The correct answer is x = 3
15x²+16x+4 =0 (ax² +bx +c=0)
Δ = b²-4ac =256 - 4×15×4 =16
x1 = (-b+√Δ) / 2a = (-16+√16) / 30 =( -16+4) / 30 = -12/30 = - 2/5
x2 = (-b -√Δ) / 2a = (-16 -√16) / 30 = (-16 -4) /30 = -20/30 = -2/3
1) pages per minute is the rate. the rate is the slope pages/minutes = .4
y=.4x or y=2/5(x)
2)birdhouses per day is the slope. = .6
y=.6x or y=3/5(x)
3) miles per hour is the slope. 500/8=62.5
y=62.5x
4) square feet per minute is the slope. 40/9 =4.444444444
y=4.4444444444x or y=40/9(x)
5)miles per minutes is the rate. 5/41 is the slope.
y=5/41(x)
6) the rate is square feet per minute. 450/30=15
y=15x
(a) The sum of length and width is half the perimeter, so the breadth in terms of length (x) in cm will be
.. breadth = 34 -x
(b) Then the expression for the area (in cm^2) is
.. area = length*breadth
.. 253 = (x)(34 -x)
.. x^2 -34x +253 = 0 . . . . . subtract the right side, eliminate parentheses
.. (x -11)(x -23) = 0 . . . . . . . factor
.. x = 11 or 23
The dimensions of the rectangle are 11 cm by 23 cm.
In general, the volume

has total derivative

If the cylinder's height is kept constant, then

and we have

which is to say,

and

are directly proportional by a factor equivalent to the lateral surface area of the cylinder (

).
Meanwhile, if the cylinder's radius is kept fixed, then

since

. In other words,

and

are directly proportional by a factor of the surface area of the cylinder's circular face (

).
Finally, the general case (

and

not constant), you can see from the total derivative that

is affected by both

and

in combination.