What is the answer to x+4=6 1/4

A group of 19 boys and 18 girls are attending a pottery class. Each pottery table can seat 6 people.

Licemer1 [7]

Answer:

7

Step-by-step explanation:

37 People / 6 is 6.18 Rounded up is 7

3 0

3 years ago

At hogan airport an airplane off 12 minutes how many airplane take off in 5 hours

dusya [7]

25 Planes can take off. Divide 60 (minutes) by 12 and it should give you 5. Take that five and multiply it by the number of hours they are asking for (5). 5*5=25.

3 0

3 years ago

How to solve this problem. I don’t know how to do this and need help desperately

Iteru [2.4K]

There are 4 possibilities for cone or cup to hold your ice cream. There are 3 different sizes to choose from. There are 20 flavors of ace-cream, and then 15 choices of topping. Assuming you must choose 1 flavor of ice cream and 1 topping as the question implies, there are then 4*3*20*15 = 3600 different combinations to choose from. Answer is D: 3600

4 0

4 years ago

For the inverse variation equation xy=k what is the constant of variation k when x=-3 And y=-2

ELEN [110]

ANSWER

The constant of variation is 6.

EXPLANATION

The inverse variation equation is:

$xy = k$

We want to find the constant of variation, when x=-3 and y=-2.

We substitute the values for x and y to get,

$- 3 \times - 2 = k$

Multiply out the left hand keeping in mind that negative times negative yields a positive result.

This implies that;

$k= 6$

Hence the constant of variation is 6.

8 0

3 years ago

Read 2 more answers

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:

a)

Highest (-3,-3)

Lowest (2,2)

b)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

a)

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

b)

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