Answer:
ST = 32
Step-by-step explanation:
First let's call r the radius of the circle, so:
SU = UT = r
Using the formulas of secant and tangent segments in a circle, we have that:
tangent and tangent: QR^2 = QP^2
7x - 19 = 4x + 2
3x = 21
x = 7
tangent and secant:
QP^2 = QS * QT
(4x + 2)^2 = (34 - r) * (34 + r)
900 = 1156 - r^2
r^2 = 256
r = 16
ST = SU + UT = 2*r = 16*2 = 32
Answer:
it is 9x/4 -9
Step-by-step explanation:
This would be rational. If it were an irrational number, the integers on the right side of the decimal would go on forever.
12 I think because its half 24 and 3 x4 =12
The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.