The work done by
is
![\displaystyle\int_C\vec F\cdot\mathrm d\vec r](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r)
where
is the given curve and
is the given parameterization of
. We have
![\mathrm d\vec r=\dfrac{\mathrm d\vec r}{\mathrm dt}\mathrm dt=k(1-2t)\,\vec\imath+\vec\jmath](https://tex.z-dn.net/?f=%5Cmathrm%20d%5Cvec%20r%3D%5Cdfrac%7B%5Cmathrm%20d%5Cvec%20r%7D%7B%5Cmathrm%20dt%7D%5Cmathrm%20dt%3Dk%281-2t%29%5C%2C%5Cvec%5Cimath%2B%5Cvec%5Cjmath)
Then the work done by
is
![\displaystyle\int_0^1((t-kt(1-t))\,\vec\imath+kt^2(1-t)\,\vec\jmath)\cdot(k(1-2t)\,\vec\imath+\vec\jmath)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E1%28%28t-kt%281-t%29%29%5C%2C%5Cvec%5Cimath%2Bkt%5E2%281-t%29%5C%2C%5Cvec%5Cjmath%29%5Ccdot%28k%281-2t%29%5C%2C%5Cvec%5Cimath%2B%5Cvec%5Cjmath%29%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^1((k-k^2)t-(k-3k^2)t^2-(k+2k^2)t^3)\,\mathrm dt=-\frac k{12}](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E1%28%28k-k%5E2%29t-%28k-3k%5E2%29t%5E2-%28k%2B2k%5E2%29t%5E3%29%5C%2C%5Cmathrm%20dt%3D-%5Cfrac%20k%7B12%7D)
In order for the work to be 1, we need to have
.
Answer: I think it's 2
Step-by-step explanation: i am not dat good at math
A student model relationship with equation y=4x
Answer:
Option (4)
Step-by-step explanation:
Given inequality is,
![\frac{x}{4}\leq \frac{9}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D%5Cleq%20%5Cfrac%7B9%7D%7Bx%7D)
![\frac{x}{4}-\frac{9}{x}\leq 0](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D-%5Cfrac%7B9%7D%7Bx%7D%5Cleq%200)
![\frac{x^{2}-36}{4x}\leq 0](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D-36%7D%7B4x%7D%5Cleq%200)
x ≥ 0 [For x = 0, fraction is not defined]
(x - 6)(x + 6) ≤ 0
x - 6 ≤ 0
x ≤ 6
Or
x + 6 ≤ 0
x ≤ -6
Therefore, solution set is (-∞, -6] ∪ (0, 6]
By plotting the solution area on a number line,
Option (4) will be the answer.
Answer:
a)5 b)15
Step-by-step explanation:
5 times 11=55
15 times 3 is 45
add together is 100
5+15 is 20 questions