Answer:
Step-by-step explanation:
Since A = 50 degrees, c = 10 ,and since it is a right Triangle, then C = 90 degrees and so B = 180 - (90 +50)......... sum of angles of a triangle
B = 180 - 140
B = 40 degrees
Using sine rule : a/sin A = b / sin B = c / sin C
To calculate a, then we use a/ sin A = c / sin C , since we know c and C
i.e a/ sin 50 = 10 / sin 90
recall that sin 90 = 1
then we have a / sin 50 = 10 / 1
cross multiply
a = 10 x sin 50
a = 10 x 0.76604
a = 7.6604
We will calculate b following the same procedure
b/ sin B = c / sin C
b/ sin 40 = 10/ sin 90
b/ sin 40 = 10/ 1
b = 10 x sin 40
b = 10 x 0.64279
b = 6.4279
Therefore a ≈7.6604 , b ≈ 6.4279
Step-by-step explanation:
13.
132 miles in 3 h = 132miles/3hours = 132/3 miles/h =
= 44 miles/h
so,
how long for 110 miles ?
speed = distance/time
time = distance/speed = 110 miles / 44 miles/h =
= 110/44 h = 55/22 h =
= 5/2 h = 2.5 h
14.
60% = 60/100 = 6/10 = 3/5
15.
300% = 300/100 = 3
16.
116 2/3% = (348 + 2)/3% = 350/3% = 350/3/100 =
= 350/300 = 1 50/300 = 1 1/6
17.
19% = 19/100
18.
3.8% = 3.8/100 = 38/1000 = 19/500
19.
166 2/3% = (498 + 2)/3% = 500/3% = 500/3/100 =
= 500/300 = 5/3 = 1 2/3
20.
4/5 = 0.8 = 80%
21.
7/4 = 1.75 = 175%
22.
1/3 = 0.3333333... ≈ 33.33%
23.
2 = 200/100 = 200%
24.
0.4 = 40%
25.
0.375 = 37.5/100 = 37.5%
26.
80% of 60 = 60×80/100 = 60×4/5 = 48
27.
24% of 65 = 65×24/100 = 65×6/25 = 13×6/5 =
= 15.6
28.
115% of 138 = 138×115/100 = 138×23/20 =
= 69×23/10 = 158.7
29.
18.3% of 74 = 74×18.3/100 = 74×183/1000 =
= 37×183/500 = 13.542 ≈ 13.54
30.
6.5% of 115 = 115×6.5/100 = 115×65/1000 =
= 23×13/40 = 7.475 ≈ 7.48
31.
0.75% of 93 = 93×0.75/100 = 93×75/10000 =
= 93×3/400 = 0.6975 ≈ 0.70
![\bf \begin{array}{clclll} -6&+&6\sqrt{3}\ i\\ \uparrow &&\uparrow \\ a&&b \end{array}\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bclclll%7D%0A-6%26%2B%266%5Csqrt%7B3%7D%5C%20i%5C%5C%0A%5Cuparrow%20%26%26%5Cuparrow%20%5C%5C%0Aa%26%26b%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%0A%5Ctheta%20%3Dtan%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7Bb%7D%7Ba%7D%20%5Cright%29%0A%5Cend%7Bcases%7D%5Cqquad%20r%5Bcos%28%5Ctheta%20%29%2Bi%5C%20sin%28%5Ctheta%20%29%5D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.
thus
![\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]](https://tex.z-dn.net/?f=%5Cbf%2012%5Cleft%5Bcos%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%2Bi%5C%20sin%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%5Cright%5D)
Substitute the value of y in the equation as -1,
(-1)^2-31(-1)-17 = 1+31-17 = 15
Answer:
(x,y)→(y,-x)
Step-by-step explanation:
Parallelogram ABCD:
A(2,5)
B(5,4)
C(5,2)
D(2,3)
Parallelogram A'B'C'D':
A'(5,-4)
B'(4,-5)
C'(2,-5)
D'(3,-2)
Rule:
A(2,5)→A'(5,-2)
B(5,4)→B'(4,-5)
C(5,2)→C'(2,-5)
D(2,3)→D'(3,-2)
so the rule is
(x,y)→(y,-x)
