36 by 12:
5. 4 24/36 = 4 2/3 or 14/3 or 4.6... = x
<u>4 2/3, 14/3, 4.6... = x</u>
Answer:
9
Step-by-step explanation:
Answer:
The length of the curve is
L ≈ 0.59501
Step-by-step explanation:
The length of a curve on an interval a ≤ t ≤ b is given as
L = Integral from a to b of √[(x')² + (y' )² + (z')²]
Where x' = dx/dt
y' = dy/dt
z' = dz/dt
Given the function r(t) = (1/2)cos(t²)i + (1/2)sin(t²)j + (2/5)t^(5/2)
We can write
x = (1/2)cos(t²)
y = (1/2)sin(t²)
z = (2/5)t^(5/2)
x' = -tsin(t²)
y' = tcos(t²)
z' = t^(3/2)
(x')² + (y')² + (z')² = [-tsin(t²)]² + [tcos(t²)]² + [t^(3/2)]²
= t²(-sin²(t²) + cos²(t²) + 1 )
................................................
But cos²(t²) + sin²(t²) = 1
=> cos²(t²) = 1 - sin²(t²)
................................................
So, we have
(x')² + (y')² + (z')² = t²[2cos²(t²)]
√[(x')² + (y')² + (z')²] = √[2t²cos²(t²)]
= (√2)tcos(t²)
Now,
L = integral of (√2)tcos(t²) from 0 to 1
= (1/√2)sin(t²) from 0 to 1
= (1/√2)[sin(1) - sin(0)]
= (1/√2)sin(1)
≈ 0.59501
Answer: 
<u>Step-by-step explanation:</u>
