Answer:
By using Carl Gauss's clever formula, (n / 2)(first number + last number) = sum, where n is the number of integers, we learned how to add consecutive numbers quickly. We now know that the sum of the pairs in consecutive numbers starting with the first and last numbers is equal.
Answer:
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})]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bz%3D4%5B%5Ccos%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%20%2B%20i%5Csin%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5D%7D)
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.
Hence, the complex number that has polar coordinate of (4,-45°) is
Answer:
{x,y} = {89/37,-71/37}
Step-by-step explanation:
8x = 3y + 25
[2] x = 3y/8 + 25/8
Plug this in for variable x in equation [1]
[1] 6•(3y/8+25/8) + 7y = 1
[1] 37y/4 = -71/4
[1] 37y = -71
Solve equation [1] for the variable y
[1] 37y = - 71
[1] y = - 71/37
By now we know this much :
x = 3y/8+25/8
y = -71/37
Use the y value to solve for x
x = (3/8)(-71/37)+25/8 = 89/37
An arc is a segment of a circle. An arc measure is the measure of an angle that the arc creates in the center of a circle, while an arc length is the span of the arc. This measure can be given in degrees or radians. We can easily convert between the two using the fact that pi radians = 180 degrees.
