geno3141

To find the size of the angle when you know the cos, use cos^-1(0.324).

On hand-held calculators use (2nd) (cos) , enter 0.324 to get the answer:  71.1°.

On this calculator, use (2nd) (acos) and then enter the value.

"acos" means "arc cos", which is the inverse cosine.

Similarly, find sin^-1(0.123) and tan^-1(0.783), using (2nd) (asin) and (2nd) (atan).

2y²  =  4x³ + 2

When y = 1:                                                        When y = -1:

2(1)²  =  4x³ + 2                                                 2(-1)²  =  4x³ + 2

2  =  4x³ + 2                                                              2  =  4x³ + 2

0  =  4x³                                                                    0  =  4x³

0  =  x³                                                                      0  =  x³

--->   x  =  0                                                              --->   x  =  0

It depends upon the relative sizes of the numbers:

It could be negative:  -6 - (-2)   =  -6 + 2    =  -4

If could be zero:        -6 - (-6)   =  -6 + 6    =  0

It could be positive:  -6 - (-10)  =  -6 + 10  =  4

If you subtract a positive number from a negative number, the answer will always be negative.

You can use the slope formula:     m  =  (y2 - y1) / (x2 - x1)

(x1, y1)  =  (2, 3)                   (x2, y2)  =  (7, -4)

----->     m  =  (-4 - 3) / (7 - 2)  =  -7/5 

x² - 16x + y + 68  =  0

--->  y  =  -x² + 16x - 68

Complete the square:

--->  y + 68  =  -x² + 16 x

Factor out the negative sign:

--->  y + 68  =  -(x² - 16 x)

Complete the square by dividing the linear term by 2, squaring the rsult and adding that result to both sides:

--->  y + 68 - 64  =  -(x² - 16x + 64)

--->  y + 4  =  -(x - 8)²

The vertex is:  (8, -4)

The focal length is found using:  f  =  1/(4a)   --->   f  =  1/(4·-1)  =  -1/4

The focal point will be at (8, -4 - 1/4)  =  (8, -4 1/4)

The directrix will be:  y  =  -4 + 1/4   --->   y  =  -3 1/4

Let's see ... since there are 180° in a triangle, the third angle of the first triangle has 180° - 95° - 60°  =  25°.

Since there are  35°  in an angle of the second triangle, there is no chance that the second triangle can be congruent to the first triangle ...

It doesn't make any difference if you are using SAS, SSS, or any of the other congruences.

fI have no idea what  a² + b³  =  c⁴  has to do with the rest of the problem.

     2.347 + (x/8.253)  =  24

Subtract  2.347  from both sides:  (x/8.253)  =  21.653

Multiply both sides by 8.253:                       x  =  178.7  (approx)

If the length of one side of a cube is  x  then the area of that side is  x².

Since a cube has 6 sides, the total surface area is  6x².

If the total surface area is  48     --->     6x²  =  48

       Divide by 6:                                      x²  =  8

       Find the square root:                          x  =  √8

33.3% of 10%  =  0.333 x 0.10  =  0.0333  =  3.33%

You can use the slope formula:     m  =  (y₂ - y₁) / (x₂ - x₁)

(x₁, y₁)  =  (3, 6)                   (x₂, y₂)  =  (-1, 2)

----->     m  =  (2 - 6) / (-1 - 3)  =  -4/-4  =  1