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mathematics
precalculus

Questions and Answers of Precalculus

Use Descartes’s method to find the equation of the line tangent to each graph at the given point. y = x2 + 2; at (1, 3)
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. x2 + y2 = 10; at (1, 2)
Descartes’s method for finding tangents depends on the idea that, for many graphs, the tangent line at a given point is the unique line that intersects the graph at that point only. Apply his
Find formulas for the base b and one of the equal sides l of an isosceles triangle in terms of its altitude h and perimeter P.
Find formulas for the length l and width of a rectangle in terms of its area A and perimeter P.
A wire 60 feet long is cut into two pieces. Is it possible to bend one piece into the shape of a square and the other into the shape of a circle so that the total area enclosed by the two pieces is
A farmer has 300 feet of fence available to enclose a 4500-square-foot region in the shape of adjoining squares, with sides of length x and y. See the figure. Find x and y. X
A rectangular piece of cardboard, whose area is 216 square centimeters, is made into a cylindrical tube by joining together two sides of the rectangle. See the figure. If the tube is to have a volume
A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. See the figure. If the box
In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed
In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5 meter per hour faster than the tortoise, crosses the
The altitude of an isosceles triangle drawn to its base is 3 centimeters, and its perimeter is 18 centimeters. Find the length of its base.
Two circles have circumferences that add up to 12π centimeters and areas that add up to 120π square centimeters. Find the radius of each circle.
An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of Find the sides of the squares.
The perimeter of a rectangle is 16 inches and its area is 15 square inches.What are its dimensions?
The ratio of a to b is 4 : 3. The sum of a and b is 14. What is the ration of a - b to a + b.
The ration of a to b is 2/3. The sum of a and b is 10. What is the ratio of a + b to b - a?
The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers.
The difference of two numbers is the same as their product, and the sum of their reciprocals is 5. Find the numbers.
The product of two numbers is 10 and the difference of their squares is 21. Find the numbers.
The product of two numbers is 4 and the sum of their squares is 8. Find the numbers.
The sum of two numbers is 7 and the difference of their squares is 21. Find the numbers.
The difference of two numbers is 2 and the sum of their squares is 10. Find the numbers.
Graph each equation and find the point(s) of the intersection, if any.y = 4/x+2 and the circle x2 + 4x + y2 - 4 = 0
Graph each equation and find the point(s) of the intersection, if any.y = 4/x - 3 and the circle x2 – 6x + y2 + 1 = 1.
Graph each equation and find the point(s) of the intersection, if any.The circle (x + 2)2 + (y – 1)2 = 4 and the parabola y2 - 2y – x - 5 = 0.
Graph each equation and find the point(s) of the intersection, if any.The circle (x – 1)2 + (y + 2)2 = 4 and the parabola y2 + 4y – x + 1 = 0.
Graph each equation and find the point(s) of the intersection, if any.The line x + 2y + 6 = 0 and circule (x + 1)2 + (y + 1)2 = 5.
Graph each equation and find the point(s) of the intersection, if any.The line x + 2y = 0 and the circle (x – 1)2 + (y – 1)2 = 5.
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. ² + y³ = 2 x'y = 4
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. ,2 x² + y} = 4 y = In x
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. Sxy = 2 ху y = In x
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. х* + y 3 6 ху %3D 1
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. x* + y* = 12 xy = 2
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. + y = 2 x’y = 4
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. y = x³/2 ly = e*
Use a graphing utility to solve the system of equations. Express the solution(s) rounded to two decimal places. Sy = x/3 ly = e*
Graph the equations given in Problem 49. Data from Problem 49. y + y + x? - x – 2 = 0 y +1 + х y
Graph the equations given in Example 4. Equations From Example 4. x² + x + y² – 3y + 2 = 0 y – y x + 1 +
Solve the system. Use any method you wish. In x = 5 In y log, x = 3 + 2 log, y
Solve the system. Use any method you wish. In x = 4 In y log, x = 2 + 2 log3 y
Solve the system. Use any method you wish. Slog,(2y) = 3 | log,(4y) = 2
Solve the system. Use any method you wish. log, y = 3 |log(4y) = 5 ||
Solve the system. Use any method you wish. - 2x? + y? + 3y – 4 = 0 х У x – 2 + ||
Solve the system. Use any method you wish. y² + y + x² х — 2 = 0 y + 1 + ||
Solve the system. Use any method you wish. - ху — 2у %3D 0 2y = 0 х* ху + х + 6 %3D 0
