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It is a curve because it doesn't grow at a constant rate, so each point is higher than the previous point. As an example try to graph the points yourself

a)  cos²(x) · ( 1 + tan²(x) )  =  cos²(x) + cos²(x) ·tan²(x)  =  cos²(x) + cos²(x) · sin²(x) / cos²(x)

                                                                                          =  cos²(x) + sin²(x)  =  1

b)  tan²(x) - sec²(x) + sin²(x) + cos²(x)  =  tan²(x) - sec²(x)  =  tan²(x) - [ 1 + tan²(x) ]

                                                                                              =  tan²(x) - 1 - tan²(x)

                                                                                              =  -1

My bad. I have to plug in the  y again.

15*5-2 = 75-3 = 72

and B = 360 - 72*2 = 216

216/2 = 108, B= 108, Y= 72

a=72,

b=108

3h² - 4g⁴ + 7 + 7f² + 9g⁴ - 4h² + f² - 2

Rewriting, putting like terms together:

(3h² - 4h²) + (-4g⁴ + 9g⁴) + (7 - 2) + (7f² + f²)

=  - h² + 5g⁴ + 5 + 8t²

5y-3=3y+27

2y-3=27

2y=30

y=15.

360 - 2y = 360-30 = 330

B = 330/2

B = 115

r - r·sin(theta)  =  4

Since sin(theta)  =  y/r

r - r·(y/r)  =  4

r - y  =  4

Since  r  =  sqrt(x² + y²)

sqrt(x² + y²) - y  =  4

sqrt(x² + y²)  =  y + 4

Squaring:

x² + y²  =  y² + 8y + 16

x² - 16  =  8y

y  =  0.125x² - 2

Use the Pythagorean Theorem:  d²  =   27² + 48²     --->     d²  =  3645     --->     d  =  sqrt(3645)

If you want a decimal answer, use a calculator ...

It is a curve because it doesn't have a constant slope.

a)  Let the first root be "r", then since the roots form an arithmetic sequence, the other two roots are "r + d" and "r + 2d".

     The factors will be:  (x - r)(x - (r + d))(x - (r + 2d))  or  (x - r)(x - r - d)(x - r - 2d)

     Expanding  (x - r)(x - r - d)(x - r - 2d)  =  x³ -3rx² - 3dx² + 3r²x + 6drx + 2d²x - r³ - 3dr² - 2d²r

     which means that      a  =  -3r - 3d          b  =  3r² + 6dr + 2d²          c  =  -r³ - 3dr² - 2d²r

    2a³  =  -54r³ - 162r²d - 162rd² - 54d³

    27c  =  -27r³ - 81dr² - 54d²r

    9ab  =  -81r³ - 162r²d - 54d²r - 81r²d - 162d²r - 54d³

So, 2a³ + 27c  =  9ab

[It wasn't easy ...]

So what is the answer?

can u show an image of the circle?

( a⁵ · b² ) / ( a³ · b³ )  

cancelling out the a³ factor from both the numerator and denominator still leaves a factor of a² in the numerator:

=  ( a² · b² ) / ( b³ )  

cancelling out the b² factor from both the numerator and denominator still leaves a factor of b in the denominator:

=  a² / b

where  x = 2  and  y = 1 ... 

so  x - y  =  ???

The domain will consist of all the real numbers that do not make the denominator equal to zero.

The denominator is (4x - 3).

If you set this equal to zero:  4x - 3  =  0

                                                    4x  =  3

                                                      x  =  3/4

This is the number you cannot use; so the domain consists of all real numbers except 3/4.

There are 6 stems of 45 cm each:  6 x 45 cm  =  270 cm.

The crcumference = 2 x pi x 45 =  282.75 cm  (approximately)

Adding them together, the answer is approximately 552.75 cm.

