Answer:
4.56
Step-by-step explanation:
i see a sector hosting 2 semi circles.
this sector area will be .25 of area of circle with radius 4ft.
area of sector = .25*π*16= 4π ft^2
area of semi circle of radius 2ft = .5π*4= 2πft^2
area of 2 semicircles = 4π
the total area of sector = area of 2 semicircles - intersection area + area not covered by semi circles
4π = 4π - intersection area+area not covered by semi circles
intersection area = area not covered by semi circles
now draw a square starting from the intersection point of 2 semi circles at their upper portion. the side will be 2ft
the area of intersection will be covered in the square.
area of intersection = 2*quarter area of circle of radius 2ft - area of square
= 2*(.25π4) - 4
2π-4 = 2.28
area of intersection = area not covered by semicircle
so area of shaded region = 4.56
From the figure, we immediately have
cos(θ) = 8/17
sin(θ) = 15/17
By definition of tangent,
tan(2θ) = sin(2θ)/cos(2θ)
Recall the double angle identities:
sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1
Then
tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)
tan(2θ) = (2 × 15/17 × 8/17) / (2 × (8/17)² - 1)
tan(2θ) = -240/161
C...to show this, interchange letters: x = (y+1)/(y-1)xy-x = y + 1xy - y) = x + 1y(x-1) = x+1y = (x+1)/(x-1) ⇐ this is f-1(x) and it's identical to f(x). Note: <span>the equal sign is missing in the definitions of the functions c. & d.</span>
B) In triangles ABC and ABD, one side and one common angle are equal
Answer:
4 hours
Step-by-step explanation:
The general formula for distance, rate and time is:
d = rt, where distance is the product of rate multiplied by time
Given that one train is moving at a rate of 70 mph and one is moving at a rate of 62 mph in the opposite direction, the combined distance over time is equal to 528 miles. Using the variable 't' for time:
70t + 62t = 528
Combine like terms: 132t = 528
Divide both sides by 132: 132t/132 = 528/132 or t = 4 hours
