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3 years ago

Given the functions f(x)=1x−2+1 and g(x)=1x+5+9 .

1 answer:

8 0

For this problem you would look at the difference between the two equations. Left and right is determined by the -2 and the +5 in the problems, to get from -2 to +5, you would add 7 but (and i dont really know how to explain the reasoning for this) whenever this number is positive, it goes left and whenever it is negative, it goes right. Figuring out if it shifts up or down is the same, look at the numbers +1 and +9 in the equations. If you go from +1 to +9, you would be adding 8, and this makes it shift upward.

Therefore the answer is the third one: the graph shifts 7 units left and 8 units up

You might be interested in

What is a problem that requires adding one two the quotient

Nikolay [14]

division problem

In a division problem, the number being divided into pieces is the dividend. The number by which the dividend is divided is called the divisor. And the answer to the division problem is the quotient.

6 0

2 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

Highest (-3,-3)

Lowest (2,2)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

Simplify: - 4x 5x - 1 + 3-6x 3-6x

Vitek1552 [10]

Answer:

−45−1+3−63−6

−46−1+3−63−6

−46+2−63−6

Solution:

−46−63−6+2

Step-by-step explanation:

I hope that this is what you are looking for

Have a nice day/night

3 0

3 years ago

Please help my sister needs to turn this in soon

alexandr402 [8]

Answer:

11,059

Step-by-step explanation:

If you take the combined elevation (18,152) and subtract the elevation of Snowy Mountain (7,093), you should get 11,059.

7 0

3 years ago

Read 2 more answers

Explain how you would find 47×7/9 mentally

erastova [34]

So you move left to right like PEMDAS when it comes to adding or subtracting either or could go first and same thing applies with multiplying and dividing so for instance in this case

47*7=329
_
329/9=36.5

3 0

3 years ago