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One of the congruent angles of the isosceles triangle given above is 40° which means that the other angle, mPRQ is also 40°. Knowing that the sum of the angles of a triangle is 180°, mPQR may be calculated by,
mPQR = 180 - (mPRQ + mQPR)
Subsituting the given,
mPQR = 180 - (40 + 40) = 100°
Thus, the answer is 100°.
Answer:
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
Substitute the value of a in the equation
Hence the general solution to the differential equation is
Answer:
99 ft^2
Step-by-step explanation:
In order to find the area, you have to take the area of the rectangle and subtract it with the area of the triangle
Equation for area of a rectangle: w x L
L = 12ft
w = 10ft
12 x 10 = 120ft^2
Equation for area of a triangle: 1/2(h x b)
h = 7ft
b = 6ft
1/2(7 x 6)
1/2(42) = 21ft^2
120 - 21 = 99ft^2
1250mph you'd tear through the crust of the earth and create a supervolcano to end all of us.
Step-by-step explanation:
Never fall that fast when parachuting, only you can prevent supervolcanoes.