See here, lynx :
https://web2.0calc.com/questions/proof-of-circle-theorems
1. Inverse variation
Let the price of bananas = P and the quantity = Q (in pounds )
Then, the quantity we buy will be greater when the price decreases and less when the price increases
This can be modeled by the function
Q = k / P where k is the variation constant
2.
Discontinuity resulting in a vertical asymptote at x = 5 ⇒ f(x) = 1 / ( x - 5 )
[Occurs when the denominator of a rational function cannot be "factored out " ]
Discontinuity that results in a "hole" at x = 5 ⇒ f(x) = ( x^2 - 25) / (x - 5)
[Occurs when the denominator of a rational function can be "factored out " ]
A vertical asymptote goes through the x axis and is parallel to the y axis
1. (r - c) (3) = r(3) - c(3) =
r(3) = (3)^2+5(3)+14 = 38
c(3) = (3)^2−3(3)+4 = 4
So r(3) - c(3) = 38 - 4 = 34
The store makes a profit of $3400 in the third month of business
2. (p * c) (2) = p(2) * c(2) =
p(2) = 100−2(2) = 96
c(2) = 50+5(2) = 60
So
p(2) * c(2) = 96 * 60 = $5760 when the price per customer = $60
Angle OBQ = 90 ⇒ a radius meeting a tangent forrns a right angle
Angle CBO = 90 - 2x ⇒ ( m ∠OBQ - m∠ CBQ = m ∠ CBO)
Angle OCB = Angle CBO ⇒ In triangle OCB....OB = OC...so the angles opposite these sides are also equal
And in triangle DOC, DO = OC.....so angle CDO = angle DCO = x
So angle BCD = angle OCB + angle ACD = 90 - 2x + x = 90 - x
And minor arc DB = 2 * m∠ DCB = 180 - 2x [ an inscribed angle is measures1/2 of its intercepted arc ] = angle DOB
So......major arc DB = (360) - ( 180 - 2x) = 180 + 2x
And an angle external to a circle and formed by two secants, is equal to one half the difference of the intercepted arcs. This means that
y = (1/2) [ measure of major arc DB - measure of minor arc DB ]
y = (1/2) [ (180 + 2x) - (180 - 2x ) ]
y = (1/2) ( 2x + 2x)
y = (1/2) (4x)
y = 2x
Any that are not divisible by 3 or 5
7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 56, 58, 59
If I didn't miss any....I get 29
2)In the figure with four circles below, let A1 be the area of the smallest circle, let A2 be the area of the region inside the second-smallest circle but outside the smallest circle, and so on. If A1 = A2 = A3 = A4 then find the ratio of the largest radius to the smallest radius.
We can imagine these circles to be concentric..the area between them would still be the same
Without a loss of generality....let the smallest radius = 1
And let the next largest radius = b
And we don't need to worry abut "pi" ... it wll "cancel" in the compuations
The Area of the second smallest circle - Area of smallest circle = Area of smallest circle
b^2 - 1^2 = 1^2
b^2 = 1^2 + 1^2
b^2 = 2
b = √2
Call the radius of the next-to-largest circle "c" ..... so...
Area of this circle - Area of circle with radius "b" = Area of smallest circle
c^2 - 2 = 1
c^2 = 3
c = √3
A call the radius of largest circle = "d"
Area of this circle - Area of circle with radius "c" = Area of smallest circle
d^2 - 3 = 1
d^2 = 4
d = 2
So.... the ratio of the largest circle's radus to the smallest is just
2 / 1 = 2
Let's look at the 6 x 6 case, first
Notice that the number of "vertical" segments is 6(7)
And the number of "horizontal" segments is 6(7)
This implies that the number in a 10 x 10 array should be
2 (10) (11) = 220
I'm assuming that when the problem says " 2s to the right and left and the return to its original position " that the total period is 4 seconds.....
So.... the period is 4 seconds ....
The amplitude is 3
The sine fuction seeks to model this best
In the form
y = Asin (Bx)
A = amplitude = 3
To find B, we need to solve this
B = 2pi / period = 2pi/ 4 = pi/2
So....our function becomes
y = 3sin ( (pi/2) * x )
Here's the graph ....two periods are shown :
https://www.desmos.com/calculator/skrl7kbslk
i believe there is a "formula" for this
We have a pattern of 3 x 3 "boxes"
The possible rectangles = [ 3(4) / 2] * [ 3(4)/2] = [ 6 ] * [ 6 ] = 36
Answered here :
https://web2.0calc.com/questions/three-concentric-circles_1#r1
