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mathematics
calculus

Questions and Answers of Calculus

Find the maximum value of z=2xy-3x2-5y2 subject to the constraint x+y=5.
Find the maximum value of z = x2y subject to x + y = 6, x ≥ 0, y ≥ 0.
Find the maximum value of the function z=x3y2 subject to the x + y=10, x ≥ , y ≥ 0.
Find the maximum value of the function z=2xy-2x2-4y2 subject to the condition x+2y=8.
Find the minimum value of z=2x2+y2-xy subject to the constraint 2x+y=8.
Find the maximum value of z = xy subject to 9x2+25y2=450; x ≥ 0, y ≥ 0.
In below Problems, find the second partials.(a) zxx (b) zyy (c) zxy (d) zyx1. z = x2y - 3xy2. z = 3x3y4 -x2/y23. z = x2ey24. z = In (xy + 1)
Test z =16 - x 2 - xy - y2 + 24y for maxima and minima.
Test z = x3 + y3 - 12x - 27y for maxima and minima.
Find the minimum value of z = 4x2 + y2 subject to the constraint x + y =10.
Find the maximum value of z = x4y2 subject to the constraint x + y =9, x ≥ 0, y ≥ 0.
Suppose that the utility function for two goods X and Y is given by U = x2y. (a) Write the equation of the indifference curve for a consumer who purchases 6 units of X and 15 units of Y. (b) If the
The accumulated value A of a monthly savings plan over a 20-year period is a function of the monthly contribution R and the interest rate r%, compounded monthly, according to(a) Find the accumulated
The monthly benefit B (in thousands of dollars) from a retirement account that is invested at 9% compounded monthly is a function of the account value V (also in thousands of dollars) and the number
The number of units of sales of a product, S, is a function of the dollars spent for advertising, A, and the product's price, p. Suppose S=f (A, p) is the function relating these quantities. (a)
The joint cost, in dollars, for two products is given by C(x, y) = x2√y2 + 13. Find the marginal cost with respect to (a) x if 20 units of x and 6 units of y are produced. (b) y if 20 units of x
Suppose that the production function for a company is given by Q = 80K 1/4 L3/4 where Q is the output (in hundreds of units), K is the capital expenditures (in thousands of dollars), and L is the
The demand functions for two related products, product A and product B, are given by qA = 400 - 2pA -3pB qB = 300 - 5pA -6pB where pA and pB are the respective prices in dollars. (a) Find the
Suppose that the demand functions for two related products, A and B, are given bywhere pA and pB are the respective prices in dollars. Determine whether the products are competitive or complementary.
The weekly profit (in dollars) from the sale of two products is given by P(x,y) = 40x + 80y - x2- y2 where x is the number of units of product 1 and y is the number of units of product 2. Selling how
Suppose a company has two separate plants that manufacture the same item. Suppose x is the amount produced at plant I and y is the amount at plant II. If the total cost function for the two plants is
If the utility function for two commodities is U=x2y, and the budget constraint is 4x+5y=60, find the values of x and y that maximize utility.
Suppose a company has the Cobb-Douglas production function z = 300 x 2/3 y 1/3 where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose
The table gives the average annual U.S. wage from 2011 and projected through 2021.(a) Use linear regression to find the best linear model for the wage as a function of the number of years after 2010.
The table gives the number of women and the number of men (both in millions) in the U.S. civilian labor force for selected years from 1950 and projected to 2050.(a) Let x represent the millions of
In below Problems, find zx and zy. 1. z = 4x2y3 +x/y 2. z = √x2 + 2y2 3. z = (xy+1)-2 4. z = ex2y3 5. z exy + y in x
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss.
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss in detail.
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss briefly.
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Briefly.
Find the number of Internet users in Oceania/ Australia in 2013. Write your answer in standard form.
Find the area of each square.1. A square with side length of 7 meters.2.
Which world region had the smallest number of Internet users in 2008?
Translate each phrase into a variable expression. Use x to represent a number. 1. Five subtracted from a number 2. Seven more than a number 3. Ten divided by a number 4. The product of 5 and a
Which world region had the greatest number of Internet users in 2008?
