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3 years ago

The perimeter of the regular polygon shown is 18 cm

Mathematics

1 answer:

kirill115 [55]3 years ago

4 0

A polygon has 5 sides you can find the length of one side by dividing the total perimeter of 18 by the number of sides of 5. giving you 3.6

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What is the length of the third side of the window frame below?

Nostrana [21]

Answer:

C 40 inches

Step-by-step explanation:

You can use the pythagorean theorem to solve for the second leg. When you plug in 42 for a and 58 for c, you get 42^2 + b^2 = 58^2, then you can isolate b, which should be 40 inches.

8 0

3 years ago

Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1

Varvara68 [4.7K]

I assume there are some plus signs that aren't rendering for some reason, so that the plane should be $x+y+z=1$ .

You're minimizing $d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2}$ subject to the constraint $f(x,y,z)=x+y+z=1$ . Note that $d(x,y,z)$ and $d(x,y,z)^2$ attain their extrema at the same values of $x,y,z$ , so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

$L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)$

Take your partial derivatives and set them equal to 0:

$\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}$

Adding the first three equations together yields

$2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43$

and plugging this into the first three equations, you find a critical point at $(x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)$ .

The squared distance is then $d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43$ , which means the shortest distance must be $\sqrt{\dfrac43}=\dfrac2{\sqrt3}$ .

7 0

3 years ago

. Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A. Circle all of

egoroff_w [7]

Answer:

the answer is b I know this because I'm a very young person but I'm a very young man who has been a great person for the last two decades so I'm not really into this

Step-by-step explanation:

I just don't want you back in here and you know this because I know this because you are a good friend of yours but you have no reason for me not knowing that I was in love and you are a great man but you have no idea how to do this 6AM 6AM I know this because you have to be with him to be a great person to be able and be able and be happy and you will have a great time

PERIOD BOO

3 0

3 years ago

ASAP PLEASEEEEEEEE

shtirl [24]

Answer:

x = -122/13 OR 9.3846

Step-by-step explanation:

First, take a look at the second equation. Add 8x to the other side.

-7y= 8x -18

Then, divide by -7 to get a regular "y=" equation.

y= 8/7x -18/7

Move on the the first equation. Let's get "y" by itself. Add 3x to the other side.

y= 3x +15

Considering both equations are equal to Y, set them equal ( except the "y" part )

8/7x - 18/7 = 3x + 15

Multiply all by seven so that there are no fractions.

8x - 18 = 21x + 105

Subtract 8x from both sides.

-17 = 13x + 105

Subtract 105 from both sides.

-122 = 13x

Divide by 13 on both sides.

x = 9.3846

Or if you don't want decimals, just say x = -122/13

Quick Note: I made a mistake. I had looked at the second equation at -18. The answer is incorrect but the method of solving is correct. Also, make sure to plug in the value of x to get Y.

5 0

3 years ago

Question 11 (True/False Worth 1 points)

konstantin123 [22]

True. These answers show a relationship because you add eight every time the pack goes higher.

8 0

3 years ago

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