Finda + b, 2a + 3b, |a|, and |a − b|.a = 5i + j, b = i − 2j

Step-by-step explanation:

Given the complex notations a = 5i + j, b = i − 2j, we are to evaluate the following:

1) a + b

= 5i+j + (i-2j)

= 5i+j+i-2j

collect like terms

= 5i+i+j-2j

= 6i-j

Hence a+b = 6i-j

2) 2a+3b

= 2(5i+j) + 3(i-2j)

open the parenthesis

= 10i+2j+3i-6j

collect like terms

= 10i+3i+2j-6j

= 13i-4j

Hence 2a+3b = 13i-4j

3) |a| = √x²+y²

Given a = 5i+j; x = 5, y = 1

|a| = √5²+1²

|a| = √25+1

|a| = √26

4) |a-b|

First we need to calculate a-b

=  a - b

= 5i+j - (i-2j)

open the parenthesis

= 5i+j-i+2j

collect like terms

= 5i-i+j+2j

= 4i-3j

|a-b| = √4²+(-3)²

|a-b| = √16+9

|a-b| = √25

|a-b| = 5

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}