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Andre45 [30]
3 years ago
15

Which number is larger -3.4 or -3 1/2 (BTW this is a fraction)? How will graphing these numbers on a number line help you determ

ine which number is larger?
PLEASE HELP ME OUT!!!!!!
Mathematics
1 answer:
valkas [14]3 years ago
3 0

Answer:

-3.4

Step-by-step explanation:

negative numbers are reverse counting on the line graph.

-3 1/2 is -3.5

-3.4 VS. -3.5

since it is reverse, -3.4 is greater

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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
M∠1=119∘ and m∠2=61∘.<br> What is m∠3?
marin [14]

Answer:

m∠3 = 119°

Step-by-step explanation:

All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.

4 0
2 years ago
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Can someone help meee
pickupchik [31]

Step-by-step explanation:

29+1/5r=

29+(1/5×-1/2)

29+1/10

291/10

=29.1

4 0
3 years ago
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podryga [215]

Answer:

y=|x-1|-1

Step-by-step explanation:

hope that helps :)

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Consider the following system of equations.
lukranit [14]
If you plot them you will see that the intersect each other in two different points.
The solution of a system of equations is the set of points of intersection of the graphs of the equations.
The answer is D.
3 0
3 years ago
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