Let x be the number
Subtracting 8 from this = x - 8
Multiplying this by 5 = 5(x - 8)
And this = 20
So....we have
5(x - 8) = 20 divide both sides by 5
x - 8 = 4 add 8 to both sides
x = 12
Ant....I assume that we have a decagon [ regular polygon of 10 sides ] inscribed in a circle??......if so....
The radius, r, of the circle can be found as
r / sin 72 = 10/ sin 36
r = 10sin72 / sin 36 = 5 (1 + √5 )
So....the perimeter of the arc [ arc length of 1/10 of the circle ] is
2pi r / 10 =
2pi [ 5 ( 1 + √5)] / 10 = pi * (1 + √5) units ≈ 10.17 units
OK.....hope that helped
Thanks, tertre.....!!!!
Yeah.... I should have labeled the "65" as "Both"
The number of students who didn't take either =
460 - (75 + 65 + 280 ) = 42
We aren't summing 75 + 30 [ remember that some of this "sum" is being "double-counted"]
We are just noting that 73/460 take only Science.....65/460 take Both and 280/460 take Math
So [ 73 + 65 + 280 ] / 460 = 418/460 take only Math, only Science, or Both
And 42 /460 take neither
Oh yeah.....
In the form
Ax + By = C
The slope is given by -A /B
So....the line -2x + 3y = 1 has the slope = - (-2) / 3 = 2/3
Hope that helps
460 * .30 = 138 take Science
460 * .75 = 345 take Math
Ant.......according to your info....it should be 65 ???
Here's the Venn Diagram
Correct, Ant !!!
Multiples of 6 and 4 from 0 - 170 =
12, 24, 36, 48, 60, 72, 84, 96, 108, 120,132, 144, 156, 168
The line will have the slope = 2/3
The derivative of x^(1/2) = 1 / ( 2√x)
So....to find the x coordiniate of A
2/3 = 1 / ( 2√x)
( 2√x) = 3/2 square both sides
4x = 9/4
x = 9/16
So....the y coordinate of A is (9/16)^1/2 = 3/4
And the equation of the tangent line is
y = (2/3) (x - 9/16) + 3/4
y = (2/3)x - 9/24 + 3/4
y = (2/3)x + 9/24
24y = 16x + 9
16x - 24y = -9
