6/10 of an inch= 0.6
7 (times) 0.6 (equals) 4.2
Answer:
V = 63π / 200 m^3
Step-by-step explanation:
Given:
- The function y = f(x) is revolved around the x-axis over the interval [1,6] to form a spherical surface:
y = √(42*x - x^2)
- The surface is coated with paint with uniform layer thickness t = 1.5 mm
Find:
The volume of paint needed
Solution:
- Let f be a non-negative function with a continuous first derivative on the interval [1,6]. The Area of surface generated when y = f(x) is revolved around x-axis over the interval [1,6] is:
![S = 2*\pi \int\limits^a_b { [f(x)*\sqrt{1 + f'(x)^2} }] \, dx](https://tex.z-dn.net/?f=S%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5Ea_b%20%7B%20%5Bf%28x%29%2A%5Csqrt%7B1%20%2B%20f%27%28x%29%5E2%7D%20%7D%5D%20%5C%2C%20dx)
- The derivative of the function f'(x) is as follows:
- The square of derivative of f(x) is:
- Now use the surface area formula:
![S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2} *\sqrt{1 + \frac{(21-x)^2}{42x-x^2 } }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2+(21-x)^2} }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2+441-42x+x^2} }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{441} }] \, dx\\S = 2*\pi \int\limits^6_1 { 21} \, dx\\\\S = 42*\pi \int\limits^6_1 { dx} \,\\\\S = 42*\pi [ 6 - 1 ]\\\\S = 42*5*\pi \\\\S = 210\pi](https://tex.z-dn.net/?f=S%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%20%5B%5Csqrt%7B42x-x%5E2%7D%20%2A%5Csqrt%7B1%20%2B%20%5Cfrac%7B%2821-x%29%5E2%7D%7B42x-x%5E2%20%7D%20%7D%5D%20%5C%2C%20dx%5C%5C%5C%5CS%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%20%5B%5Csqrt%7B42x-x%5E2%2B%2821-x%29%5E2%7D%20%7D%5D%20%5C%2C%20dx%5C%5C%5C%5CS%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%20%5B%5Csqrt%7B42x-x%5E2%2B441-42x%2Bx%5E2%7D%20%7D%5D%20%5C%2C%20dx%5C%5C%5C%5CS%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%20%5B%5Csqrt%7B441%7D%20%7D%5D%20%5C%2C%20dx%5C%5CS%20%3D%202%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%2021%7D%20%5C%2C%20dx%5C%5C%5C%5CS%20%3D%2042%2A%5Cpi%20%5Cint%5Climits%5E6_1%20%7B%20dx%7D%20%5C%2C%5C%5C%5C%5CS%20%3D%2042%2A%5Cpi%20%5B%206%20-%201%20%5D%5C%5C%5C%5CS%20%3D%2042%2A5%2A%5Cpi%20%5C%5C%5C%5CS%20%3D%20210%5Cpi)
- The Volume of the pain coating is:
V = S*t
V = 210*π*3/2000
V = 63π / 200 m^3
I got.......6x^3 + 5x^2 - 3x - 2................not sure though
Answer:
a) so if you're looking for a then you substitute the a in the problem so the real question would be answered by simply doing this. 3 times (do this first) 6 times 3. so it would end up looking like this if you did it in your head. 6x3=18 then 18x3= 54 so the answer for ten after you did all the math would equal out to be 54.
d) so you're going to substitue the d again, for what it tells you d equals. in this case, d= a negative 2 so, 5 x do this first -2 x 4 = so if you did this in your head you would end up with -2 x 4 = -8 because anything times a negative is turned into a negative. so that is why the answer is -8 for the first part. then you multiply that answer by 5 because we all like the 5 dollar foot longs. so carry that into an answer of - 40. because we all know we want to be younger once we reach 40.
r) 5times -3 equals -15 times 2 would be... ding ding ding 30 because a negative times a negative is a positive. think of negatives this way. when you frown it's your smile upside down. ok so a frown is a negative, if you multiply a negative to a negative it's like turning your frown upside down. so you end up with a positive! ok?! so there. the secrets of life and math.
call me for the rest of the answers... this is too much to write down.
Step-by-step explanation:
8/11--------> 16
to find the total number of fish, divide 16 by 8 and multiply it by 11,
16÷8=2
2×11=22
total number of fish= 22
check,
22÷11×8=16
if you want to find the number of fish without the red stripes,
8/11--------> 16
11/11------->22
3/11--------->?
you can either subtract 16 by 22=6
or
22÷11×3=6
hope this helps......
