Applications 11: Exponential and Logarithmic Equations

Z.The regular selling price of merchandise sold in a store includes a margin of62 % based on selling price. During a sale, an item which cost the store $ 231.25 was marked down 47 %. For how much was the item sold? Approximate to the nearest 100th.

A microscope is listed for $ 477.00 less 19 2/3 %, 9 %, 7.7 %. What is the equivalent single rate of discount that was allowed? Give your answer in percentage to the nearest 100th.

The Scientific Store received an invoice for $ 6710.00 dated July 13, terms5/10, 2/30,n/90, for a shipment of skis. Calculate the partial payments made 20 July to reduce the balance to $ 4000.00 Round to the nearest 100th.

20. Aiden married and claims 3 withholding allowances. His weekly gross earnings are $1,086.00. His state withholding is 2.5% of gross earnings, and his retirement fund deduction is $50.00. Find Aiden's weekly net pay.Information regarding tax percentage rates is provided below.

(a) Find the volume of the region that lies inside z = x2 + y² and below the plane z = 16.[6 marks] ) Solve the following differential equations subject to the given conditions: \text { (i) } v \frac{d v}{d x}=\frac{3}{(x+1)^{2}}, \text { with } v=2 \text { when } x=0 =) Solve the following integral problem: \int \frac{2 x+10}{x^{2}-2 x-3} d x 2 x y+\left(x^{2}+1\right) \frac{d y}{d x}=x \cos \left(x^{2}\right), \text { with } y=5 \text { when } x=0

On 19 June, an invoice dated 18 June for $ 6250.00 less 17 %, 16 %, terms5/10, n/30, was received by Heisenberg Distributors. What is the amount due if the invoice is paid in-full on 27 June? Round to the nearest 100th.

13)The daily demand for a product is normally distributed with a mean of 80 and a standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is $20. The item costs $8and the carrying rate per year is 10% of the item cost. Determine the reorder point to satisfy 90%of the orders. (8)

22. Monica is single and claims 2 withholding allowances. Her monthly gross earnings are $4, 286.00. Monica's state withholding is $2.75% of gross earnings, and her medical insurance payment is $145.00 per pay period.Find Monica's monthly net pay.

) Given two vectors, r1=3î + 2f – 3k and r2=2î + ĵ + k, show that both vectors lie inthe plane 5x – 9y – z = 0. (Note that the vector equation of a plane in the-summary sheets uses \mathbf{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k}) Find an equation of a plane that is perpendicular to the plane, 5x - 9y – z = 0,and in which the vector r2= 2î + ĵ + k lies. \text { Given the position vectors of three points } a=\hat{\imath}+\hat{\jmath}+\hat{k}, b=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \mathbf{c}=3 \hat{\imath}+2 \hat{\jmath}+ 3k, find the equation of the plane passing through all three points.

Write the following simultaneous equations as a matrix equation of the form Ax=b,clearly identifying A, x and b: 3 x-4 y+z=1 x \quad-z=3 x-y+z=0 (b) Find the inverse of the matrix found in part (a) and use it to solve the equations tofind the values of x, y and z.[5 marks] (c) Find the composite transformation matrix that first reflects an object in the y-axisand then applies a shear in the x-direction of TT/4 radians. \text { (d) Determine the eigenvalues and corresponding eigenvectors of the matrix }\left[\begin{array}{ll} 2 & 1 \\ 4 & 5 \end{array}\right] \text {. }