Key to Dodd's Algebra: Containing All the Problems, and the More Difficult Equations, in that Work. With Their Solutions: Designed to Facilitate the Labor of TeachersPratt, Oakley & Company, 1859 |
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Σελίδα 3
... Progressions .... 57 Problems in Permutations and Combinations .. 65 Exercises on Rationalization and Pure Equations . 67 Complete Equations in which the Unknown Quantity is contained in a Surd Expression .... 70 Equations of a ...
... Progressions .... 57 Problems in Permutations and Combinations .. 65 Exercises on Rationalization and Pure Equations . 67 Complete Equations in which the Unknown Quantity is contained in a Surd Expression .... 70 Equations of a ...
Σελίδα 57
... Progression is 3 , the common difference of the terms is 2 , and the number of terms 20. What is the last term ? and the sum of all the terms ? The last term ... progression be ( 117 ) PROBLEMS IN PROGRESSIONS . 57 Problems in Progressions.
... Progression is 3 , the common difference of the terms is 2 , and the number of terms 20. What is the last term ? and the sum of all the terms ? The last term ... progression be ( 117 ) PROBLEMS IN PROGRESSIONS . 57 Problems in Progressions.
Σελίδα 58
... progression be 40 , and the fifth term 70 , what will the fourth term be ? The fourth term will be 1 ( 40 + 70 ) = 55 , ( 179 ) . 6. If the first term of an Arithmetical progression be 5 , and the fifth term 30 , what will the second ...
... progression be 40 , and the fifth term 70 , what will the fourth term be ? The fourth term will be 1 ( 40 + 70 ) = 55 , ( 179 ) . 6. If the first term of an Arithmetical progression be 5 , and the fifth term 30 , what will the second ...
Σελίδα 59
... progression is 100 , and the number of terms 21 , what must the common difference be that the sum of the series may be 1260 ? Let x represent the common difference ; then 100-20 represents the last term ( 176 ) ; and 200-20x 2 × 21 ...
... progression is 100 , and the number of terms 21 , what must the common difference be that the sum of the series may be 1260 ? Let x represent the common difference ; then 100-20 represents the last term ( 176 ) ; and 200-20x 2 × 21 ...
Σελίδα 60
... progression whose first and second terms are 12 and 15 respectively . Let x represent the third term ; then 12 : x :: 15-12 : x - 15 , ( 182 ) . This proportion will give x = 20 , ( 170 ) . 14. What is the first term of an harmonical ...
... progression whose first and second terms are 12 and 15 respectively . Let x represent the third term ; then 12 : x :: 15-12 : x - 15 , ( 182 ) . This proportion will give x = 20 , ( 170 ) . 14. What is the first term of an harmonical ...
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100 represents 2x represents adding similar terms arithmetical means Arithmetical progression asked the ages bushels Clearing this Equation common difference Completing the square Divide the number Dividing both sides easily found Equation of fractions Equation will give Extracting the square Find the values find x=2 found equal fourth Equation Geometrical progression hence less number Let x represent Multiplying number of days number of gallons number of hours number of miles number of pounds number of shillings number of terms number of yards problem rate per cent ratio of percentage remainder represent A's share represent the greater represent the length represent the less represent the sum represents the amount represents the distance represents the interest represents the number represents the percentage second Equation square rods square root Squaring both sides Substituting these values Substituting this value third Equation Transposing uniting similar terms value of x whence whole number
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Σελίδα 156 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Σελίδα 143 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Σελίδα 13 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from, home, it lasted the woman 30 days ; how many days would the man be in drinking it alone ? Ans.
Σελίδα 27 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Σελίδα 146 - Two persons, A and B, can perform a piece of work in 16 days. They work together for four days, when A being called off, B is left to finish it, which he does in 36 days. In what time would each do it separately?
Σελίδα 172 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Σελίδα 31 - Two pedestrians start from the same point; the first steps twice as far as the second, but the second makes 5 steps while the first makes but one. At the end of a certain time they are 300 feet apart. Now, allowing each of the longer paces to be 3 feet, how far will each have travelled?
Σελίδα 152 - There were 22 sailors to every three guns, and 10 over ; also, the whole number of hands was five times the number of soldiers and guns together. But after an engagement, in which the slain were* one-fourth of the survivors, there wanted 5 men to mako 13 men to every two guns: required, the number of guns, soldiers and sailors.
Σελίδα 22 - To divide the number 36 into three such parts that ~ of the first, ^ of the second, and } of the third may be all equal to each other ? Ans.
Σελίδα 59 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.