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2 years ago

11

Para abastecer o seu carro com 30 litros de gasóleo a Inês demorou 1 minuto e 40 segundos. Com a mesma mangueira, quanto tempo é

necessário para encher um recipiente com a forma de um cone e uma semiesfera com 10 cm de raio e, o cone, com 10 cm de altura?

1 answer:

olga2289 [7]2 years ago

4 0

Answer:

hahdg duchy jejeurur y ed sethi. riruru. udhrhru. ueeh

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The base of a rectangular pyramid has dimensions 3 feet by 9 feet. The height of the pyramid is 11 feet.

AveGali [126]

Answer:

99

Step-by-step explanation:

1. rectangular pyramid formula:

2. V=lwh/3

3. 99 = (3)(9)(11)/3

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2 years ago

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It takes has a 20 minutes to walk to school . it takes Andre 80% as long to walk to school how long dose it take Andre to walk t

Blizzard [7]

You have to find 80% of 20.
Since 80% is equal to 0.8, you multiply 20 by 0.8 to get 16

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2 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

Dara has 12 red counters. She has 7 more red counters than yellow counters. How many yellow counters does Dara have?

pantera1 [17]

12 red counters

7 more red counters than yellow counters

12 - 7 = 5 yellow counters

Dara has 5 yellow counters.

5 0

3 years ago

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What is the Slope of the line

vampirchik [111]

Answer:

$m=\frac{-3}{4}$

Step-by-step explanation:

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Simply plug in 2 coordinates into the slope formula to find slope <em>m</em>:

$m=\frac{-4-(-1)}{5-1}$

$m=\frac{-4+1}{4}$

$m=\frac{-3}{4}$

5 0

2 years ago