# Project #31376 - math

Be sure to show all of your work.

Simplify the following expressions using the imaginary number i:

5√-12

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√-8

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3√-7

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-3√-200

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Write the following numbers using the imaginary number i, and then performed the

3√-9 • 2√-49

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√-12 • √-36

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i√-36 – i2

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3√-9 + 2√4-9

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Simplify the following expressions using the imaginary number i when needed:

i 8

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i 75

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(i 2 ) (i 6)

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Simplify and rationalize the denominators. Show all your work.

4√-3/2

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-3√-2/27

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√-4/27

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Perform the operation indicated in each problem below:

(8 + 6i) + (2 + i)

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-9 +(4 - 2i)

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(1 + i) – (1 - i)

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3i– (4 + 15i)

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Perform the operation indicated in each problem below:

(√2 + 3i)(√2 - 3i)

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(√27 - 3i)(√3 + i)

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(√2 – i√3) (√2 + i√3)

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2i( 3i – 2)

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(3 - 6i)2

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Determine the sum or difference in geometric terms, and then check it algebraically.

Remember that a – b = a + (-b). Show all your work

(8 - 5i) – (2 + 3i)

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(-6 + i) – (-2 -3i)

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(3 + i) + (-2 + 2i) + (8 - 2i)

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Solve the following equations using the quadratic formula.

x2 - 4x + 13 = 0

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x2 + 49 = 0

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x2 + 5x + 8 = 0

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x2 - 3x + 4 = 0

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Find the first three terms in each series, using the given rule. Show all your work.

tn =3n – 1

tn =n + 11

tn =5(2)n

tn =(-2)n

Now, find the rule for each sequence by defining tn.

1, ½, 1/3, ¼, …

2 4, 6, 8,…

Determine whether or not the following sequences can be defined as arithmetic

sequences. Write “yes” or “no.” If it is an arithmetic sequence, state the common

2, 4, 8, 16

2, 4, 6, 8

Find the first three terms of the sequence given the following values for a and d.

a = 5; d = -3

a = 1; d = 8

If the following finite arithmetic term has 15 terms total, then find the last term for

each sequence listed. Show all your work.

1, 5, 9

Find the position number for the term with value of 24 in each sequence. Show all

-25, -18, -11

-9, -6, -3

Find the sum for each of the following arithmetic series below. Use the summation

formula to find the sums. Show all your work.

A series with six terms, the first term is nine and the common difference is

twelve.

A series with five terms, the first term is 5.7 and the common difference is 1.4.

Find the sum of the first 21 terms in a series where a = 20 and t21= 400. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.

Now, find n and Sn for the following arithmetic series below. Show all your work.

2 + 4 + 6 + 8+ …+ 60

Determine if the following sequences would or would not be classified as geometric

sequences. Write “Yes” or “No” for your final answer and explain why. Show all

1, ½, ¼, 1/8

6, -6, 6, -6

Find the first three terms in each of the geometric sequences below, given the

values of a and r. Show all your work.

a = 3/8, r = 4

a = -4, r = 3 -

Use the formula Sn =a (1 - rn ) ÷ (1 – r) to find the sum Sn for each of the geometric

series, given the value for a, r, and n. Show all your work.

a = 6, r = 3, n =4

a = 4, r = ¼, n = 4

Nadia invested \$1,500.00 into a savings account. Her investment will earn her

1% increase every month. The interest is also invested at the same rate. What

is the total interest that she will earn over a two-year period? Show all your

work. \$404.60.

 Subject Mathematics Due By (Pacific Time) 05/23/2014 12:00 am
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