Decide whether the given number is a solution of the given equation. 1. Is 5 a solution of n + 12 = 20 - 3? 2. Is 23 a solution of n - 8 = 10 + 6? 3. Is 14 a solution of 30 = 3(n - 3)? 4. Is 20 a
Determine which numbers in each set are solutions to the corresponding equations. 1. 7n = 77; {6,11,20} 2. n - 150; { 125, 145, 175} 3. 5(n + 4) = 90; {14, 16, 26} 4. 3n - 8 = 28; {3, 7, 15}
Round to the given place. 1. 842 to the nearest ten 2. 258,371 to the nearest hundred-thousand
1. Is 9 a solution of 5n - 6 = 40? 2. Is 3 a solution 2n - 6 = 5n - 15? 3. A manufacturer of drinking glasses ships his delicate stock in special boxes that can hold 32 glasses. If 1714 glasses are
1. Find the sum of 74, 342, and 918. 2. Find the sum of 49, 529, and 308.
1. Subtract 7965 from 25,862. 2. Subtract 4349 from 39,007.
1. The distance from Washington, DC, to New York City is 205 miles. The distance from New York City to New Delhi, India, is 7318 miles. Find the total distance from Washington, DC, to New Delhi if
1. Find the perimeter of each figure.2.
Write each whole number in words. 1. 7640 2. 46,200,120
Use the Internet Use by World Regions table for Exercises 31 and 32. 1. Find the increase in Internet users in Europe from 2008 to 2013. 2. Find the difference in the number of Internet users in 2013
The following bar graph shows the monthly savings account balances for a freshman attending a local community college. Use this graph to answer Exercises 33 through 36.1. During what month was the
Round to the given place. 1. 43 to the nearest ten 2. 45 to the nearest ten 3. 876 to the nearest ten 4. 493 to the nearest hundred 5. 3829 to the nearest hundred
Round to the given place. 1. 57,534 to the nearest thousand 2. 39,583,819 to the nearest million 3. 768,542 to the nearest hundred-thousand
Estimate the sum or difference by rounding each number to the nearest hundred 1. 3785 +648+ 2866 2. 5925 - 1787 3. A group of students took a week-long driving trip and traveled 630, 192, 271, 56,
Write each whole number in expanded form. 1. 3158 2. 403,225,000
1. Find the product of 6 and 250.2. Find the product of 6 and 820.3. A golf pro orders shirts for the company sponsoring a local charity golfing event. Shirts size large cost $32 while shirts size
Find the area of each rectangle.1.2.
Write each whole number in standard form. 1. Eighty -one thousand, nine hundred \ 2. Six billion, three hundred four million
1. Find the quotient of 92 and 5. 2. Find the quotient of 86 and 4. 3. A box can hold 24 cans of corn. How many boxes can be filled with 648 cans of corn? 4. One mile is 1760 yards. Find how many
Find the number of Internet users in 2013 in Europe. Write your answer in standard form.
Write each whole number in words. 1. 316 2. 5445 3. 42,009 4. 3,204,000 5. 47,033,107
Determine the place value of the digit 5 in each whole number. 1. 905 2. 6527 3 79,050,000 4. 51,682,700
Write each number in the sentence in words. (Do not write the years in words.)1. Between 1990 and 2010, Brazil lost 553,170 square kilometers of forest area.2. In 2012, there were 124,681 patients in
Write each whole number in standard form.. 1. Four thousand, four hundred sixty-eight 2. Seventy-three thousand, two 3. Sixteen million, four hundred five thousand, sixteen 4. Two million, twelve 5.
Write the whole number in each sentence in standard form. 1. The average distance between the surfaces of the Earth and the Moon is about two hundred thirty four thousand miles.2. The world's
Write each whole number in expanded form. 1. 789 2. 6040 3. 20,215 4. 99,032 4, 47,703,029
The table shows the beginning year of recent eruptions of major volcanoes in the Cascade Mountains.1. Mount Baker erupted in the 1700s. Locate, then write this eruption year in standard form. 2.
The table shows the top ten popular breeds of dogs in 2012 according to the American Kennel Club. The breeds are listed in the order of number of registrations.1. Which breed has more dogs
Check to see whether each number written in standard form matches the number written in words. If not, correct the number in words. See the Concept Check in this section.1.2. If a number is written
For below Exercises, identify which number is the minuend and which number is the subtrahend. See the second Concept Check in this section. 1. 2863 - 1904 2. Find 86 decreased by 25. 3. In your own
Check each addition below. If it is incorrect, find the correct answer. 1. 773 ...659 + 481 ..1913 2. 19 ...214 ...49 + 651 ...923
Identify each answer as correct or incorrect. Use addition to check. If the answer is incorrect, write the correct answer. 1. 478 ...- 89 ...389 2. 7615 ...- 547 ...7168
Fill in the missing digits in the problem. 1. 10, 4 ..- 8 5 4 ..710
Find the perimeter of each figure. 1.2.3.4.
