Statement

At a local farmer’s market , Jodi bought 3 pounds of Ashmead’s kernel Apples for $4.47 at the McDougal Orchards stand At that ra

snow_tiger [21]

Answer:

Cost of the 5 pounds of Ashmend’s kernel apples is $7.5

Step-by-step explanation:

As given

At a local farmer’s market , Jodi bought 3 pounds of Ashmead’s kernel Apples for $4.47 at the McDougal Orchards stand .

i.e

3 pounds = $ 4.47

Now find out the cost of 1 pound of Ashmend kernel apples .

$The\ cost\ of\ 1\ pound\ of\ Ashmend\ kernel\ apples = \frac{4.47}{3}$

= $ 1.5 (Approx)

Cost of 5 pounds of Ashmend’s kernel apples = Amount of apples × Cost of 1 pounds of apples .

= 5 × 1.5

= $ 7.5

Therefore the cost of the 5 pounds of Ashmend’s kernel apples is $7.5 .

7 0

3 years ago

Tina runs a hot dog stand. On Wednesday morning, she had 80 dozen hot dogs at her stand. The graph shows the number of hot dogs

KATRIN_1 [288]

Sunday: 45
Monday: 20
Tuesday: 0
All together: 65

6 0

2 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

The shadow cast by a lampshade has a boundary in the shape of a hyperbola defined by the equation StartFraction (y minus 3) squa

andrew11 [14]

Answer:

A THE LOCATION OF THE LIGHT BULB

I got this right on the assignment

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Can someone help me please

Ipatiy [6.2K]

The price of the shoes times .06 will give you the abswer

5 0

3 years ago