Concept explainers
Carefully read through the list of terminology we’ve used in Unit 3. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence.
building up
conditional equation
direct variation
equation
equivalent
equivalent equations
exchange rate
generalizing
inequality
line of best fit
linear equation
literal equation
proportion
rate of change
slope
solution
solution to a system
solving a system
system of equations
terms
x intercept
y intercept
A _______________ can be either true or false, depending on what value we choose for the variable quantity.
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PATHWAYS TO MATH LITERACY (LL)W/CONNECT
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- Question 3 (a) Find the principal part of the PDE AU + UÃ + U₁ + x + y = 0 and determine whether it's hyperbolic, elliptic or parabolic. (b) Prove that if U(r, 0) solves the Laplace equation in R², then so is V(r, 0) = U (², −0). (c) Find the harmonic function on the annular region = {1 < r < 2} satisfying the boundary conditions given by U(1, 0) = 1, U(2, 0) = 1 + 15 sin(20). [5] [7] [8]arrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answer Plz .arrow_forward7. (a) (i) Express y=-x²-7x-15 in the form y = −(x+p)²+q. (ii) Hence, sketch the graph of y=-x²-7x-15. (b) (i) Express y = x² - 3x + 4 in the form y = (x − p)²+q. (ii) Hence, sketch the graph of y = x² - 3x + 4. 28 CHAPTER 1arrow_forward
- - (c) Suppose V is a solution to the PDE V₁ – V× = 0 and W is a solution to the PDE W₁+2Wx = 0. (i) Prove that both V and W are solutions to the following 2nd order PDE Utt Utx2Uxx = 0. (ii) Find the general solutions to the 2nd order PDE (1) from part c(i). (1)arrow_forwardSolve the following inhomogeneous wave equation with initial data. Utt-Uxx = 2, x = R U(x, 0) = 0 Ut(x, 0): = COS Xarrow_forwardCould you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward
- (a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS Xarrow_forwardQuestion 3 (a) Find the principal part of the PDE AU + Ux +U₁ + x + y = 0 and determine whether it's hyperbolic, elliptic or parabolic. (b) Prove that if U (r, 0) solves the Laplace equation in R2, then so is V (r, 0) = U (², −0). (c) Find the harmonic function on the annular region 2 = {1 < r < 2} satisfying the boundary conditions given by U(1, 0) = 1, U(2, 0) = 1 + 15 sin(20).arrow_forward1c pleasearrow_forward
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