Solve. 1. Find the sum of 802 and 6487. 2. Find the total of 89, 45, 2, 19, and 341. 3. Find the difference of 16 and 5. 4. What is 712 increased by 38? 5. Find 25 less 12. 6. Find 86 subtracted
1. The population of California is projected to grow from 39,136 thousand in 2010 to 44,126 thousand in 2020. What is California's projected population increase over this time period? 2. A stereo
A river basin is the geographic area drained by a river and its tributaries. The Mississippi River Basin is the third largest in the world and is divided into six sub-basins, whose areas are shown in
The decibel (dB) is a unit of measurement for sound. Every increase of 10 dB is a tenfold increase in sound intensity. The bar graph shows the decibel levels for some common sounds. Use this graph
The table shows the number of Target stores in ten states. Use this table to answer below Exercises?1. Which of the states listed in the table has the fewest Target stores? 2. How many Target stores
Round each whole number to the given place. 1. 273 to the nearest ten 2. 846 to the nearest ten 3. 8494 to the nearest hundred 4. 898 to the nearest ten 5. 82,198 to the nearest thousand
Round each whole number to the given place. 1. 42,682 to the nearest ten-thousand 2. 179,406 to the nearest hundred 3. 96,501 to the nearest thousand 4. 99,995 to the nearest ten 5. 39,523,698 to
Complete the table by estimating the given number to the given place value.1.2. 3.
The state of California contains 171,874 miles of urban and rural highways. Round this number to the nearest thousand. Round each number to the indicated place.
Kareem Abdul-Jabbar holds the NBA record for points scored, a total of 38,387 over his NBA career. Round this number to the nearest thousand.
According to the U.S. Population Clock, the population of the United States was 316,539,415 in August 2013. Round this population figure to the nearest million. Round each number to the indicated
The average salary for a football player in 2012 was $1,900,000. Round this average salary to the nearest million. Round each number to the indicated place.
U.S. farms produced 3,112,500,000 bushels of soybeans in 2011. Round the soybean production figure to the nearest ten-million. Round each number to the indicated place.
Estimate the sum or difference by rounding each number to the nearest ten. 1. 52 ...33 ...15 + 29 2. 555 - 235
Estimate the sum or difference by rounding each number to the nearest hundred.1. 4050...3133+ 12202. 1989- 18703. 799...1655+ 271
Three of the given calculator answers below are incorrect. Find them by estimating each sum. 1. 522 + 785 1307 2. 542 + 789 + 198 2139 3. 5233 + 4988 9011
Solve each problem by estimating.1. Suppose you scored 89, 97, 100, 79, 75, and 82 on your biology tests. Round each score to the nearest ten to estimate your total score.2. The Gonzales family took
The following table shows a few of the airports in the United States with the largest volumes of passengers. Complete this table. The first line is completed for you.1.2.
1. Find one number that when rounded to the nearest ten is 5700. 2. On August 23, 1989, it was estimated that 1,500,000 people joined hands in a human chain stretching 370 miles to protest the
Use the distributive property to rewrite each expression. See Example 2. 1. 5(8 + 2) 2. 6(1 + 4 ) 3. 12(12 + 3)
Multiply. See Example 3. 1. 79 ..× 3 2. 638 ..× 5 3. 882 × 2 4. 9021 × 3
Multiply. See Example 1. 1. 55 - 1 2. 27 . 0 3. 6.7.0 4.1.41
Multiply.1. 91× 722. 526× 233. 708× 214. (720)(80)5. (593)(47)(0)
Multiply. 1. (240)(1)(20) 2. 1357 × 79 3. 807 × 127 4. 1234 × 567 5. 426 × 110
Find the area and the perimeter of each rectangle. See Example 6.1.2.
Estimate the products by rounding each factor to the nearest hundred. See Example 9. 1. 982 × 650 2. 111 × 999
Without actually calculating, mentally round, multiply, and choose the best estimate. 1. 2872 × 12 = a. 2872 b. 28,720 c. 287,200 d. 2,872,000 2. 706 × 409 = a. 280 b. 2800 c. 28,000 d. 280,000
Solve. 1. Multiply 70 by 12. 2. Find the product of 9 and 900. 3. Find 3 times 3310. 4. One ounce of hulled sunflower seeds contains 14 grams of fat. How many grams of fat are in 8 ounces of hulled
1. An apartment building has three floors. Each floor has five rows of apartments with four apartments in each row. a. How many apartments are on 1 floor? b. How many apartments are in the building?
1. A house measures 45 feet by 60 feet. Find the floor area of the house.2. Recall from an earlier section that the largest commercial building in the world under one roof is the flower auction

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