2008 MATH 436 PART C |

17) The area of the rectangle is the polynomial 5*x*² + 38*x* – 63. The diagonal measures 52 cm. Find the perimeter.

**Solution:**

- 5

- Now,

- We expand to get: 25

- We collect terms: 26

- We divide by 26:

- This means

- Perimeter = 2(

18) *f*(*x*) = – 2/3 *x* + 6. **V** is the vertex of the parabola and the *x*-intercept of *f*.

We know that *f*(63) = *g*(16). Find the rule of correspondence for the parabola (and the coordinates of point **P)**.

**Solution:**

- We now know that (16, – 36) is a point on the parabola.

- The vertex is the

- Now we find the rule:

- Now substitute (16, – 36) to find

- The rule of correspondence is

19) A print shop gets an order for **212, 000** items that are either **newspapers, magazines **or** books.** The job is worth **$61, 650.00** and the shop charges **$0.12/newspaper**, **$0.60**/magazine and **$3.90** per book. In this job, the number of magazines is equal to the number of books and there is also a different number of newspapers to print. The print machines break down after printing

**153, 214** of the **newspapers** for the job. How many more newspapers must they print to complete that part of the job?

**Solution:**

- Let

Let

- Our system of equations is:

- We'll

- 0.12 (212, 000 – 2

- 4.26

- The

20) Line 1 (*l*_{1}) and Line 2 (*l*_{2}) are parallel to each other while Line 3 (*l*_{3}) is parallel to the *y-*axis. The equation of **Line 1 is 5 x + 4y – 564 = 0**. Points

**Solution:**

- First, we find the coordinates of P which is 2/5 the way to E.

- Change in

- so FP = 2/5(40) = 16, and DF = 2/5(50) = 20.

- We add 16 to 32 to get 48 and we subtract 20 from 75 to get 55.

- Point P is (48, 55). We already know it is

- Now we find perpendicular distance between P and Line 1.

- Point P is a teeny weeny bit closer to Line 3 than it is to Line 1.

22) A carpenter is going to cut off the top of a right circular cone with height *H* = 17.6 *dm.* and base radius *r* = 4.8 *dm*. to use the *frustrum* or base to build a table. The volume of the frustrum is 106.16 *dm*³. Find *h* the height of the small cone he cut from the big one.

**Solution:**

- First, we find the Volume of the whole cone using

- Volume (big cone) :

- Now we find the Volume of the small cone by subtraction:

- Volume (small cone) : 424.64 – 106.16 = 318.48

- The

- We find

- This tells us that

25) There was a long story about a mouse and a motion detector. Here's the picture.

**Solution:**

- First, we find angle AEF using the law of Cosines.

- We know that ,where

- From the triangle AEF:

- In triangle ADE:

- Area = ½(4 cos 38°)(4 sin 38°) =

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