Differential equations Questions and Answers
![Solve the differential equation with the given conditions 21 f x 12x 6x 1 and f 1 5](https://media.kunduz.com/media/sug-question-candidate/20240411114827096307-6582777.jpg?w=256)
High School Calculus
Differential equationsSolve the differential equation with the given conditions 21 f x 12x 6x 1 and f 1 5
![f x x2 3x 4 X 2](https://media.kunduz.com/media/sug-question-candidate/20240311152832069328-6201330.jpg?w=256)
![a To graph the relation P 1 5 x 2 4x 60 we ll plot points for different values of x and calculate the corresponding P values using equation Then we ll plot these points on a graph b This relation is quadratic because it has a squared term x 2 in the equation Another way to see this is by noting that the graph of a quadratic equation is a parabola and the given equation has the form of a quadratic function the c The direction of opening of the parabola is downward because the coefficient of the x 2 term 1 5 is negative Since the coefficient of the x 2 term negative the parabola opens downward indicating that the profit function has a maximum We know this because the coefficient of x 2 is negative is d To find the P intercept we set x 0 in the equation and solve for P P 1 5 0 2 4 0 60 60 The P intercept is 0 60 This represents the initial profit of the company in 2020 when x 0 Yes it makes sense that this is a new company because at the beginning in 2020 the profit is 60 million As the company grows and operates the profit can increase or decrease based on various factors](https://media.kunduz.com/media/sug-question-candidate/20240311050042604276-6624523.jpg?w=256)
High School Calculus
Differential equationsa To graph the relation P 1 5 x 2 4x 60 we ll plot points for different values of x and calculate the corresponding P values using equation Then we ll plot these points on a graph b This relation is quadratic because it has a squared term x 2 in the equation Another way to see this is by noting that the graph of a quadratic equation is a parabola and the given equation has the form of a quadratic function the c The direction of opening of the parabola is downward because the coefficient of the x 2 term 1 5 is negative Since the coefficient of the x 2 term negative the parabola opens downward indicating that the profit function has a maximum We know this because the coefficient of x 2 is negative is d To find the P intercept we set x 0 in the equation and solve for P P 1 5 0 2 4 0 60 60 The P intercept is 0 60 This represents the initial profit of the company in 2020 when x 0 Yes it makes sense that this is a new company because at the beginning in 2020 the profit is 60 million As the company grows and operates the profit can increase or decrease based on various factors
![10 Use the diagram to answer the following questions Let m ADB 0 a Which segment represents csc 0 b Find the value of 0 How do you know c Find AB A 2](https://media.kunduz.com/media/sug-question-candidate/20240306083534245925-5923485.jpg?w=256)
High School Calculus
Differential equations10 Use the diagram to answer the following questions Let m ADB 0 a Which segment represents csc 0 b Find the value of 0 How do you know c Find AB A 2
![a f x 1 M 2 1 0 1 1 Find g 2 g 2 and g 2 2 5 6 7 8 The function f is continuous on the interval 2 7 and consists of three line segments and a semi circle as shown in the figure above The function g is defined by g x d Let h x f 5x 9 Find h 3 2 X J f t dt 2 b Find the x coordinate of the critical points on g x on the interval 2 7 Classify each critical point found in part b as a relative minimum relative maximum or neither for g Justify your answers c Find the interval s where g is increasing and concave down Justify your answer](https://media.kunduz.com/media/sug-question-candidate/20240301001426750209-6651710.jpg?w=256)
High School Calculus
Differential equationsa f x 1 M 2 1 0 1 1 Find g 2 g 2 and g 2 2 5 6 7 8 The function f is continuous on the interval 2 7 and consists of three line segments and a semi circle as shown in the figure above The function g is defined by g x d Let h x f 5x 9 Find h 3 2 X J f t dt 2 b Find the x coordinate of the critical points on g x on the interval 2 7 Classify each critical point found in part b as a relative minimum relative maximum or neither for g Justify your answers c Find the interval s where g is increasing and concave down Justify your answer
![Choose the correct graph and explain your choice 1 y tan 20 A B D x fr Cr 12 T 3r 2x 27 3x 3](https://media.kunduz.com/media/sug-question-candidate/20240223170057237443-5923485.jpg?w=256)
High School Calculus
Differential equationsChoose the correct graph and explain your choice 1 y tan 20 A B D x fr Cr 12 T 3r 2x 27 3x 3
![4 A particle moves along a line so that its position at any time t 0 is given by the function s t t 3t 8t 5 where s is measured in meters and t is measured in seconds a Find the instantaneous velocity at any time t b When is the particle at rest c Find the acceleration of the particle at any time t d What is the displacement of the particle for the first 3 seconds](https://media.kunduz.com/media/sug-question-candidate/20240222215702994390-6582777.jpg?w=256)
High School Calculus
Differential equations4 A particle moves along a line so that its position at any time t 0 is given by the function s t t 3t 8t 5 where s is measured in meters and t is measured in seconds a Find the instantaneous velocity at any time t b When is the particle at rest c Find the acceleration of the particle at any time t d What is the displacement of the particle for the first 3 seconds
![1 Let f x 2e x and g x 5x At what value of x do the graphs of f and g have parallel tangents a 0 445 b 0 366 Graph of f c 0 344 d 0 251](https://media.kunduz.com/media/sug-question-candidate/20240221014009650512-6582777.jpg?w=256)
High School Calculus
Differential equations1 Let f x 2e x and g x 5x At what value of x do the graphs of f and g have parallel tangents a 0 445 b 0 366 Graph of f c 0 344 d 0 251
![Standard 6 NR 4 1 The ratio of squirrels to pigeons in the park is 15 to 125 Which statement describes this relationship O There are 3 squirrels for every 25 pigeons in the park O There are 3 squirrels for every 5 pigeons in the park O There are 5 squirrels for every 3 pigeons in the park There are 25 squirrels for every 3 pigeons in the park](https://media.kunduz.com/media/sug-question-candidate/20240216225211995574-6102902.jpg?w=256)
High School Calculus
Differential equationsStandard 6 NR 4 1 The ratio of squirrels to pigeons in the park is 15 to 125 Which statement describes this relationship O There are 3 squirrels for every 25 pigeons in the park O There are 3 squirrels for every 5 pigeons in the park O There are 5 squirrels for every 3 pigeons in the park There are 25 squirrels for every 3 pigeons in the park
![y x5 5x 4x a Find the zeros algebraically Enter your answers as a comma separated list If there are no real zeros enter DNE X b Use a graphing utility to graph the function y O 4 4 4 2 y A 2 4 X 4 y M 4 2](https://media.kunduz.com/media/sug-question-candidate/20240211050817680798-6052188.jpg?w=256)
High School Calculus
Differential equationsy x5 5x 4x a Find the zeros algebraically Enter your answers as a comma separated list If there are no real zeros enter DNE X b Use a graphing utility to graph the function y O 4 4 4 2 y A 2 4 X 4 y M 4 2
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