28. an open top box is to be formed by cutting out squares from the corners of a 50 centimeter x 30 centimeter rectangular sheet of material. The height of the box must be a whole number of centimeters. What size squares should be cut out to obtain the box with maximum volume.

a. Understanding the problem: If 6 centimeter x 6 centimeter squares are cut from from the corners, the height of the box will be 6 centimeters. In this case, what would the width and length of the box be?

b. Devising a plan: One plan for solving this problem is to systematically consider corner squares of increasing size. What is the largest square with whole-number dimensions that can be cut from the corners and still produce a box?

c. Carrying out the plan: Complete the following table and use inductive reasoning to predict the size of the corner squares needed to obtain the box of maximum volume.

d. Looking back: The preceding table shows that as the size of the squares at the corners increase, the volume of the box increases for awhile and then decreases. Try a few more sizes for the squares, using whole numbers for dimensions to see if you can obtain a greater volume for the box.

Question: when x^4 + px^3 + qx^2 + rx + 6 is divided by x + 1, x -1 and x + 2, the remainder are 6, 12 and 6 respectively. Find the values of p, q and r.

The volume and weight of items A, B, C, D are shown in the following table.

(1) How can a shipment of 16 items be made if the shipment has a total volume of 1200 in³

and total weight 4800 lb?

(2) Is there any way to ship exactly 5 items of type C?

a furniture company is deciding whether or not to sell a certain type of dining room set. the company believes that the profit in dollars, P, is related to the number of dining room sets produced and sold, x, by the function P(x)= -0.6x^2 +1800x - 186,000. what is the maximum profit that the company can expect?

You are moving into a new apartment and realize you need a rug to cover the floor. You know a great local store that sells rugs of any dimension you want. They charge a fixed rate per square foot.

(a.) Your new place needs a 12 ft by 18 ft rug. You notice that these sides are 50% longer than the rug from your old place. What were the dimensions of the old rug?

(b.) You know that a 4 ft by 6 ft rug from the same place will cost you $16. How much should your new 12 ft by 18 ft rug cost you?

Extra Credit (5 points): When checking your email, you “coincidentally” get an ad for a website offering 12 ft by 18 ft rugs for $60. Should you go with this other company instead? Give your reasoning.

Discuss How does Islamic microfinance encourages stability in investments?

Topic about (application of geometry in real life)

Page 337, Problems 57, 58, 59

57. Compound Interest If $10,000 is invested at an interest rate

of 3% per year, compounded semiannually, find the value of

the investment after the given number of years.

(a) 5 years (b) 10 years (c) 15 years

58. Compound Interest If $2500 is invested at an interest rate

of 2.5% per year, compounded daily, find the value of the

investment after the given number of years.

(a) 2 years (b) 3 years (c) 6 years

59. Compound Interest If $500 is invested at an interest rate of

3.75% per year, compounded quarterly, find the value of the

investment after the given number of years.

(a) 1 year (b) 2 years (c) 10 years

The gross domestic product, G, of Switzerland was 310 billion dollars in 2007. Give a formula for G (in billions of dollars) t years after 2007 if G increases by

a. 3% per year

b. 8 billion dollars per year.

Suppose that (a) holds. Determine the year when Switzerland's GDP reaches 410 billion dollars.

The new flyer is one of the largest Ferris wheels in the world standing at 165meters tall. The Flyer boards at the bottom of its rotation from a platform 15 meters from the ground. Each capsule takes 30 minutes to complete one full rotation.

1. Draw and label a diagram of the new flyer.

2. How many rotations does each capsule make in

1 hour? ______ 2 hours?____ t hours?_____

3. How many radians does each capsule sweep in

1 hour?_____ 2 hours?_____ t hours?_____

4. Write an equation for H, the height of a capsule in meters, as a function of t, the time in hours since the capsule boarded.

The temperature in Gavin's oven is a sinusoidal function of time. Gavin sets his oven so that it has a maximum temperature of 290°F and a minimum temperature of 210°. Once the temperature hits 290°, it takes 20 minutes before it is 290° again. Gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 260°. He puts the cake into the oven when it is at 250° and rising. How long will Gavin need to leave the cake in the oven? (Round your answer to the nearest minute.)

Q1). For the function, do the following.

f(x) = 3/x from  a = 1  to  b = 2.

(a) Approximate the area under the curve from a to b by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351, rounding to three decimal places.

(b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.

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Q2). According to a study, each additional year of education increases one's income by 17%. Therefore, with x extra years of education, your income will be multiplied by a factor of 1.17^x. How many additional years of education are required to double your income? That is, find the x that satisfies 1.17^x = 2. (Round your answer to one decimal place.)

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Q3). A running track consists of a rectangle with a semicircle at each end, as shown below. If the perimeter is to be exactly 400 yards, find the dimensions (x and r) that maximize the area of the rectangle. [Hint: The perimeter is 2x + 2πr.] (Round your answers to the nearest yard.)

Solve the following SSA triangle. Indicate whether the given measurements result in no​ triangle, one​ triangle, or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth. A equals 45degrees°​, a equals 57​, c equals 63