○ + ○ + ○= 30 ○ + ¤¤ + ¤¤= 18 ¤¤ - ☆☆= 2 ☆ + ○ × ¤= ? What is the ?

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$$

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

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

7 0

4 years ago

A bag contains 3 red marbles and 4 blue marbles a marble is taken at random from the bag and replaced another marble is taken fr

Phoenix [80]

Answer:

honestly i think its 1/4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

mariarad [96]

Answer:

$p_v =P(z>2.087) =0.0184$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

$\sigma=2.5$

And the statistic is given by this formula:

$z=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sigma\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}$

Where z follows a normal standard distribution

The system of hypothesis on this case are:

Null hypothesis: $\mu_c \leq \mu_t+1$

Alternative hypothesis: $\mu_c >\mu_t+1$

Or equivalently:

Null hypothesis: $\mu_c - \mu_t \leq 1$

Alternative hypothesis: $\mu_c-\mu_t>1$

Our notation on this case :

$n_c =45$ represent the sample size for group control

$n_t =45$ represent the sample size for group treatment

$\bar X_c =5.2$ represent the sample mean for the group control

$\bar X_t =3.1$ represent the sample mean for the group treatment

And now we can calculate the statistic:

$z=\frac{(5.2-3.1)-(1)}{2.5\sqrt{\frac{1}{45}}+\frac{1}{45}}=2.087$

And now we can calculate the p value using the alternative hypothesis:

$p_v =P(z>2.087) =0.0184$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.

5 0

3 years ago

− ( − ) = what is x

skelet666 [1.2K]

Answer:

There is no x the equation so there is really no answer for x

Step-by-step explanation:

5 0

3 years ago

A swimming pool is being filled at the rate of 4600 pt/min (pints per minute). How many pints per second is this?

kenny6666 [7]

276,000

explanation: multiply 4600 by 60

8 0

3 years ago

Read 2 more answers

○ + ○ + ○= 30○ + ¤¤ + ¤¤= 18¤¤ - ☆☆= 2☆ + ○ × ¤= ?What is the ?