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4 years ago

Fill in the blank to make a FALSE inequality: −5 ≤ _____

Mathematics

1 answer:

Ierofanga [76]4 years ago

5 0

Answer: -10, or any number less than -5

Step-by-step explanation:

Think about a number line. Any value to the left of -5 is less than -5. Any value to the right is greater than -5. To make the inequality false, any number less than -5 will work.

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

BartSMP [9]

Answer:

x -y =4

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

= (1- -4)/(5 - 0)

= (1+4)/(5-0)

5/5

= 1

Then we can use slope intercept form

The slope is 1 and the y intercept is -4

y = mx+b

y = 1x-4

We want it in standard form

Ax + By = C where A is a positive integer

Subtract x from each side

-x +y = -4

Multiply by -1

x -y =4

8 0

3 years ago

Write the equation of the conic section satisfying the given conditions. focus at the pole, e = 3/4, horizontal directrix 2 unit

hjlf

Answer:

The equation in the polar form is;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$

Step-by-step explanation:

e = 3/4 > 1, we have an hyperbola

The polar equation of a conic is of the form;

For vertical directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}$

For horizontal directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}$

Where;

k = Distance from the focus to the directrix = 2

We have;

$r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

$r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

Which gives the equation in the polar form as follows;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$ .

8 0

3 years ago

Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.

Vedmedyk [2.9K]

Compute the gradient of $f$ .

$\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle$

Set this equal to the zero vector and solve for the critical points.

$3x^2-6y = 0 \implies x^2 = 2y$

$-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}$

$\implies x^2 = \pm2\sqrt{2x}$

$\implies x^4 = 8x$

$\implies x^4 - 8x = 0$

$\implies x (x-2) (x^2 + 2x + 4) = 0$

$\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0$

$\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0$

The last case has no real solution, so we can ignore it.

Now,

$x=0 \implies 0^2 = 2y \implies y=0$

$x=2 \implies 2^2 = 2y \implies y=2$

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

$H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}$

Check the sign of the determinant of the Hessian at each of the critical points.

$\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0$

which indicates a saddle point at (0, 0);

$\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0$

We also have $f_{xx}(2,2) = 12 > 0$ , which together indicate a local minimum at (2, 2).

3 0

2 years ago

Radius BE is a perpendicular bisector of chord AC. What is the measure of

Mrrafil [7]

Answer:

A. 100

Step-by-step explanation:

50 + 50 + 100

6 0

3 years ago

Read 2 more answers

What’s the awnser(can someone do these for me i’m begging you my parents are gonna kill me)

puteri [66]

Answer:

-3/2

(2x-14)/3

(-2,-6)

Step-by-step explanation:

I solved the first one for you already ( -3/2)

To make a line perpindicular to another line they need to intersect at a 90 degree angle. To do this the slope of the lines have to be the negative reciprical (take the fraction, flip it, and apply a negative sign to it)

If you do this to -3/2 you get 2/3

If we follow our y=mx+b equation from before we (so far) have

2/3x+b=y

which means that we just need to solve for b

We also know that it crosses the point (7,0) which means that if we plug in 7 for x and 0 for y we can solve for b

we have

(2/3)*7+b=0

Solve for B

14/3+b=0

b= -14/3

Which means our equation looks like this

(2x-14)/3

our two equations look like this

(-3/2)x-9

(2x-14)/3

We need to find where their coordinates are the same (where they intersect)

We can do this by setting them equal to each other and then solving for x

we have

(-3/2)x-9=(2x-14)/3

solve for x

-4.5x-27=2x-14

-13= 6.5x

x= -2

Now that we know what x equals we can plug this into any of our two beginning equations

(-3/2)*-2-9=y

3-9=y

-6=y

Which means our coordinates are (-2,-6)

if you have any questions let me know

6 0

3 years ago