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kherson [118]
2 years ago
13

Select all the angles of rotation that produce symmetry for this flower.

Mathematics
1 answer:
Sedaia [141]2 years ago
3 0

Answer:

Angles of rotation that produce symmetry are the angles that we can rotate the image, and the end result will be the starting image. (the angles are always measured from the x-axis)

Here we can clearly see that in each quadrant we have a petal of the flower.

Then the angles that change one quadrant into other quadrant will produce symmetry.

Those angles are:

90°, 180°, 270°, 360°, etc.

We can define the set of those angles as:

A {n*90° I n ∈ Z}

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Simplify the expression where possible.<br><br> (-5x 2)^3
Drupady [299]
-1000x^3 hope this helps

3 0
3 years ago
Read 2 more answers
Marle placed two orders at the same restaurant last month. In one order, she received 5 trays of lasagna and 3 trays of
user100 [1]

Answer:

$25.25-lasagna, $12.25-garlic bread

Step-by-step explanation:

  5L+3G=163

- 4L+4G=150

______________

 4(5L+3G=163)

-5(4L+4G=150)

_____________

20L+12G=652

-20L-20G=-750

_____________

          -8G=-98

         -8G/-8 = -98/-8

               G=$12.25

now plug that into G in any of the 2 equations at the top and you can solve for L(price of lasagna)

5 0
3 years ago
Find the critical points of the function f(x, y) = 8y2x − 8yx2 + 9xy. Determine whether they are local minima, local maxima, or
NARA [144]

Answer:

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

Step-by-step explanation:

The function is:

f(x,y) = 8\cdot y^{2}\cdot x -8\cdot y\cdot x^{2} + 9\cdot x \cdot y

The partial derivatives of the function are included below:

\frac{\partial f}{\partial x} = 8\cdot y^{2}-16\cdot y\cdot x+9\cdot y

\frac{\partial f}{\partial x} = y \cdot (8\cdot y -16\cdot x + 9)

\frac{\partial f}{\partial y} = 16\cdot y \cdot x - 8 \cdot x^{2} + 9\cdot x

\frac{\partial f}{\partial y} = x \cdot (16\cdot y - 8\cdot x + 9)

Local minima, local maxima and saddle points are determined by equalizing  both partial derivatives to zero.

y \cdot (8\cdot y -16\cdot x + 9) = 0

x \cdot (16\cdot y - 8\cdot x + 9) = 0

It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:

\left \{ {{-16\cdot x + 8\cdot y=-9} \atop {-8\cdot x + 16\cdot y=-9}} \right.

The solution of the system is (3/8, -3/8).

Let assume that y = 0, the nonlinear system is reduced to a sole expression:

x\cdot (-8\cdot x + 9) = 0

Another solution is (9/8,0).

Now, let consider that x = 0, the nonlinear system is now reduced to this:

y\cdot (8\cdot y+9) = 0

Another solution is (0, -9/8).

The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:

H = \frac{\partial^{2} f}{\partial x^{2}} \cdot \frac{\partial^{2} f}{\partial y^{2}} - \frac{\partial^{2} f}{\partial x \partial y}

The second derivatives of the function are:

\frac{\partial^{2} f}{\partial x^{2}} = 0

\frac{\partial^{2} f}{\partial y^{2}} = 0

\frac{\partial^{2} f}{\partial x \partial y} = 16\cdot y -16\cdot x + 9

Then, the expression is simplified to this and each point is tested:

H = -16\cdot y +16\cdot x -9

S1: (0,0)

H = -9 (Saddle Point)

S2: (3/8,-3/8)

H = 3 (Local maximum or minimum)

S3: (9/8, 0)

H = 9 (Local maximum or minimum)

S4: (0, - 9/8)

H = 9 (Local maximum or minimum)

Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:

S2: (3/8,-3/8)

f(\frac{3}{8} ,-\frac{3}{8} ) = - \frac{27}{64} (Local minimum)

S3: (9/8, 0)

f(\frac{9}{8},0) = 0 (Local maximum)

S4: (0, - 9/8)

f(0,-\frac{9}{8} ) = 0 (Local maximum)

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

4 0
3 years ago
Sanjay read 56 pages of his book this weekend.This is 35% of the pages in the book.How many pages are in Sanjays book?
Maurinko [17]
1. 56 : 35 = 1.6
2. 1.6* 100 = 160
3. The answer is 160
3 0
3 years ago
Erify that f has an inverse. then use the function f and the given real number a to find (f −1)'(a). (hint: see example 1. if an
zhannawk [14.2K]

The function

... f(x) = (x+2)/(x-1) = 1 + 3/(x-1)

is symmetrical about the line y=x, hence is its own inverse.


We can evaluate the desired derivative directly.

... f'(x) -3/(x-1)²

so f'(2) is

... f'(2) = -3/(2-1)²


(f^{-1})(2)=-3

8 0
3 years ago
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