3 / [ x² - 2x - 15 ]  =  3 / [ (x - 5)(x + 3) ]   =   3(x + 4) / [ (x - 5)(x + 3)(x + 4) ]  or  (3x + 12) / [ (x - 5)(x + 3)(x + 4) ] 

8x / [ x² - x - 20 ]  =  8x / [ (x - 5)(x + 4) ]  =  8x(x + 3) / [ (x - 5)(x + 4)(x + 3) ]  or  (8x² + 24x) / [ (x - 5)(x + 3)(x + 4) ] 

theta  =  -2·pi / 3

Take the tangent of both sides:

tan( theta )  =  tan( -2·pi / 3 )  =  sqrt(3)

Since  tan( theata )  =  y / x

     y / x  =  sqrt(3)

          y  =  sqrt(3)·x

If you place this angle on a rectangular grid

--  cos(x) < 0 means that the terminal side of theangle must be in either quadrant II or quadrant III

--  tan(x) > 0 means that the terminal side of theangle must be in either quadrant I or quadrant III.

Therefore, the terminal side of the angle is in quadrant III.

Since tan(x) = 4, the point in quadrant III can be (-1, -4).

This means that the radius is  sqrt( (-1)² + (-4)² ) = sqrt(17).

Therefore, sin(x)  =  -4/sqrt(17)  and  cos(x)  =  -1/sqrt(17).

You can use the formula:  sin(2x)  =  2·sin(x)·cos(x)

and any of the formulas for cos(2x); one of them being cos(2x)  =  1 - sin²(x).

3)  Since each block is 1.0 m by 1.0 cm, its area is 1.0 cm².

     Count up the number of whole blocks and add to that answer what you believe is an estimate of each of the partial blocks.

4)  a)  You might have a circular swimming pool and need to find its volume ...

     b)   Measuring the distance around the circular swimming pool ...

5)  a)  Area  =  pi · r²     [Find the radius first by dividing the diameter by 2.]

     b)  The top half is one-half of the answer from part a).

You have a 45-45-90 right triangle whose hypotenuse is 90.

To find either of the sides of this triangle, divide the hypotenuse by sqrt(2).

So, your answer is  90 / sqrt(2).

Now, use your calculator to get a decimal answer ...

The median is the middle number.

If you have a set of numbers that start with 1 and increase by 1 each time, then the median of an odd number of these numbers is also the mean of the first number and the last number.

(You can check this out by starting with 1 and choosing any odd number of numbers.)

So, if you find the mean of 1 and 123456789 (that is:  (1 + 123456789)/2 ), you will also be finding the median.

(x,y)  =  (2 sqrt2 cos pi/12   ,    -  2 sqrt2 sin pi/12 )

1)  adj side = 4;  hyp = 5;  cos(?)  =  adjj/hyp; cos(?)  =  4/5;  ?  =  cos^-1(4/5)

2)  adj side = 6;  hyp = 8;  cos(?)  =  adjj/hyp; cos(?)  =  6/8;  ?  =  cos^-1(6/8)

3)  opp side = 4;  adj side = 13;  tan(?)  =  opp/adj;  tan(?)  =  4/13;  ?  =  tan^-1(4/13)

4)  opp side = 8;  adj side = x;  tan(51)  =  opp/adj;  tan(51)  =  8/x;  x·tan(51)  =  8;  x  = 8/tan(51)

In each case, find the area of the outer figure and subtract the areas of the inner figures.

1)  Area of the outer figure:  A  =  12 cm x 12 cm  =  -------       

      Area of an inner circle:  A  =  pi·3²  =  --------                       

      Area of the other circle:  A  =  pi·3²  =  --------                     

      Final answer:  answer #1 - answer #2 - answer #3  =  -------

2)  The radius of the outer circle is 8 cm + 4 cm  =  12 cm.

     Area of the outer circle:  A  =  pi·12²  =  -------                     

     Area of the top inner circle:  A  =  pi·4²  =  -------                 

     Area of the bottom inncer circle:  A  =  pi·8²  =  --------         

     Final answer:  answer #1 - answer #2 - answer #3  =  -------

No, your solution is not correct, but thank you for trying to help! It's still greatly appreciated!