Tutors Answer Your Questions about expressions (FREE)
Question 1180555: Greetings,
I am having troubles solving this question and confused on how to start: If f (x1, x2) = a + bx1 + cx2 + dx1x2, what is f (x1 + k, x2) - f (x1, x2)?
Do i just plug in x1 + k every time I see x1 for the first part?
If you could provide the solution and a brief explanation thank you!
Click here to see answer by math_tutor2020(3817)  |
Question 1181183: JC bought a new car for $22,600. Its value is declining by $3500 per year. Let x be the year since JC bought the car, and y be the value of the car for year x. Write an equation in terms of x and y to estimate the value of the car for a given year.
Click here to see answer by ikleyn(52831)  |
Question 1181227: Alice, Bob, and Cindy each drive about1000 miles per month. Alice drives a truck which gets 10 mpg. Bob drives a 20 mpg car. Cindy drives a smaller vehicle which averages 40mpg. The goal is to find the 3 friend’s “average”mpg...Computing the regular arithmetic mean of the 3 mpg will lead to an incorrect average. Instead, there are two alternatives. One, invert each mpg to get gpm then compute the arithmetic mean, then re-invert back to mpg[this method is called a Harmonic Mean]. Two, find the total number of miles driven and the total number of gallons used, then divide.Execute one or both of these methods and compare/contrast to the incorrect arithmetic mean. The three friends plan to buy newer, more efficient vehicles. Alice’s new truck will get 13mpg. Bob is upgrading toa 28mpg car.Cindy is looking at a 55mpg hybrid. Who will save more gasoline with these upgrades? What upgraded mpg would the other two have needed in order to save the same amount? Again,there are two ways to find the answers. One, compare the gpm for each person’s new car to their old car. Then find out how many gpm are saved by each person. Finally, take the largest saved gpm and apply that savings to the other two before inverting back. Two, compare the gallons used for each person’s new car to their old car (each month). Then take the largest saved number of gallons and apply to the other two.
Click here to see answer by ikleyn(52831) |
Question 1182967: I am trying to figure out how to write a mathematical statement for the following question:
"Jill was playing a game with her sister. Jill was down by 5. After her next turn, she was down by 3. Write a mathematical statement that represents this scenario."
Should the statement be written as x - 5, x - 3 ?
Click here to see answer by Theo(13342)  |
Question 1183856: Hello please help me solve this mathematical induction question, using "replacement method" of Mathematical Induction prove that for all integers n > or equal to 1:
1^3 + 3^3 + 5^3 + ... to n terms = n^2 * (2n^2 - 1)
Thank you
Click here to see answer by ikleyn(52831) |
Question 1183852: If x+y equals an  odd number and x+z equals an even number, each of the following could be true EXCEPT
A. x is even and y is odd
B. y is even and z is odd
C. X and z are even and y is odd
D. x and y are even and z is odd.
Click here to see answer by ikleyn(52831) |
Question 1184045: A. Let g(t) be the solution of the initial value problem
4t(dy/dt)+y=0, t>0,
with g(1)=1.
Find g(t).
g(t)= My answer is t^(-1/4), is correct.
B. Let f(t) be the solution of the initial value problem
4t(dy/dt)+y=t^4
with f(0)=0.
Find f(t).
f(t)= My answer is 1/4t^(1/3), it's wrong
C. Find a constant c so that
k(t)=f(t)+cg(t)
solves the differential equation in part B and k(1)=14.
c=
Click here to see answer by robertb(5830)  |
Question 1184057: Solve xy′=9y−4x,y(1)=2.
(a) Identify the integrating factor, α(x).
α(x) = My answer is x^(-9), correct.
(b) Find the general solution.
y(x)= My answer is x/2+Cx^9 , correct.
Note: Use C for the arbitrary constant.
