Find the rectangular coordinates of the point (-3,1/2pi)

the area of a children’s square playground is 50m squared, what is the exact length of the playground

butalik [34]

Answer:

$\displaystyle 5\sqrt{2}\:m.$

Step-by-step explanation:

Sinse squares are equal in length all around, this formula applies:

$\displaystyle s^2 = A → \sqrt{50} = \sqrt{s^2} \\ \\ 5\sqrt{2} = s$

Therefore, the length of the playground is $\displaystyle 5\sqrt{2}$ metres.

* Just in case you could not figure out how to find the square root of fifty, here is how using perfect squares:

$\displaystyle \sqrt{50} → \sqrt{2 \times 25} \\ \\ 5\sqrt{2}$

Sinse we are dealing with measurements, we only want the NON-NEGATIVE root.

I am joyous to assist you at any time.

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The velocity of a turtle is recorded at 1 minute intervals (in meters per second). Use the right-endpoint approximation to estim

aliina [53]

Answer:

The total distance that the turtle traveled during the 5 seconds recorded is $Distance \:traveled\approx 3.838\:\frac{m}{s}$

Step-by-step explanation:

To estimate distance traveled of an object moving in a straight line over a period of time, from discrete data on the velocity of the object, we use a Riemann Sum. If we have a table of values

$\left\begin{array}{ccccccc}time\:=\:t_i&t_0=0&t_1&t_2&...&t_n\\velocity\:=\:v(t_i)&v(t_0)&v(t_1)&v(t_2)&...&v(t_n)\end{array}\right$

where $\Delta t=t_i-t_{i-1}$ , then we can approximate the displacement on the interval $[t_{i-1},t_i]$ by $v(t_{i}) \times\Delta t$ .

Therefore the distance traveled of the object over the time interval $[0,t_n]$ can be approximated by

$Distance \:traveled\approx |v(t_1)|\Delta t+|v(t_2)|\Delta t+...+|v(t_n)|\Delta t$

This is the right endpoint approximation.

We are given a table of values for <em>v(t)</em>

$\left\begin{array}{cccccccc}t(sec)&0&1&2&3&4&5\\v(t)&0.078&0.83&0.75&0.98&0.853&0.425\end{array}\right$

Applying the right endpoint approximation formula we get,

$\Delta t = 1\sec$

$Distance \:traveled\approx |v(t_1)|\Delta t+|v(t_2)|\Delta t+|v(t_3)|\Delta t+|v(t_4)|\Delta t+|v(t_5)|\Delta t\\\\Distance \:traveled\approx 0.83(1)+0.75(1)+0.98(1)+0.853(1)+0.425(1)\\\\Distance \:traveled\approx 3.838\:\frac{m}{s}$