The circumference of a circle is (pi) x (diameter)
The circumference of the cupcake is (pi) x (5 cm)
Halfway around is (1/2) x (pi) x (5 cm) = (2.5 pi cm) = <em>about 7.85 cm</em>
The 'why' appears up above, in the first 2 lines of this solution.
3.33 seconds.
<u>Explanation:</u>
We can find the speed of the body using the formula,
Speed = Distance traveled in meters / time taken in seconds
= 450 m / 30 seconds
= 15 m/s
So per second the distance traveled by the body is 15 m.
So time needed to travel 50 m can be found as,
time = distance/speed
= 50 m / 15 m /s
= 3.33 s
The work done by
along the given path <em>C</em> from <em>A</em> to <em>B</em> is given by the line integral,

I assume the path itself is a line segment, which can be parameterized by

with 0 ≤ <em>t</em> ≤ 1. Then the work performed by <em>F</em> along <em>C</em> is
![\displaystyle \int_0^1 \left(6x(t)^3\,\vec\imath-4y(t)\,\vec\jmath\right)\cdot\frac{\mathrm d}{\mathrm dt}\left[x(t)\,\vec\imath + y(t)\,\vec\jmath\right]\,\mathrm dt \\\\ = \int_0^1 (288(3t-1)^3-8(2t+5)) \,\mathrm dt = \boxed{312}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%286x%28t%29%5E3%5C%2C%5Cvec%5Cimath-4y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%29%5Ccdot%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Bx%28t%29%5C%2C%5Cvec%5Cimath%20%2B%20y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%5D%5C%2C%5Cmathrm%20dt%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E1%20%28288%283t-1%29%5E3-8%282t%2B5%29%29%20%5C%2C%5Cmathrm%20dt%20%3D%20%5Cboxed%7B312%7D)
Answer:
The lenses with different focal length are four.
Explanation:
Given that,
Radius of curvature R₁= 4
Radius of curvature R₂ = 8
We know ,
Refractive index of glass = 1.6
When, R₁= 4, R₂ = 8
We need to calculate the focal length of the lens
Using formula of focal length

Put the value into the formula



When , R₁= -4, R₂ = 8
Put the value into the formula



When , R₁= 4, R₂ = -8
Put the value into the formula



When , R₁= -4, R₂ = -8
Put the value into the formula



Hence, The lenses with different focal length are four.