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2 years ago

How many ways can the letters of the word ORGANISM be arranged so the third letter is G?

2 answers:

5 0

7 * 6 * 5 * 4 * 3 * 2 = 5,040 ways. It's just the number of ways the OTHER seven letters can be arranged. That's "seven factorial".

babunello [35]2 years ago

4 0

Since we know the third letter is going to be "G" anyway, it might be easier if we just look at the ways in which we can arrange the seven other letters. In other words, how many ways can we arrange "ORANISM"? Now it becomes a simple factorial problem.
7 things to be arranged:
7! = 7*6*5*4*3*2*1 = 5040
There are exactly 5,040 ways in which the letters of ORGANISM can be arranged such that the third letter is G.

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If 2x2 + y2 = 17 then evaluate the second derivative of y with respect to x when x = 2 and y = 3. Round your answer to 2 decimal

Vera_Pavlovna [14]

Answer:

y''=-1.26

Step-by-step explanation:

We are given that $2x^2+y^2=17$

We have evaluate the second order derivative of y w.r.t. x when x=2 and y=3.

Differentiate w.r.t x

Then , we get

$4x+2yy'=0$

$2x+yy'=0$

$yy'=-2x$

$y'=-\frac{2x}{y}$

Again differentiate w.r.t.x

Then , we get

$2+(y')^2+yy''=0$ $(u\cdot v)'=u'v+v'u)$

$2+(y')^2+yy''=0$

Using value of y'

$yy''=-2-(-\frac{2x}{y})^2$

$y''=-\frac{2+(-\frac{2x}{y})^2}{y}$

Substitute x=2 and y=3

Then, we get $y''=-\frac{2+(\frac{4}{3})^2}{3}$

$y''=-\frac{18+16}{9\times 3}=-\frac{34}{27}$

Hence,y''=-1.26

6 0

2 years ago

Conor has a roll of fence that is 25 feet long. He needs 8 yards of fence to go around a flower bed. Does he have enough fence t

vlabodo [156]

Answer:

Yes he has enough fence to go round the flower bed.

Step-by-step explanation:

1 yard = 3 feet

25 feet = 25/3 = 8.33 yards

Yes he has enough fence to go round the flower bed.

8 0

2 years ago

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto

Gre4nikov [31]

$\begin{cases}y=2x-2\\y=2x+2\end{cases}\implies\begin{cases}-2x+y=-2\\-2x+y=2\end{cases}$

For these lines, let $u=-2x+y$ .

$\begin{cases}y=2-x\\y=4-x\end{cases}\implies\begin{cases}x+y=2\\x+y=4\end{cases}$

And for these, let $v=x+y$ .

Now,

$\begin{cases}u=-2x+y\\v=x+y\end{cases}\implies \begin{bmatrix}u\\v\end{bmatrix}=\underbrace{\begin{bmatrix}-2&1\\1&1\end{bmatrix}}_{\mathbf T}\begin{bmatrix}x\\y\end{bmatrix}$

The vertices of $S$ in the x-y plane are (0, 2), (2/3, 10/3), (2, 2), and (4/3, 2/3). Applying $\mathbf T$ to each of these yields, respectively, (2, 2), (2, 4), (-2, 4), and (-2, 2), which are the vertices of a rectangle whose sides are parallel to the u-v plane.