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Y_Kistochka [10]

4 years ago

14

Jayson takes a total of 5 hours of swimming lessons per week.if each lesson is 5/6 of an hour how many lessons does he take per

week

2 answers:

skelet666 [1.2K]4 years ago

5 0

We want an answer in # of lessons. To obtain this, divide 5 hours by
( 5/6 hour / lesson ). "hour" and "hours" will drop out, leaving you with the # of lessons:

5 hours
----------------- = 6 lessons (answer)
5/6 hour
------------
1 lesson

IRINA_888 [86]4 years ago

3 0

5/1 / 5/6 = 5/1 x 6/5 = 6

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Is the number 2 prime or composite

statuscvo [17]

The number 2 is prime

4 0

4 years ago

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Find the absolute maximum and minimum values of f on the set D. f(x, y) = x3 − 3x − y3 + 12y + 1, D is quadrilateral whose verti

mojhsa [17]

$D$ is the set of points,

$\left\{(x,y)\mid-2\le x\le2,x\le y\le3\right\}$

Check for critical points:

$f(x,y)=x^3-3x-y^3+12y+1\implies\begin{cases}f_x=3x^2-3=0\implies x=\pm1\\f_y=-3y^2+12=0\implies y=\pm2\end{cases}$

Of these 4 points, only 2 belong to $D$ , (-1, 2) and (1, 2), for which we have

$\begin{cases}f(-1,2)=19\\f(1,2)=15\end{cases}$

Now look for extrema along the boundary.

If $x=-2$ , then

$f(-2,y)=-y^3+12y-1\implies f'(-2,y)=-3y^2+12=0\implies y\pm2$

We have $f'(-2,y)>0$ for $-2$ and $f'(-2,y)$ for $2$ , which indicates a local maximum at $y=2$ and minima at the endpoints of this boundary. So

$\begin{cases}f(-2,2)=15\\f(-2,-2)=-17\\f(-2,3)=8\end{cases}$

If $x=2$ , then

$f(2,y)=y^3+12y+3\implies f'(2,y)=-3y^2+12=0\implies y=\pm2$

We have $f'(2,y)$ for $2$ , so we have extrema at the endpoints of this boundary.

$\begin{cases}f(2,2)=19\\f(2,3)=12\end{cases}$

If $y=x$ , then

$f(x,x)=9x+1\implies f'(x,x)=9>0$

which tells us $f$ is strictly increasing on this boundary, giving the extrema we already know about,

$\begin{cases}f(-2,-2)=-17\\f(2,2)=19\end{cases}$

If $y=3$ , then

$f(x,3)=x^3-3x+10\implies f'(x,3)=3x^2-3=0\implies x=\pm1$

We have $f'(x,3)>0$ for $-2$ and $1$ , and $f'(x,3)$ for $-1$ . This indicates a maximum at $x=-1$ and a minimum at $x=1$ , with

$\begin{cases}f(-2,3)=8\\f(-1,3)=12\\f(1,3)=8\\f(2,3)=12\end{cases}$

From this analysis, we find that $f$ attains an absolute maximum of 19 at (-1, 2) and (2, 2), and an absolute minimum of -17 at (-2, -2).

4 0

3 years ago

Find the vertex of the parabola<br> y= x^2-2x-1<br> vertex (?,?)

SpyIntel [72]

$y=ax^2+bx+c\\\\vertex:(x_v;\ y_v)\\\\x_v=\frac{-b}{2a}\ and\ y_v=f(x_v)$

$y=x^2-2x-1\\\\a=1;\ b=-2;\ c=-1\\\\x_v=\frac{-(-2)}{2\cdot1}=\frac{2}{2}=1\\\\y_v=1^2-2\cdot1-1=1-2-1=-2\\\\Answer:(1;-2)$

5 0

3 years ago

Read 2 more answers

When negative five is subtracted from a number the result is 10 find the number

levacccp [35]

Answer: second option.

Step-by-step explanation:

Let be "x" the unknown number.

According to the information provided in the exercise, 10 is the result of the subtraction of "x" and -5.

Based on this, you can write the following equation:

$x-(-5)=10$

To find the value of "x" you must remember the multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-$

Then:

$x-(-5)=10\\\\x+5=10$

Finally, subtracting 5 from both sides of the equation, you get:

$x+5-(5)=10-(5)\\\\x=5$

3 0

3 years ago

HAVE TO EVALUATE SHOW WORK !!!!!<br><br> 2ny + x

Ivan

Answer:

9

Step-by-step explanation:

2ny + x

Start with n and y

n= 3/4

y = 6

2*n*y = 2* 3/4 * 6 2 * 6 = 12

12 * 3/4 = 36 / 4 = 9

There are many ways to do this. I have chosen one that does not require cancellation.

7 0

3 years ago