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3 years ago

HELP PYTHAGORAS THEOREM

Mathematics

2 answers:

Sidana [21]3 years ago

8 0

Answer:

Step-by-step explanation:

Yes

finlep [7]3 years ago

4 0

So the hypotenuse is the ladder's length, which is 6m, and the base of the 'triangle' is 1.5m. Therefore, you do 6^2 - 1.5^2 = 36 - 2.25 = 33.75. Then, you just square root it to get 5.80948m. Hope this helps!

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What is the simplified form of 2/x^2-x - 1/x?

Pachacha [2.7K]

Answer: $\bold{(C)\ \dfrac{3 - x}{x(x-1)}}$

Step-by-step explanation:

$\dfrac{2}{x^2-x}-\dfrac{1}{x}$

$=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}$

$=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}\bigg(\dfrac{x-1}{x-1}\bigg)$

$=\dfrac{2}{x(x-1)}+\dfrac{-x+1}{x(x-1)}$

$=\dfrac{2-x+1}{x(x-1)}$

$=\dfrac{3-x}{x(x-1)}$

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:

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

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

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

without looking not picking a red hat from a box that holds 20 red hats, 30 blue hats, 15 green hats, and 25 white hats

PolarNik [594]

There are 90 hats all together. from just red the fraction is 20/90. 20 divide by 90 = .22
there is a 22% chance.

5 0

3 years ago

Last questions on this quiz (I always get confused on finding the x value)

zimovet [89]

For the first one, we know that is a right angle. right angles are 90 degrees. if we subtract 90 - 49 that equals 41. so the second value needs to equal 41. since we have a 3 there already, we are going to subtract 41-3, which is 38. x = 38

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3 years ago

After Halloween, Chad had 213 bags of candy. If Chad gives 123 bags of candy to his little brother, how many bags of candy will

stellarik [79]

Answer:

90 bag

Step-by-step explanation:

no of bags will he have left=213-123

=90 bags of candy

3 0

3 years ago