Answer:
Given the function in the question
f(x) = |x-3| + 2
a) state the name of the function
Absolute value function
since it is similar to f(x) = |x|
b) identify the independent and dependent variable
x = independent variable (input variable)
f(x) or y = dependent variable (output variable)
The variable which we assign the value we call the independent variable, and the other variable is the dependent variable, since it value depends on the independent variable.
c) identify the rule
A function is an equation that has only one answer for y for every x.
d) evaluate the function
given x = -5
f(-5) = |-5 - 3| + 2
= |-8| + 2
= 8 +2
= 10
Answer:
x = 20
Length = 20ft
Width = 12ft
Step-by-step explanation:
A = 240
x^2 - 8x = 240
x^2 - 8x - 240 = 0
x^2 - 20x + 12x - 240 = 0
x(x-20) + 12(x-20) = 0
(x+12)(x-20) = 0
x = 20
x = -12 (which we discard since x is a length)
So the dimensions are 20ft and 20-8 = 12ft
Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
Since we know that LCM of both 625&575 is 14375, we must find the hours it took for both planes to arrive at this same destination.
Plane 1(625): Took 23 hours to arrive.
Plane 2(575): Took 25 hours to arrive.
Therefore, the answer should be from 23-25 hours to arrive or if looking for middle number, 24 hours exactly.
Hope this helps.
Answer:
Function 1:
The starting point is (0,0.5)
As x increases, y increases
Function 2:
The starting point is (0,3)
As x increases, y decreases
Step-by-step explanation:
In order to find the starting point, we need to plug in x=0.
As we plug in increasing numbers into function#1, the y-value increases
As we plug in increasing numbers into function #2, the y-value is decreasing
