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Assume that 3 divides n, and that 3 doesn't divide m. Prove that 3 doesn't divide n + m. (Suggest n=3k, n=3k+1, and n=3k+2 to satisfy all integers n for some integer k.)
For some unknown reason, we desire to spend exactly $100 on 100 animals at Animal Rescue Society. Dogs cost $15 each, cats are $1, and mice are four for the dollar. We have to purchase at least one
Two particles A and B break loose from the comet. They've the same density. The radius of A is 10 times that of B. The gravitational force on A is ___ that on B.
In study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browswer.
Is it possible to find out the intersection of two matrices if the matrices don't equal each other. Say, H = (1,2,3,4) which is a 2x2 matrix and K= (5,6,7,8) which is a 2x2 matrix. So what would HnK
A 200 liter tank initially haves 100 liters of pure brine. Pure water is added at the rate of 2 L/min, and well-stirred mixture is drained at a rate of 1 L/min. How much brine remains when the tank
A vertical conical tank which is the 10ft tall with radius of 6 feet at the top is full of water. How much work is done to empty bottom two feet of water over the top of tank? THEN, empty the top t
Transform homogeneous equation dy/dx=sqrt x^2+xy+y/2x+y into seperable first-order equation by using the appropriate substitution. You do not need to solve the resulting equation.
A 200 liter tank initially haves 100 liters of pure brine. Pure water is added at the rate of 2 L/min, and well-stirred mixture is drained at the rate of 1 L/min. How much brine remains when the ta
Determine the approximate solution to the initial value problem dy/dx = 4x+1/2y;y(0)=1 at the point x = 1, using a single step of size h = 1.
Transform the homogeneous equation dy/dx=sqrt x^2+xy+y/2x+y into seperable first-order equation by using the appropriate substitution. You do not need to solve the resulting equation.
Find out the roots of the simultaneous nonlinear equations (x-4)^2 + (y-4)^2 = 5 x^2 + y^2 = 16 Employ a graphical approach to obtain your initial guesses.
A population of fish in the lake grows at the rate proportional to its population. There are originally 600 fish in the lake and in the absence of any outside factors, the population will double in
A population of fish in lake grows at the rate proportional to its population. There're originally 600 fish in the lake and in absence of any outside factors, the population will double in 4 months
Find out the roots of the simultaneous nonlinear equations (x-4)^2 + (y-4)^2 = 5 x^2 + y^2 = 16 Use a graphical approach to obtain your initial guesses. Determine refined estimates with the two-equ
The air in the room 50 ft by 20 ft by 8 ft tests 0.2% carbon dioxide. Starting at t=0, outside air testing 0.05% carbon dioxide is admitted to room. How many cubic feet of this outside air should b
A DNA chain is string of As, Ts, Gs, and Cs. How many DNA chains are there of length 12 which have the following properties? Has string of 10 or more consecutive Gs.
Suppose that the risk free rate is 3.5%. Determine the premium of one-year call option with strike price of $38.50, if the profit of the buyer of the call is $4.78 and stock spot price is $44.34 at
Find out the current i at any time t after the switch is closed. 3 Determine the maximum current that can be obtained from the simple circuit?
Determine the relation between recursion and induction? How do you go about finding an explicit (closed-form) formula for a recursion relation?
Prove the following Theorem. If (X,d) is a metric space, then there is bounded metric on X which is equivalent to d. recall: When we say a metric p is bounded, we mean that there exists an M >0
Find the value of k so that the given differential equation is exact. (y^3 + kxy^4 ? 2x) dx + (3xy^2 + 24x^2(y^3)) dy = 0.
Find out whether the given differential equation is exact. If it is exact, solve it. (y ln y ? e?xy) dx + (1/y + x ln y) dy = 0.
The following data can be employed to approximate the integral: M = ?3? ÷ 2 0 cos x dx N1(h) = 2.356194 N1(h ÷ 2) = -0.4879837 N1(h ÷ 4) = -0.8815732 N1(h ÷ 8) = -0.97091
Show that the following equation has a solution of the form u(x,y) = e^(ax+by). Find the constants a and b: u_xx + u_yy = 5e^(x-2y)