Answer: x=-0.4
Step-by-step explanation:
Answer:
$395
Step-by-step explanation:
Answer:
The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 1250.51 ft
Step-by-step explanation:
The arch is represented by the equation
y = - .000495 x² + .619 x where x and y are in ft .
We can write this equation in the form
y = - a x² + bx
The vertex is on the line
x = b / 2a
= .619 / 2 x .000495
= 625.25
Putting the value in the equation above
y = - .000495 ( 625.25)²
= 193.51 ft
This value will give us the depth of river .
To know the width of bridge we shall have to solve the quadratic equation
- .000495 x² + .619 x = 0
x = [- .619 ± √ ( .619)² - 0] / 2 x .000495
= - .619 + 625.25 and
x = - .619 - 625.25
Difference = 625.25 x 2 = 1250 .51 ft.
So the width of the bridge will be 1250 .51 ft .
Answer:
C: a reflection across the y axis rotated 180 degrees
Step-by-step explanation:
The y axis is a vertical line, the same like that the trapezoid is flipped across
The trapezoid is rotated 180 degrees across the y axis
Hmm, the 2nd derivitve is good for finding concavity
let's find the max and min points
that is where the first derivitive is equal to 0
remember the difference quotient
so
f'(x)=(x^2-2x)/(x^2-2x+1)
find where it equals 0
set numerator equal to 0
0=x^2-2x
0=x(x-2)
0=x
0=x-2
2=x
so at 0 and 2 are the min and max
find if the signs go from negative to positive (min) or from positive to negative (max) at those points
f'(-1)>0
f'(1.5)<0
f'(3)>0
so at x=0, the sign go from positive to negative (local maximum)
at x=2, the sign go from negative to positive (local minimum)
we can take the 2nd derivitive to see the inflection points
f''(x)=2/((x-1)^3)
where does it equal 0?
it doesn't
so no inflection point
but, we can test it at x=0 and x=2
at x=0, we get f''(0)<0 so it is concave down. that means that x=0 being a max makes sense
at x=2, we get f''(2)>0 so it is concave up. that means that x=2 being a max make sense
local max is at x=0 (the point (0,0))
local min is at x=2 (the point (2,4))