Answer:
its C
Step-by-step explanation:
Answer:
Step-by-step explanation:
a=42,b=58,A=36°
![\frac{sin B}{b} =\frac{sin~ A}{a} \\sin~B=\frac{b \times ~sin~ A}{a} \\\\sin~B=\frac{58 \times sin~36}{42} \\B=sin ^{-1}( \frac{58 \times sin~36}{42} ) \approx 54^\circ](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20B%7D%7Bb%7D%20%3D%5Cfrac%7Bsin~%20A%7D%7Ba%7D%20%5C%5Csin~B%3D%5Cfrac%7Bb%20%5Ctimes%20~sin~%20A%7D%7Ba%7D%20%5C%5C%5C%5Csin~B%3D%5Cfrac%7B58%20%5Ctimes%20sin~36%7D%7B42%7D%20%5C%5CB%3Dsin%20%5E%7B-1%7D%28%20%5Cfrac%7B58%20%5Ctimes%20sin~36%7D%7B42%7D%20%29%20%5Capprox%2054%5E%5Ccirc)
<span>This is the term used to describe economic systems in which the basic economic questions are answered based on a socially, pre-established way.</span>
Compare 1/7 to consecutive multiples of 1/9. This is easily done by converting the fractions to a common denominator of LCM(7, 9) = 63:
1/9 = 7/63
2/9 = 14/63
while
1/7 = 9/63
Then 1/7 falls between 1/9 and 2/9, so 1/7 = 1/9 plus some remainder. In particular,
1/7 = 1/9¹ + 2/63.
We do the same sort of comparison with the remainder 2/63 and multiples of 1/9² = 1/81. We have LCM(63, 9²) = 567, and
1/9² = 7/567
2/9² = 14/567
3/9² = 21/567
while
2/63 = 18/567
Then
2/63 = 2/9² + 4/567
so
1/7 = 1/9¹ + 2/9² + 4/567
Compare 4/567 with multiples of 1/9³ = 1/729. LCM(567, 9³) = 5103, and
1/9³ = 7/5103
2/9³ = 14/5103
3/9³ = 21/5103
4/9³ = 28/5103
5/9³ = 35/5103
6/9³ = 42/5103
while
4/567 = 36/5103
so that
4/567 = 5/9³ + 1/5103
and so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/5103
Next, LCM(5103, 9⁴) = 45927, and
1/9⁴ = 7/45927
2/9⁴ = 14/45927
while
1/5103 = 9/45927
Then
1/5103 = 1/9⁴ + 2/45927
so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/45927
One last time: LCM(45927, 9⁵) = 413343, and
1/9⁵ = 7/413343
2/9⁵ = 14/413343
3/9⁵ = 21/413343
while
2/45927 = 18/413343
Then
2/45927 = 2/9⁵ + remainder
so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/9⁵ + remainder
Then the base 9 expansion of 1/7 is
0.12512..._9
There are two ways to do this
Method 1:
Find (fg)(x) first
(fg)(x) = f(x)*g(x)
(fg)(x) = (x^2-19)*(20-x)
(fg)(x) = 20x^2-x^3-380+19x
(fg)(x) = -x^3+20x^2+19x-380
Then plug in x = -10
(fg)(x) = -x^3+20x^2+19x-380
(fg)(-10) = -(-10)^3+20(-10)^2+19(-10)-380
(fg)(-10) = -(-1000)+20(100)+19(-10)-380
(fg)(-10) = 1000+2000-190-380
(fg)(-10) = 3000-570
(fg)(-10) = 2430
-----------------------------------------
Method 2:
Find f(-10)
f(x) = x^2 - 19
f(-10) = (-10)^2 - 19
f(-10) = 100 - 19
f(-10) = 81
Find g(-10)
g(x) = 20-x
g(-10) = 20-(-10)
g(-10) = 20+10
g(-10) = 30
Multiply the two results
(fg)(-10) = f(-10)*g(-10)
(fg)(-10) = 81*30
(fg)(-10) = 2430
-----------------------------------------
Whichever method you pick, the answer is: 2430