All categories

3 years ago

What is the right answer for this question?

Mathematics

1 answer:

My name is Ann [436]3 years ago

8 0

The answer is J because a rational number is anything that can be written as a fraction and a integer is a whole number. Since 16/4 simplifies to 4 and square root of 9 simplifies to 3, this would be the correct answer.

You might be interested in

Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

Looks like $f(x,y)=x^2+y^2-x^2y+7$ .

$f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1$

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

The latter two critical points occur outside of $D$ since $|\pm\sqrt2|>1$ so we ignore those points.

The Hessian matrix for this function is

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}$

The value of its determinant at (0, 0) is $\det H(0,0)=4>0$ , which means a minimum occurs at the point, and we have $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

$f(-1,y)=8-y+y^2$

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

If $y=-1$ , then

$f(x,-1)=2x^2+8$

which has 3 extreme values, but the previous cases already include them.

Hence $f(x,y)$ has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

3 0

3 years ago

Which of the following equations is modeled by the graph.

Sergio [31]

Answer:

a = 50t

Step-by-step explanation:

The graph goes through (0,0) so the y intercept is 0

a=5t

a=50t

a=50 + t not it

a=10t

The slope is y/x since the y intercept is 0

m = 50/1 = 50

The equation for the line is

y = 50x+0

y = 50x

Using the variables given

a = 50t

5 0

3 years ago

Given the line -2 + 2y = 5 , find the perpendicular line that goes through (1, -3). HeLP ME PLEASEE QUICK

brilliants [131]

Answer:

x=1

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula y − y 1 = m ( x − x 1 ) to find the line perpendicular to − 2 + 2 y = 5 .

4 0

3 years ago

Can someone help me?

kirza4 [7]

Answer:

C. -36 3/10

Step-by-step explanation:

4 2/5 = 22/5

22/5 = 4.4

4.4(-8.25)

-36.3 = -36 3/10

Have a great day :3

8 0

3 years ago

The label on a gallon of ice cream shows the total fat contents as 9 grams (g) of which 6 grams are saturated fat. What is the r

Lunna [17]

The ratio is (saturated fat) : (total fat) ----- 6 grams : 9 grams ----- Divide both sides by 3 ----- 6/3 grams : 9/3 grams ----- 2 grams : 3 grams ----- 2:3 is the ratio ----- You can also represent it in fraction form : 2/3

5 0

3 years ago