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Zigmanuir [339]

4 years ago

10

The volumes of two similar prisms are 891 cm3 and 33 cm3. The surface area of the larger prism is 153 cm2. What is the surface a

rea of the smaller prism?

1 answer:

Kitty [74]4 years ago

7 0

I think it would be 271

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Someone help please and thank you!!

svlad2 [7]

Https://www.symbolab.com/solver/function-asymptotes-calculator this is a good asymptote calculator

4 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

<em>x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3 </em>

<em> </em>

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

PLZZZZZZZZZZ I WILL GIVE BRAINLIEST AND 15PTS!!!!!!!!!!!!!!

vazorg [7]

Answer: ( 0, 2 )

Step-by-step explanation:

You have to put coordinates of each graph on these equations y = -x + 2 and y = (1/2)x + 2. If putting coordinates satisfies both equations, then that coordinate will be the solution.

For example, let's put (0, 2) to equations.

y = -x + 2

2 = -0 + 2

2 = 2, true

y = (1/2)x + 2

2 = (1/2) × 0 + 2

2 = 2, true

So, ( 0, 2 ) is the solution.

7 0

3 years ago

Read 2 more answers

What value of X makes this equation true negative 2X +3 equals -15

Radda [10]

Answer:

The answer is -9

7 0

3 years ago

Read 2 more answers

What is the inverse of the given equation y=7x^2-3?

NARA [144]

Answer:

The inverse of this equation would be y = $\sqrt{\frac{x - 3}{7} }$

Step-by-step explanation:

To find the inverse of any equation, start by switching the y and x values. Then solve for the new y value. That equation will be your inverse.

y = 7x^2 - 3

x = 7y^2 - 3

x + 3 = 7y^2

$\frac{x-3}{7}$ = y^2

$\sqrt{\frac{x - 3}{7} }$ = y

5 0

3 years ago