geno3141

Volume = length x width x height

7 1/2  =  7.5                                                           1/4  =  .25

17 3/4  =  17.75                                                     1/8  =  .125

Volume  =  7.5 x 17.75 x 9   =               <---  answer  (calculator time!)

9i x 5i  =  (9x5) x (i x i)  =  45i²

Since i²  =  -1:      45i²  =  45(-1)  =  -45

In this right triangle, when referring to ∠B, the name given to side a is "adjacent" and the name given to side c is "hypotenuse".

Again referring to ∠B, cos = adjacent/hypotenuse, so:  cos(∠B) = a/c   --->  cos(∠B)  =  5/13.

To find the size of ∠B, use cos^-1   --->  ∠B  =  cos^-1(5/13)  --->   ∠B  =  67.38°.

No.

For example, say that x = 30°:

cos(30°)  =  √3/2     (approximately 0.8660)

sec(x) = 1 / cos(x)   --->   sec(30°)  =  1 / (√3 / 2)  =  2/√3    (approximately 1.1547)

-sec(30°) + 1  =  -2/√3 + 1   (approximately -0.1547)

And, this isn't cos(30°).

A formula for the n^th term of a geometric sequence is:  t_n  =  a·r^n-1  

     where a is the first term, n is the number of the term, and r is the common ratio.

If the fifth term is 972 and the common ratio is 3  --->   t₅  =  972 and r = 3:   

     t₅  =  a·3^5-1   --->     972  =  a·3⁴   --->   972  =  a·81   --->   a  =  972/81  =  12

m^-5  =  1/m⁵

32  =  2⁵

m^-5  =  1/32   --->  1/m⁵  =  1/2⁵   --->   m⁵  =  2⁵   --->  m  =  2

1 oz  =  29.5735 ml   (approximately)

So:  1 oz / $20.00  =  29.5735 ml / $20.00

You can set up a proportion:

--->    29.5735 ml / $20.00  =  1 ml / x

cross multiply:  29.5735 · x  =  20.00 · 1

--->                                  x  =  $0.68

Use the distance formula:     d  =  √[ (x2 - x1)² + (y2 - y1)² ]

   (x1, y1) = (-1, 5)  --->   x1 = -1     y1 = 5

   (x2, y2) = (0, 4)   --->   x2 = 0      y2 = 4

--->   d  =  √[ (x2 - x1)² + (y2 - y1)² ]

--->   d  =  √[ (0 - -1)² + (4 - 5)² ]

--->   d  =  √[ (1)² + (-1)² ]

--->   d  =  √[ 1 + 1 ] 

--->   d  =  √2

 ....   finish this with a calculator   ....

Multiply the area of one of the bases by 2 and add that answer to the lateral area (area of the sides).

The reason that you multiply the area of the base by 2 is because you have two bases, the top and the bottom.

If you want a decimal approximation, you can use the calculator:  √(25/35) = 0.8451546547...

If you want it into simplest radical form:  √(25/35)  =  √(5/7)  =  √5 / √7

   To simplify, multiply the numerator and the denominator by the denominator:

            √5 / √7   x   √7 / √7    =    √35 / √49    =    √35 / 7