Can someone please Find the Y, the equation to find it is in the top middle. I need the Y found for all 5 X points

Find T, N, and kappa for the plane curve Bold r left parenthesis t right parenthesis equalsleft parenthesis 7 Bold cos t plus

pickupchik [31]

Answer:

Step-by-step explanation:

r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j

$\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j$

$=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)$

$\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t$

$\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j$

$\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1$

$\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}$

$K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}$

Using eq (1) and (2)

$K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }$

7 0

3 years ago

If a dice is rolled 18 times, how many times is the number 2 expected to come up? *

mart [117]

Answer:

the answer is B. 3 times

that's what I think

8 0

3 years ago

$84 increased by 120 percent

Elanso [62]

$\rm 84+120\% \\ \\ 84+ \frac{12\not0\cdot84}{10\not0}= \\ \\ 84+ \frac{1008}{10}= \\ \\ 84+100,8=\\ \\ \bold{184,8\$}$

5 0

3 years ago

Michael has finished 25% of an art project that has taken

Nostrana [21]

It will take him 16 hours. Hope it helps

7 0

3 years ago

Can someone help me with these Algebra 1 questions, they are pretty tough and i need help since i don't fully understand it yet.

Hatshy [7]

I will answer second attachment and after since I can't see the firs attachment

2nd attachment

if x is negative, then the first number gets infinitely small
look at the second number, the first 2 is -2 which is wrong since it should be +2
3rd option is not because if x=-2, then y=1
answer is D

3rd attachment
2nd: f(x)=60*1.15^x
3rd: no xint
6th: after 7.86 years value tripples
7th maybe: after 8 years value is 183.51, not exatly 184.00

4th attachment
nth score is
f(n)=57+4(n-1)
9th is
f(9)=57+4(9-1)
57+32=89
answer is C 89

5th
f(t)=23000(1.02)^t
t=time in years from 23000

4 0

3 years ago