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Oduvanchick [21]
3 years ago
15

SOMEONE MAKE A ENDING PARAGRAPH about someone rescuing me QUICK 40 POINTS!!!!

Mathematics
1 answer:
scZoUnD [109]3 years ago
4 0

Answer:

Although, my life can't end here, life has so much more to offer me. I collected the last of my strength to swim up to to surface where I can be released from the horrors of the deep waters. I swallowed gulps of the chlorine water and my eyes ached from being open for to long. I wrestled the clenching fists of the water that urged me to stay with them. I swam, and swam, swam, until I reached my hands out for help, and that's when I knew I made it. I could feel hands from above grasping me and helping me climb out of the bitter cold pool. I ran into my mother's arms, as a gush of relief spread through my body. The relief of staying in my mothers arm, that helped me forget the isolated pits of the dark waters.

Sorry if it's not that good! I'm not the best writer, and you don't have to use this ending paragraph if you don't want to!!

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Consider the curve of the form y(t) = ksin(bt2) . (a) Given that the first critical point of y(t) for positive t occurs at t = 1
mafiozo [28]

Answer:

(a).   y'(1)=0  and    y'(2) = 3

(b).  $y'(t)=kb2t\cos(bt^2)$

(c).  $ b = \frac{\pi}{2} \text{ and}\  k = \frac{3}{2\pi}$

Step-by-step explanation:

(a). Let the curve is,

$y(t)=k \sin (bt^2)$

So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value x_{0}  which lies in the domain of f where the derivative is 0.

Therefore,  y'(1)=0

Also given that the derivative of the function y(t) is 3 at t = 2.

Therefore, y'(2) = 3.

(b).

Given function,    $y(t)=k \sin (bt^2)$

Differentiating the above equation with respect to x, we get

y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)]

Applying chain rule,

y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)  

(c).

Finding the exact values of k and b.

As per the above parts in (a) and (b), the initial conditions are

y'(1) = 0 and y'(2) = 3

And the equations were

$y(t)=k \sin (bt^2)$

$y'(t)=kb2t\cos (bt^2)$

Now putting the initial conditions in the equation y'(1)=0

$kb2(1)\cos(b(1)^2)=0$

2kbcos(b) = 0

cos b = 0   (Since, k and b cannot be zero)

$b=\frac{\pi}{2}$

And

y'(2) = 3

$\therefore kb2(2)\cos [b(2)^2]=3$

$4kb\cos (4b)=3$

$4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$

$2k\pi\cos 2 \pi=3$

2k\pi(1) = 3$  

$k=\frac{3}{2\pi}$

$\therefore b = \frac{\pi}{2} \text{ and}\  k = \frac{3}{2\pi}$

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Answer:

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