The expression (2 + 3in2 is equal to 2 -5 + 12i -5

A store sells tea cups in sets of 9 and saucers in sets of 12. The store sold the same number of individual cups and saucers in

BlackZzzverrR [31]

The first five multiples of 9 are 9 18 27 36 45 I hope that's what you mean.

The prime factors of 9 and 12 are

9: 3 * 3

12: 3 * 2 * 2

The LCM is 3*3*2*2 is 36

The store sold 4 sets of cups ans 3 sets saucers. Answer

6 0

4 years ago

Bill has a rectangular garden that is 3 1/2 feet by 4 1/2 feet. A bag of fertilizer covers 5 1/4 square feet. What is the minimu

sveta [45]

Answer:

3

Step-by-step explanation:

3.5*4.5=15.75 ft^2

15.75/5.25=3 bags

8 0

3 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:

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

x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3

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

I need help with 1 and 2

oee [108]

1) -149, -1; -148, -2; -147, -3
2) No, according to the commutative property of addition, it does not matter the order they are put in.

Hope this helps!

6 0

4 years ago

Read 2 more answers

(2,4) is perpendicular to y:2x

Luda [366]

Answer:

is a Step-by-step explanation:

combination

A selection in which order has no importance.A mathematical symbol, or combination of symbols, representing a value, or relation. Example:

2

+

2

=

4

.equation

A mathematical statement that says two expressions have the same value; any number sentence with an

=

.

ordered pair

Set of two numbers in which the order has an agreed-upon meaning, such as the Cartesian coordinates

(

x

,

y

)

, where the first coordinate represents the horizontal position, and the second coordinate represents the vertical position.

solution

1. The value of a variable that makes an equation true.

2. In chemistry, a solution is a homogeneous mixture composed of only one phase.

4 0

3 years ago