Please help me i really want to know the answerand the explanation for this problems
1 answer:
Answer:
M = 4.33885225095
Step-by-step explanation:
Area of the square ABFE = 10² = 100
M = 100 - (2P + Q)
Let’s calculate 2P + Q :
The area 2P + Q = area ΔABC + area of sector ACE + area of sector BCF
Note :
ΔABC is an equilateral triangle
m∠CBF = m∠CAE = 30°
area ΔABC = (CG × AB)÷2 = (8.660254037844×10)÷2 = 43.30127018922
CG = √(10^2 - 5^2)=8.660254037844 (Pythagorean theorem)
area of sector BCF = area ΔACE = 100π ÷ 12 = (8.333333333333)π
then
Area 2P + Q = area ΔABC + area sector ACE + area sector BCF
= 43.30127018922+(100÷12)π+(100÷12)π
= 43.30127018922+ (8.333333333333)π + (8.333333333333)π
= 95.66114774905
Conclusion:
M = 100 - (2P + Q) = 100-95.66114774905 = 4.33885225095
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A(−3,−2), B(−2,2), C(2,−2)
The orthocenter is the meet of the altitudes. We see AC is parallel to the x axis so the perpendicular is the altitude through B.
Between A and B we have slope (2 - -2)/(-2 - -3) = 4 so perpendicular slope -1/4 through C(2,-2):
For the y coordinate of the orthocenter we substitute in x=-2.
So the orthocenter is (x,y)=(-2,-1)
Answer: (-2,-1)
Answer:
2. The airplane will crash into the ground after 5 seconds.
3. The domain of the function is [0,30] and range of the function is .
Step-by-step explanation:
2.
Ariana initial attempt is modeled by the function,
where, h is the height in feet and x is the time in seconds of the paper airplanes path.
If airplane crash into the ground, then ,
Equate each factor equal to 0.
Therefore the airplane will crash into the ground after 5 seconds.
3.
The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.
The value of t must be positive because time can not be negative.
Find the zeros of the function.
The leading coefficient is negative, so the it is a downward parabola. Since the zeros of the function are 0 and 30, therefore the function is negative before 0 and after 30.
The height can not be negative, so the domain of the function is
The vertex of a downward parabola is the maximum point.
Vertex of a parabola,
Put t=15 it in the equation.
The range of the function is
Therefore the domain of the function is [0,30] and range of the function is .