In: Advanced Math
Demand for propane is given by D(x) = 6.5 − 0.25x, and supply is given by S(x) = 2.1 + 0.15x, where x is in gallons per month customer and D(x) and S(x) are dollars per gallon. Find the followings:
(c) Assume a price ceiling of $3 per gallon of propane is imposed. Find the point (Xc, Pc)
(d) Find the new producer surplus and the new consumer surplus at (Xc, Pc).
(e) Find the deadweight loss.
In: Advanced Math
In: Advanced Math
a. Prove the Archimedes result that the area of a section of a parabola equals times the area of the inscribed triangle of the same height. (You may use calculus here.)
b. In what sense can one consider Archimedes to be the inventor of calculus?
c. Find at least five axioms equivalent to the parallel lines axiom. Give the dates when they were proposed and the person that proposed them.
In: Advanced Math
What interest will be earned if $6600 is invested for 8 years at 12% compounded monthly? (Round your answer to the nearest cent.) $
In: Advanced Math
(a) Show that the diagonal entries of a positive definite matrix are positive numbers.
(b) Show that if B is a nonsingular square matrix, then BTB is an SPD matrix.(Hint. you simply need to show the positive definiteness, which does requires the nonsingularity of B.)
In: Advanced Math
For the following exercises, use the given information about the polynomial graph to write the equation.
Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (2, 15).
In: Advanced Math
For the following exercises, use the given information about the polynomial graph to write the equation.
Degree 5. Roots of multiplicity 2 at x = 3 and x = 1, and a root of multiplicity 1 at x = −3. y-intercept at (0, 9)
In: Advanced Math
For the following exercises, evaluate the expressions, writing the result as a simplified complex number.
1/i11 – 1/i21
In: Advanced Math
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.
Contains (1, −6) has the shape of f(x) = 3x2 . Vertex has x-coordinate of −1.
In: Advanced Math
This problem deals with the RC circuit shown to the right containing a resistor (R ohms), a capacitor (C farads), a switch, a source of emf, but no inductor. The differential equation for this circuit is given below.
R(dQ/dT)+1/c(Q)=E(t)
this is an equation for the charge Q(t) on the capacitor at time t. Note that I(t)=Q'(t). Use the values R=100, C=5.0x10^-4, Q(0)=0, and E(t)=100cos120t to find (a) and (b) below:
a: find Q(t) and I(t)
b: What is the amplitude of the steady-state current?
In: Advanced Math
Complex Variable Evaluate the following integrals:
a) int_c (z^2/((z-3i)^2)) dz; c=lzl=5
b) int_c (1/((z^3)(z-4))) dz ; c= lzl =1
c) int_c (2(z^2)-z+1)/(((z-1)^2)(z+1)) dz ; c= lzl=3
(Details Please)
In: Advanced Math
Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations
x = t(v0 cos(θ))
and
y = h + (v0 sin(θ))t − 16t2.
The center field fence in a ballpark is 10 feet high and 400 feet
from home plate. The ball is hit h = 3 feet above the
ground. It leaves the bat at an angle of θ degrees with
the horizontal at a speed of 107 miles per hour (see figure).
(a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and θ.)
| x | = | |
| y | = |
(b) Use a graphing utility to graph the path of the ball when
θ = 15°. Is the hit a home run?
YesNo
(c) Use a graphing utility to graph the path of the ball when
θ = 23°. Is the hit a home run?
YesNo
(d) Find the minimum angle at which the ball must leave the bat in
order for the hit to be a home run. (Round your answer to one
decimal place.)
°
In: Advanced Math
Find the smallest positive integer x that satisfies the system of congruences
x ≡ 3 (mod 5).
x ≡ 5 (mod 7).
x ≡ 7 (mod 11)
In: Advanced Math
Find the system of equations to model the problem. Don't solve the system.
A paper company produces high grade, medium grade and low grade paper. The number of tons of each grade produced from a ton of pulp depends on the source of the pulp. The following table shows three different sources and the amount of each grade of paper that can be produced from one tonne of pulp from each source.
(Number of tons)
High grade Medium grade Low grade
Pulp from Brazil 0.6 0.3 0.1
Domestic pulp 0.5 0.3 0.2
Recycled pulp 0.3 0.4 0.3
The company has received an order for 11 tons of high grade paper, 15 tons of medium grade paper, and 14 tons of low grade paper. How many tons of each type of pulp must be used to accurately fulfill this order? Establish a system of linear equations. Let x, y, and z equal the number of tons of Brazilian pulp, domestic pulp, and recycled pulp, respectively, needed to fulfill the order.
In: Advanced Math