In: Math
In: Math
The function
D(t) = 43.1224(1.0475)^t. gives the number of master’s degrees, in
thousands, conferred on women in the United States t years after
1960. Find the number of master’s degrees earned by women in 1984,
in 2002, and in 2010. Then estimate the number of master’s degrees
that will be earned by women in 2020.?When will the number of
master’s degrees earned by women in the U.S. reach a million?
In: Math
Sketch a graph of f(x)= -2(x-1)^2(x+1), based on all the data about zeros, long run behavior, etc.
In: Math
Question from college algerba webworks:
Find the x and y intercept of
9log6(8-4x)+18
In: Math
The total cost of two calculators and four math sets is R440.00, If a calulator cost R40 more than a math set, what is the cost of each?
In: Math
Three consecutive integers multiply together to give -120
a)Determine a polynomial equation to represent this situation.
b)Using your equation from part (a), determine the three consecutive integers that multiply together to give -120.
In: Math
Consider the matrix B =
−1 1 1 2
−1 1 0 3
−2 2 1 −4
(a) Find ||B||F.
(b) It can be shown (See Saito, Lecture Notes, 5.7) that the 1-norm of a matrix A ∈ Rm×n can be written as ||A||1 = max 1≤j≤n||aj||1 whereaj is the jth column of A. Find||B||1.
(c) Find ||B||2.
(d) It can be shown (See Saito, Lecture Notes, 5.9) that the ∞-norm of a matrix A ∈ Rm×n can be written as kAk∞ = max
In: Math
A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. The perimeter of the window is 8m. (a)Write the area of A of the window as a function of r. (b) What dimensions (length and breadth of a rectangle, radius of semicircle will produce a window of maximum area? Write these dimensions in terms of pie and simplify as far as possible.
In: Math
Suppose θ is an acute angle in a right triangle. Given tan(θ)=1/5, evaluate: 1-sin^2(θ)
In: Math
(a) Find the equation of a plane π that contains the line in the intersection of the planes x+y+3z =
2andx−y+z=1andtheorigin. Howmanysuchplanesarethere?
(b) What if instead of the origin we ask for the plane containing the same line and the point
(0, −1/4, 3/4)? What changes?
(c) Back to the plane π you found in item a, let Rπ be the reflection across π. Pick an explicit
In: Math
identify the equation . If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its centre, vertices, and foci ; if a hyperbola, give its centre, vertices, foci, and asymptotes.
(x + 1)^2/4 - y^2/9−=1
In: Math
Profit = Revenue - Cost
P(x) = R(x) - C(x)
Given: R(x) = x^2 - 30x
Given: C(x) = 5x + 100
X is hundreds of items sold / P, R, C are in hundreds of dollars
(1) Determine the Initial Cost?
(2) Determine the maximum Profit and number of items required for that profit?
(3) Determine the maximum Revenue and number of items required for that revenue?
(4) Find the break even points, P(x) = 0. What do the values represent in relation to the business?
In: Math
Top Toys is planning a new radio and TV advertising campaign. A radio commerical costs $300 and a TV ad costs $2000. A total budget of $20,000 is allocated to the campaign. However, to ensure that each medium will have at least one radio commercial and one TV ad, the most that can be allocated to either medium cannot exceed 80% of the total budget. It is estimated that the first radio commerical will reach 5000 people, with each additional commercial reaching only 2000 more people. For TV, the first ad will reach 4500 people, and each additional ad an additional 3000 people. How should the budgeted amount be allocated between radio and TV?
In: Math