Let:
Philadelphia be point a
Pittsburgh be point b
Distance traveled by Michelle be x
Distance traveled by Rich be 305 x
The general formula is:
distance = velocity (time)
substituting the values:
michelle: X = 65(t)
rich: 305 - X = 70 t
substituting both equations gives:
X = 146.562 miles
t = 2.26 hours or 2 hours and 15 mins
The domain are all valid values for x (the independent variable) that can be used in an equation.
We have to look at any potential values of x which won't work. Easily put: in algebra, just look for values of x which cause either division by zero, or the square root of negative numbers.
A couple of examples:
y=2x+4
You can insert any negative or positive value, or zero, for x and get a valid equation. Therefore the domain is the set of all real numbers. Answers are usually written as:
x: {R}, or simply 'all real numbers'.
what about y=2/(x-1)
In this equation, x appears in the denominator. If x-1=0, then division by zero would occur.
Solve: x-1≠0
x≠1
In set notation:
x: (-∞,1)∪(1,∞)
Parentheses are next to the 1, as the domain comes up to 1, but does not include 1.
Read left to right, the domain is "negative infinity to 1, exclusive, in union with 1 to positive infinity"
Answer:
X = 4
Step-by-step explanation:
In the equation add 3 to both sides of the equation
1/2x-3+3=2-3/4x+3
Simplify
1/2x = -3/4x + 5
Add 3/4x to both sides
1/2x + 3/4x = -3/4x + 5 + 3/4x
Simplify
5/4x=5 Multiply both sides by 5
5x=20 divide both sides by 5
5x divided by 5 and 20 divided by 5
=4
Answer:
2/π ≈ 0.637 m/s
Step-by-step explanation:
The rate of change of area with respect to time is ...
A = πr²
dA/dt = 2πr·dr/dt
Filling in given values in the above equations, we can find r and dr/dt.
25π = πr² ⇒ r = 5
20 = 2π·5·dr/dt
dr/dt = 20/(10π) = 2/π . . . . meters per second
The radius is increasing at the rate of 2/π ≈ 0.637 meters per second.
