The pair is any numbers, 1 positive and one negative, that add up to -3.
Here is a sample;
(-5, 2)
4*5,2*12,in any even number way
Answer:
0
1
Step-by-step explanation:
First question:
You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.
![\dfrac{a}{\sin A} = \dfrac{b}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Ba%7D%7B%5Csin%20A%7D%20%3D%20%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%20)
![\dfrac{10}{\sin 30^\circ} = \dfrac{40}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B10%7D%7B%5Csin%2030%5E%5Ccirc%7D%20%3D%20%5Cdfrac%7B40%7D%7B%5Csin%20B%7D%20)
![\dfrac{1}{0.5} = \dfrac{4}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B0.5%7D%20%3D%20%5Cdfrac%7B4%7D%7B%5Csin%20B%7D%20)
![\sin B = 2](https://tex.z-dn.net/?f=%20%5Csin%20B%20%3D%202%20)
The sine function can never equal 2, so there is no triangle in this case.
Answer: no triangle
Second question:
You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.
![\dfrac{b}{\sin B} = \dfrac{c}{\sin C}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%20%3D%20%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D%20)
![\dfrac{10}{\sin 63^\circ} = \dfrac{}{\sin C}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B10%7D%7B%5Csin%2063%5E%5Ccirc%7D%20%3D%20%5Cdfrac%7B%7D%7B%5Csin%20C%7D%20)
![\sin C = \dfrac{8.9\sin 63^\circ}{10}](https://tex.z-dn.net/?f=%20%5Csin%20C%20%3D%20%5Cdfrac%7B8.9%5Csin%2063%5E%5Ccirc%7D%7B10%7D%20)
![C = \sin^{-1} \dfrac{8.9\sin 63^\circ}{10}](https://tex.z-dn.net/?f=%20C%20%3D%20%5Csin%5E%7B-1%7D%20%5Cdfrac%7B8.9%5Csin%2063%5E%5Ccirc%7D%7B10%7D%20)
![C \approx 52.5^\circ](https://tex.z-dn.net/?f=%20C%20%5Capprox%2052.5%5E%5Ccirc%20)
One triangle exists for sure. Now we see if there is a second one.
Now we look at the supplement of angle C.
m<C = 52.5°
supplement of angle C: m<C' = 180° - 52.5° = 127.5°
We add the measures of angles B and the supplement of angle C:
m<B + m<C' = 63° + 127.5° = 190.5°
Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.
Answer: one triangle
Answer: 24
A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.
the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.
The general equation for the vertical hyperbola is
[ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1
The conjugate axis of the vertical hyperbola is y = k
Length of the conjugate axis = 2b
According to the question k = 2, h = -1, a = 4, b = 12
Length of the conjugate axis = 2b = 2 * 12 = 24
Learn more about hyperbola here :
brainly.com/question/3351710
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