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3 years ago

8(10)2y = 7200 What the answer

Mathematics

1 answer:

garik1379 [7]3 years ago

7 0

Answer:

y = 45

Explanation:

(8)(10)(2)y = 7200

[ Simplify both sides of the equation ]

160y = 7200

[ Divide both sides by 160 ]

160y / 160 = 7200 / 160

y = 45

Check:

8(10)2(45) = 7200

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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

OK so this is not a question, but a call for help. I do home school all day everyday and I get so bored. My friends live an hour

Nina [5.8K]

Hi!!!, i used to be home schooled. IT WAS THE WORST. I've had to go through what your going through right now for 2 years. I'm in the 8'th grade. and i've been wanting to meet new friends.

4 0

3 years ago

Nate and his friends are building a skateboard ramp for an upcoming contest. The length of the ramp on the blueprint is 7.6 inch

ICE Princess25 [194]

Answer:

30.4 feet.

Step-by-step explanation:

We have been given the length of the ramp on the blueprint is 7.6 inches. The scale on the blueprint is 1 inch to 4 feet. We are asked to find the actual length of the ramp.

We will use proportions to solve our given problem as:

$\frac{\text{Actual length}}{\text{Scale length}}=\frac{4\text{ ft}}{1\text{ inch}}$

Now, we will substitute the scale length of ramp in our proportion as:

$\frac{\text{Actual length}}{7.6 \text{ Inches}}=\frac{4\text{ ft}}{1\text{ inch}}$

$\frac{\text{Actual length}}{7.6 \text{ Inches}}\cdot 7.6 \text{ Inches}=\frac{4\text{ ft}}{1\text{ inch}}\cdot 7.6 \text{ Inches}$

$\text{Actual length}=4\text{ ft}\cdot 7.6$

$\text{Actual length}=30.4\text{ ft}$

Therefore, the actual length of the ramp would be 30.4 feet.

7 0

3 years ago

Rod is paid $85 to install a screen door and $115 to install a wooden door. In one week he installed 18 doors and was paid a tot

Rainbow [258]

Answer:Rod installed 7 screen doors

Step-by-step explanation:

Step 1

Let the number of screen door = x

And the number of wooden doors = y

since he installed 18 doors , we have that

screen door + wooden doors = 18

x + y = 18------ equation 1

Also the cost to install a screen door -= $85

and to install a wooden door = $115

And he was therefore paid a total of $1850

Therefore

85x + 115 y = $1860------- equation 2

Step 2----- Solving

x + y = 18------ equation 1

85x + 115 y = $1860------- equation 2

Multiplying equation 1 BY 85

85x + 85y= 1530------- equation 3

85x + 115 y = $1860------- equation 4

subtracting from equation 1 from (2)

115y- 85y= 1860-1530

30y=330

y = 330/30 = 11

To find x

x+ y=18

x= 18-y

x= 18-11= 7

Rod installed 7 screen doors and 11 wooden doors.

8 0

3 years ago

If 1 candy bar weighs 3 ounces what is the weight of 11 candy bars

Vera_Pavlovna [14]

Answer:

33 ounces

Step-by-step explanation:

Just multiply. If one weights 3 ounces 11x3=33

6 0

3 years ago

Read 2 more answers