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3 years ago

Evaluate x(–y + z) for x = –1, y = 2, and z = 5. 7 –7 3 –3

1 answer:

8 0

X(-y+z)

When x is -1, y is 2, and z is 5, replace these letters with the numbers associated with them, you get

=-1(-2+5)
=-1(-2)+(-1)(5)
=2-5
=-3

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I'll mark the best or the first as brainliest.

FinnZ [79.3K]

Answer:

Here the error is 

 $\pi {r}^{2}$ 

It should have been ,

 $2\pi {r}^{2}$ 

Step-by-step explanation:

Corrected formula:

 $2\pi {r}^{2} + 2\pi rh$ 

 $= 2\pi ({5}^{2}) + 2\pi(5)(10.6)$ 

 $= 50\pi + 106\pi$ 

 $= 156\pi$ 

 $= 489.84 {yd}^{2}$ 

 $approx . \: 489.8 {yd}^{2} (ans)$ 

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3 years ago

If a simple machine reduces the strength of a force, what must be increased?

ch4aika [34]

I think the answer is C. The distance over which the force is applied. Hope this helps!

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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.

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3 years ago

Help plz i will give brainliest

jasenka [17]

Answer:

(If needed explanation ask in the comments! ty)

Hope This Helps! •v•

6 0

2 years ago

Kurt has a collection of 155 United States and Canadian stamps. He has 1.5 times as many United States stamps as Canadian stamps

stealth61 [152]

Kurt has 93 United States stamps in his collection

Step-by-step explanation:

The given is:

Kurt has a collection of 155 United States and Canadian stamps
He has 1.5 times as many United States stamps as Canadian stamps

We need to find how many United States stamps Kurt has in his collection

Assume that kart has x Canadian stamps

∵ kart has x Canadian stamps

∵ He has 1.5 times as many United States stamps as Canadian stamps

- That means the number of United States stamps is 1.5 times

the number of the Canadian stamps

∴ The number of the United States stamps = 1.5 x

∵ Kurt has a collection of 155 United States and Canadian stamps

- Add the two numbers of stamps and equate the answer by 155

∴ x + 1.5 x = 155

- Add like terms

∴ 2.5 x = 155

- Divide both sides by 2.5

∴ x = 62

∵ The number of United States stamps = 1.5 x

∴ The number of United States stamps = 1.5(62)

∴ The number of United States stamps = 93 stamps

Kurt has 93 United States stamps in his collection

Learn more:

You can earn more about the simple equation in brainly.com/question/11306893

#LearnwithBrainly

5 0

3 years ago