Let ABC be a triangle in the 3rd quadrant, right-angled at B.
So, AB-> Perpendicular BC -> Base AC -> Hypotenuse.
Given: sinθ=-3/5 cosecθ=-5/3
According to Pythagorean theorem, square of the hypotenuse is equal to the sum of square of the other two sides.
Therefore in triangle ABC, 〖AC〗^2=〖AB〗^2+〖BC〗^2 ------
--(1)
Since sinθ=Perpendicular/Hypotenuse ,
AC=5 and AB=3
Substituting these values in equation (1)
〖BC〗^2=〖AC〗^2-〖AB〗^2
〖BC〗^2=5^2-3^2
〖BC〗^2=25-9
〖BC〗^2=16
BC=4 units
Since the triangle is in the 3rd quadrant, all trigonometric ratios, except tan
and cot are negative.
So,cosθ=Base/Hypotenuse Cosθ=-4/5
secθ=Hypotnuse/Base secθ=-5/4
tanθ=Perpendicular/Base tanθ=3/4
cotθ=Base/Perpendicular cotθ=4/3
Answer:
no solution
Step-by-step explanation:
y = -2x + 3
6x + 3y = -3
the substitution method means you plug one equation into the next, because the first equation gives us a solution for y we can go ahead and plug that into y of the second equation
6x + 3(-2x + 3) = -3
6x - 6x + 9 = -3
9 = -3
which is false meaning that there are no solutions and the lines don't touch at any point
Answer:
Water left in tank is 
gallons.
Step-by-step explanation:
Given :
Capacity of tank = 9.5 gallons 
Water taken out of tank =
gallons
We have to find the water left in the tank.
Water left in the tank = Total capacity of tank - water taken out of tank
=
Taking LCM of (3,10)= 30
Solving further, we get,
Thus, Water left in tank is gallons..
Answer:
Step-by-step explanation:
MX = XN
5r² + 2r + 52 = 4r² + 12r + 27
5r² - 4r² + 2r - 12r + 52 - 27 = 0
r² - 10r + 25 = 0
(r - 5)² = 0
r - 5 = 0
r = 5
4r² + 12r + 27
4•5² + 12•5 + 27
4•25 + 60 + 27
100 + 60 + 27
187
The Second one
I hope I helped you.