(c) Solve the initial value problem y(1)=2.
y(x)= My anwer is x/2-((x-4)/(2x^9))x^9, but is a wrong
Click here to see answer by MathLover1(20850)  |
Question 1184076: The differential equation
y−2y^3=(y^5+2x)y′
can be written in differential form:
M(x,y)dx+N(x,y)dy=0
where M(x,y)=My answer is x/y^2, wrong
------N(x,y)= My answer is y^3-((2x)/y^3), wrong
The term M(x,y)dx+N(x,y)dy becomes an exact differential if the left hand side above is divided by y^3. Integrating that new equation, the solution of the differential equation is
My answer (x/y^2)-(y^3/3)-2x=C , correct
Click here to see answer by robertb(5830) |
Question 1184693: In this problem you will use variation of parameters to solve the nonhomogeneous equation t^(2)y′′+ty′−4y=3t^(3)+2t^(2)
A. Plug y=tn into the associated homogeneous equation (with "0" instead of "3t3+2t2") to get an equation with only t and n.
My answer n(n-1)t^n+nt^n-4t^n=0 , CORRECT
B. Solve the equation above for n (use t≠0 to cancel out the t).
You should get two values for n, which give two fundamental solutions of the form y=t^(n).
My answer y1= t^2 , y2= 1/t^2 , W(y1,y2)= -4/t , CORRECT
C. To use variation of parameters, the linear differential equation must be written in standard form y′′+py′+qy=g. What is the function g?
My answer g(t)= 3t+2 , CORRECT
D. Compute the following integrals.
∫y1g/W dt= -3/20t^5-1/8t^4 , CORRECT
∫y2g/W dt= -1/4(3t+2ln(t)) , CORRECT
E. Write the general solution. (Use c1 and c2 for c1 and c2).
y=c1t^2+c2/t^2-3/20t^7-1/8t^6-3/4*1/t+2/t^2ln(t) , WRONG
Click here to see answer by robertb(5830) |
Question 1186674: The differential equation
y+y3=(y5+2x)y′
can be written in differential form:
M(x,y)dx+N(x,y)dy=0
where
M(x,y)=
, and N(x,y)=
.
The term M(x,y)dx+N(x,y)dy becomes an exact differential if the left hand side above is divided by y3. Integrating that new equation, the solution of the differential equation is
=C.
Click here to see answer by Edwin McCravy(20060)  |
Question 1186838: Have I simplified the below algebraic expession correctly?
a^3-27/2a^3-18a
Factor the expressions that are not already factored.
2a(a−3)(a+3)
(a−3)(a
2
+3a+9)
Cancel out a−3 in both numerator and denominator.
2a(a+3)
a
2
+3a+9
Expand the expression with answer of:
a^2+3a+9/2a^2+6a
Thank you
Click here to see answer by MathLover1(20850) |
Question 1186845: Have I answered the 2 product and quotient of each given expression below?
PROBLEM 1
X^2-Y^2/(X=Y)^2 times 2x+2y/3x -----------I come up with (x+y)(2x+2y)/3x(x-y)
PROBLEM 2
X^2+3X-28/X^2-16 Divided by x^2-1/x+4 ------- I come up with x+7/x^2-1
Thank you
Click here to see answer by MathLover1(20850) |
Question 1186845: Have I answered the 2 product and quotient of each given expression below?
PROBLEM 1
X^2-Y^2/(X=Y)^2 times 2x+2y/3x -----------I come up with (x+y)(2x+2y)/3x(x-y)
PROBLEM 2
X^2+3X-28/X^2-16 Divided by x^2-1/x+4 ------- I come up with x+7/x^2-1
Thank you
Click here to see answer by MathTherapy(10555)  |
Question 1186845: Have I answered the 2 product and quotient of each given expression below?
PROBLEM 1
X^2-Y^2/(X=Y)^2 times 2x+2y/3x -----------I come up with (x+y)(2x+2y)/3x(x-y)
PROBLEM 2
X^2+3X-28/X^2-16 Divided by x^2-1/x+4 ------- I come up with x+7/x^2-1
Thank you
Click here to see answer by greenestamps(13203)  |
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