Solve the system. Use any method you wish. Зху + 2у? %3D 0 х? + ху —D 6 х* 2y² =
Solve the system. Use any method you wish. = 1 = 4
Solve the system. Use any method you wish. 6. = 6 19
Solve the system. Use any method you wish. 3 + 1 = 0 6. + 2 = 0
Solve the system. Use any method you wish. 2 + 3 = 0 3 ||
Solve the system. Use any method you wish. Зу? S 4x² + 3y² = 4 2x2 - бу? 3 —3
Solve the system. Use any method you wish. х? + 2у? %3D 16 4. y? = 24
Solve the system. Use any method you wish. [y² – x² + 4 = 0 2x? + 3y? = 6
Solve the system. Use any method you wish. 2x2 + y? = 2 x² – 2y + 8 = 0
Solve the system. Use any method you wish. 5ху + 13у? + 36 3 0 xy + 7y² = 6
Solve the system. Use any method you wish. х + 2ху 3х 10 Зx2 — 2 ху
Solve the system. Use any method you wish. x? – 3y? + 1 = 0 | 2x2 – 7y² + 5 = 0
Solve the system. Use any method you wish. (7x2 – 3y + 5 = 0 3x? + 5y? = 12 12
Solve the system. Use any method you wish. 2 3x – 2y? + 5 = 0 + 2 = 0 |2.x? - y? + 2 = 0
Solve the system. Use any method you wish. |x² – 4y² + 7 = 0 3x + y = 31 Зx
Solve the system. Use any method you wish. [2y² - | 2у? - 3ху + бу + 2х + 4 %3 0 2х — Зу + 4 — 0
Solve the system. Use any method you wish. J 4x² – 3xy + 9y² = 2x + 3y = 5
Solve the system. Use any method you wish. S2.x² | 2x? — ху + у? — 8 ху 3 4
Solve the system. Use any method you wish. x + y + 1 = 0 x² + y² + 6y – x = -5 .2
Solve the system. Use any method you wish. x² – 4y = 16 2у — х 3D 2
Solve the system. Use any method you wish. y = 2x + 1 |2x² + y² = 1
Solve the system. Use any method you wish. Sx² - y? = 21 21 (x + y = 7
Solve the system. Use any method you wish. S2.x? + y² = 18 ху %3D 4 2x2 18
Graph each equation of the system. Then solve the system to find the points of intersection. Sx² + + y = 10 ху %3D 3
Graph each equation of the system. Then solve the system to find the points of intersection. Jу 3D х? — 4 бх — 13
Graph each equation of the system. Then solve the system to find the points of intersection. Jку — ху %3D 1 у %3D 2х + 1
Graph the equation of the system. Then solve the system to find the points of intersection. x² + y? = 4 = x? – 9 У
Graph each equation of the system. Then solve the system to find the points of intersection. Sx² = *y = 1
Graph each equation of the system. Then solve the system to find the points of intersection. ху %3 4 х2 + у? 3D 8
Graph each equation of the system. Then solve the system to find the points of intersection. x² + y? = 16 x² – 2y = 8
Graph each equation of the system. Then solve the system to find the points of intersection. S x² + y² = 4 y? – x = 4 I3D
Graph each equation of the system. Then solve the system to find the points of intersection. x2 + y? = 10 10 y = x + 2
Graph each equation of the system. Then solve the system to find the points of intersection. у 3D Зх — 5 x² + y? = 5 5
Graph each equation of the system. Then solve the system to find the points of intersection. x² + y? = 8 x² + y? + 4y = 0
Graph each equation of the system. Then solve the system to find the points of intersection. x² + y? = 4 x² + 2x + y? = 0
Graph each equation of the system. Then solve the system to find the points of intersection. у %3D х — 1 у — х? — бх + 9 ||
Graph each equation of the system. Then solve the system to find the points of intersection. 2y х lx = y? – 2y
Graph each equation of the system. Then solve the system to find the points of intersection. Sy = Vĩ ly = 6 – x
Graph each equation of the system. Then solve the system to find the points of intersection. Sy = Vĩ у %3D2 — х У
Graph each equation of the system. Then solve the system to find the points of intersection. Įy = V4 - x %3D 2х + 4
Graph each equation of the system. Then solve the system to find the points of intersection. (36 х у %3 8 — х
Graph each equation of the system. Then solve the system to find the points of intersection. Гу 3 ? + 1 y : 4х + 1
Graph each equation of the system. Then solve the system to find the points of intersection. Sy = x2 + 1 y = x + 1
Graph the equation: x2 + 4y2 = 4.
Graph the equation: y2 = x2 - 1
Graph the equation: y + 4 = x2
Graph the equation: y = 3x + 2
Write the partial fraction decomposition of each rational expression. x² + 9 х x* - 2x – 8
Write the partial fraction decomposition of each rational expression. Write the partial fraction decomposition of each rational expression. 2х + 3 2. х — 9х?
Write the partial fraction decomposition of each rational expression. 4х 2x2 + 3x 2
Write the partial fraction decomposition of each rational expression. 4 2.x? 3 5x
Write the partial fraction decomposition of each rational expression. x2 3 (x² + 4)°
Write the partial fraction decomposition of each rational expression. (x + 16)
Write the partial fraction decomposition of each rational expression. .2 x + 1 x + x - 5x + 3

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