Find the sum. Write your answer in the simplest form. 2 1/2 + 5 5/8

Mathematics

2 answers:

Nostrana [21]3 years ago

7 0

Answer:

D 8 1/8

Step-by-step explanation:

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julia-pushkina [17]3 years ago

5 0

Answer:

(D) 8 1/8

Step-by-step explanation:

In solving fractions in addition or subtraction form, the easiest approach is by identify their lowest common multiple LCM

2 1/2 + 5 5/8

Let's convert the fraction to an improper fraction, so we can comfortably work with the LCM. The equation becomes:

5/2 + 45/8

The LCM here is 8.

Multiplying through by 8 becomes:

= (8) 5/2 + (8) 45/8

= (20 + 45) / 8

= 65 / 8

= 8 1/8

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What complex number is represented by the polar coordinates (4, -pi/4)

nexus9112 [7]

Answer:

$\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

$\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}$

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

$\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$