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:
197 in ^2 (answer B of the list)
Step-by-step explanation:
Notice that this figure has a total of 6 faces, four of which are rectangles (whose area is calculated as "base times height") and two trapezoids (whose area is (B+b)H/2 ).
The total surface area is therefore the addition of these six areas:
Rectangles:
5 in x 5 in = 25 in^2
5 in x 5 in = 25 in^2
5 in x 6.4 in = 32 in^2
9 in x 5 in = 45 in^2
Trapezoids:
Two of equal dimensions: B = 9 in, b = 5 in, H = 5 in
2 * (9 in + 5 in) 5 in /2 = 70 in^2
Which gives a total of (25 + 25 + 32+45 + 70) in^2 = 197 in^2
This agrees with answer B of he provided list.
Sandra has .5 of flour left after making 3 batches of cookies
Let a and b be store A and store B, respectively. Then:
3a+b=63
5a+4b=140
So
12a+4b=252
5a+4b=140
7a=112
a=16
b=15
☺☺☺☺
Answer:
-4, -3, -2, -1, 0
Step-by-step:
1st: 1/4(-8) - 2 = -4 = y
2nd: 1/4(-4) - 2 = -3 = y
3rd: 1/4(0) - 2 = -2 = y
4th: 1/4(4) - 2 = -1 = y
5th: 1/4(8) - 2 = 0 = y
