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kondor19780726 [428]
3 years ago
8

Evaluate the expression for the value given. 6a 4a; when a = 2

Mathematics
2 answers:
kap26 [50]3 years ago
8 0

Answer:

20

Step-by-step explanation:

6(a)+4(a).

6(2)+4(2)=12+8=20

final answer is 20

Kipish [7]3 years ago
8 0
The answers are
6a= 12
4a= 8
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why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a
zheka24 [161]

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

5 0
3 years ago
$800 at 7% compounded annually for 2 years
Marina86 [1]

Answer:

$115.92

Step-by-step explanation:

To calculate compound interest, which Amount - Principal but we dont know the value for amount so we find the amount first by using the formula.

               A =  P ( 1 +   <u>R</u> ) ^n

                                 100      

where p = principal    ($800)            

a =  amount       (?)

r =  interest rate    (7%)

n = time ( no of years)    (2)

A  =  800   ( 1   +   <u>7 </u>) ^2

                          100                  A = 800 ( 1 + 0.07) ^2

                                                  A = 800 ( 1.07)^2   = 800 ( 1.1449)

A = 915.92.

We then find compound interest with:    

C = Amount - Principal   =   $915.92  -  $800    =    $115.92

7 0
2 years ago
What is a capacity of 25 fl oz more than a capacity of 3 cups
nata0808 [166]
I’m guessing 2 cups or something idk
7 0
3 years ago
Only answer if you know this if i see a link its a report<br> ∞√5±x+5√15x+∞=
fenix001 [56]

Answer:

the exact form is 2/5. the decimal form is 0.4 ig

Step-by-step explanation:

8 0
3 years ago
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$4 for <br> 1<br> 4<br> of a pie. What is the cost of a whole pie?
s2008m [1.1K]

Answer:

$16

Step-by-step explanation:

1/4x4=1

So 4x4 = 16

4 0
3 years ago
Read 2 more answers
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