b. Find the real-valued solution to the initial value problem [ ví Use t as the independent variable in your answers. Y₁ (t) = Y2(t) = = y = -3y1-2y2, 5y1 + 3y2, y₁ (0) = −9, y2 (0) = 10.

1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few summers. Her sales over the first two weeks of summer were stacked according to the model S(x) =x³ – 12x2 + 36x , where x is the number of days and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 5 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Describe the weather for the summer in her lemonade-sales model. Predict the number of sales on her last sales day (August 31). Does this seem reasonable?

Ex.: Solve (2D+3D-9)x+(D² +7D-14)= 4 ...() (1)** ..(2) (D+1)x+(D+2)y=0

Find the quadratic y=ax2+bx+c that best fits the data points (−2,−37),(−1,63),(0,−43),(1,−5),(2,2) .   a=   b=   c=

2. The quadratic function y=9-x +4x written in standard form would be (1) y=-x² +4x +9 (3) y=x² – 4x +9 (2) y = x² - 9x +4 (4) y=-x² – 4x +9

9. Show that the graph of the quadratic equation in one variable Ax² + Dx + F = 0 is one line, two parallel lines, or that no real value of x satis- fies the equation, according as the discriminant D² – 4AF is zero, positive, or negative.

Is (1, 19) a solution to ys7x-13 y> 3x+ 6

Find The Values of (X, ZY 2X-24-Z=3 4x+S-22=13 3x+44-37=-7

Find the general solution of (D3-D2+D-1)y = 15sin2x using method of undetermined coefficient.

A town is endowed with an oil reserve. The total stock of oil from the reserve is 110 barrels. The town must sell all 110 barrels within two time periods, so the quantity extracted will be q1 +42 = 110, where 91, for example, is the quantity extracted in period 1. The price per barrel that the town can sell the oil for is på = 150 – in each period. There is a constant cost of extraction e = 50, such that the resource rent earned by each barrel in each period is Te = Pt – c. If the interest rate is 20%, how much oil will the town extract in period 1 and in period 2 (what should q and q2 be) if it wanted to extract efficiently (i.e. maximize profits)?