Answer :
To solve the given problems, let's break down the steps for each part.
Part 1: Finding the value of [tex]\( x \)[/tex] in the equation [tex]\( x + x = \frac{32}{40} \)[/tex].
1. Simplify the left side of the equation:
[tex]\[
x + x = 2x
\][/tex]
2. Set up the equation:
[tex]\[
2x = \frac{32}{40}
\][/tex]
3. Simplify the right side by dividing 32 and 40 both by 8:
[tex]\[
\frac{32}{40} = \frac{4}{5}
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 2:
[tex]\[
x = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5} = 0.4
\][/tex]
So, the value of [tex]\( x \)[/tex] is 0.4.
Part 2: Finding the value [tex]\( \delta + i \frac{2}{t} \)[/tex] where [tex]\( \frac{30}{150} = \frac{30 - 30}{150 - 30} = \frac{1}{50} \times 0.2 \)[/tex].
1. Simplify [tex]\( \frac{30}{150} \)[/tex]:
[tex]\[
\frac{30}{150} = \frac{1}{5} \times \frac{1}{10} = \frac{1}{50}
\][/tex]
2. Multiply it by 0.2:
[tex]\[
0.2 \times \frac{1}{50} = \frac{0.2}{50} = 0.004
\][/tex]
3. Now, let's assume an expression involving [tex]\(\delta\)[/tex], [tex]\(i\)[/tex], and [tex]\(t\)[/tex]:
[tex]\[
\delta + i \frac{2}{t} = 0.004
\][/tex]
4. Rearrange this equation to solve for [tex]\(\delta\)[/tex] in terms of [tex]\(i\)[/tex] and [tex]\(t\)[/tex]:
[tex]\[
\delta = 0.004 - i \frac{2}{t}
\][/tex]
So, the expression for [tex]\(\delta\)[/tex] is given by:
[tex]\[
\delta = 0.004 \left(\frac{-500.0i + t}{t}\right)
\][/tex]
Thus, the result for the unknowns are:
- The value of [tex]\( x \)[/tex] is 0.4.
- The expression in terms of [tex]\(\delta\)[/tex] is [tex]\(\delta = 0.004 \left(\frac{-500.0i + t}{t}\right)\)[/tex].
Part 1: Finding the value of [tex]\( x \)[/tex] in the equation [tex]\( x + x = \frac{32}{40} \)[/tex].
1. Simplify the left side of the equation:
[tex]\[
x + x = 2x
\][/tex]
2. Set up the equation:
[tex]\[
2x = \frac{32}{40}
\][/tex]
3. Simplify the right side by dividing 32 and 40 both by 8:
[tex]\[
\frac{32}{40} = \frac{4}{5}
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 2:
[tex]\[
x = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5} = 0.4
\][/tex]
So, the value of [tex]\( x \)[/tex] is 0.4.
Part 2: Finding the value [tex]\( \delta + i \frac{2}{t} \)[/tex] where [tex]\( \frac{30}{150} = \frac{30 - 30}{150 - 30} = \frac{1}{50} \times 0.2 \)[/tex].
1. Simplify [tex]\( \frac{30}{150} \)[/tex]:
[tex]\[
\frac{30}{150} = \frac{1}{5} \times \frac{1}{10} = \frac{1}{50}
\][/tex]
2. Multiply it by 0.2:
[tex]\[
0.2 \times \frac{1}{50} = \frac{0.2}{50} = 0.004
\][/tex]
3. Now, let's assume an expression involving [tex]\(\delta\)[/tex], [tex]\(i\)[/tex], and [tex]\(t\)[/tex]:
[tex]\[
\delta + i \frac{2}{t} = 0.004
\][/tex]
4. Rearrange this equation to solve for [tex]\(\delta\)[/tex] in terms of [tex]\(i\)[/tex] and [tex]\(t\)[/tex]:
[tex]\[
\delta = 0.004 - i \frac{2}{t}
\][/tex]
So, the expression for [tex]\(\delta\)[/tex] is given by:
[tex]\[
\delta = 0.004 \left(\frac{-500.0i + t}{t}\right)
\][/tex]
Thus, the result for the unknowns are:
- The value of [tex]\( x \)[/tex] is 0.4.
- The expression in terms of [tex]\(\delta\)[/tex] is [tex]\(\delta = 0.004 \left(\frac{-500.0i + t}{t}\right)\)[/tex].
