Answer:
Part 1) The domain of the quadratic function is the interval (-∞,∞)
Part 2) The range is the interval (-∞,1]
Step-by-step explanation:
we have
This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)
step 1
Find the domain
The domain of a function is the set of all possible values of x
The domain of the quadratic function is the interval
(-∞,∞)
All real numbers
step 2
Find the range
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have a vertical parabola open downward
The vertex is a maximum
Let
(h,k) the vertex of the parabola
so
The range is the interval
(-∞,k]
Find the vertex
Factor -1 the leading coefficient
Complete the square
Rewrite as perfect squares
The vertex is the point (7,1)
therefore
The range is the interval
(-∞,1]
Answer:
An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. The opposite of an ordinary annuity is an annuity due, in which payments are made at the beginning of each period.
Step-by-step explanation:
You can ask Siri. Answer is Increased 75%. “What percent is 56 out of 32.”
Answer:
2 feet 9 inches
Step-by-step explanation:
Radius = Diameter/2
Answer:
0.28cm/min
Step-by-step explanation:
Given the horizontal trough whose ends are isosceles trapezoid
Volume of the Trough =Base Area X Height
=Area of the Trapezoid X Height of the Trough (H)
The length of the base of the trough is constant but as water leaves the trough, the length of the top of the trough at any height h is 4+2x (See the Diagram)
The Volume of water in the trough at any time
=8h(8+2x)
V=64h+16hx
We are not given a value for x, however we can express x in terms of h from Figure 3 using Similar Triangles
x/h=1/4
4x=h
x=h/4
Substituting x=h/4 into the Volume, V
h=3m,
dV/dt=25cm/min=0.25 m/min
=0.002841m/min =0.28cm/min
The rate is the water being drawn from the trough is 0.28cm/min.
