If f and g are functions of time, and at time t = 3, f equals 8 and is rising at a rate of 3 units per second, and g equals 6 and is rising at a rate of 8 units per second, then the product fg equals________and is rising at a rate of _______ units per second.

Q: (4.) An even number times an odd number, and an even function times an odd function. (5.) An odd…

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Q: 5. Two functions, f and g, are related by the given equation: g(x) = f(x – 2) +3. %3D Use the…

A: Given equation

Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: 6) A function y =e-2x is defined numerically for some data range x. It can be entered using: (а) у -…

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Q: Two functions, f(x) and g(x), are graphed on the coordinate plane. y 4. (3 -6 -5 4 -3 2 -1, A -1 1 2…

A: For the given graph

Q: 10. Given the function x1 find f(-125), f(0), f(64), and draw the graph of f(x).

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Q: 40 -2 3 --10 Given the function f(x) shown above, f(x) > 0 over which intervals? Ox 2 -3 2 Ox 1

A: Given:-

Q: The functions f and g defined by F(x) =-2÷[|3x-9|] G(x)=x^2 + 9 -[ square root( x+4)÷8]-4…

A: Given:   To determine: The domains of both functions

Q: Express y as a function of x.The constant C is a positive number.

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Q: (k x+5 ;x-2

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Q: 18. A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is bent…

A: The area of a square with a side s is A=s2. Here, we have given two squares, one square has a side…

Q: 6. The function g(x) is graphed to the right. Which function below has the same roots? A. f(x) = 2(x…

A: from option 1 f(x)=2(x+1)(x+5)

Q: Find functions f and g so that f o g=H for H(x)=|2x 2 -1|.

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Q: a. The cost to remove 25% of the air pollutants is $400,000 b. If the company budgets $900,000 to…

A: Given that : A power company burns coal to generate electricity, the cost c(x) to remove x% of the…

Q: Find the functions f + g, f − g, fg, and f/g. f(x)= square root of x-10; g(x)=x3+10   f + g =…

A: We have to find f + g, f − g, f*g, and f/g. f(x)= square root of x-10; g(x)=x3+10 So the solution is…

Q: 37. There were 2000 applicants for enrollment to the freshman class at a small college in the year…

A: Given that there were 2000 applicants for enrollment to the freshman class at a small college in the…

Q: 31. The graph of which function is always below the graph of the function y (x + 1)2 + 1? O y = 1–…

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Q: 31. Let U(t) be the population of the United States, in millions, 1 years since 1900. Let C(t) be…

A: From the given data: Ut be the population of the united states in millions. And Ct be the population…

Q: 1) write the linear function f for which f(1)=3 and f(4)=0

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (a) Find the domain of the functions f(x): V(1 – x)(x – 3) and g(x) = ln(x – 2)(5 – a). Also…

A: Given, The functions, Domain is a set of x values for which the function is defined.

Q: Find the values of A, so that the function F (x) = {1-3x                         x 4    is…

A: Given  F(x)=1-3xx<4Ax2+2x-3x>4 is continuous for all values of x

Q: Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. %3D f(x) = 6x…

A: Given f(x)=6x+7 and g(x)=x² To find the point of intersection

Q: Question 10 of 25 The function f(x) = x -3x3 is decreasing on the interval A)(-00, 0] D) [0,10] B)…

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Q: An equation that defines y as a function of x is given. (a). Solve for y in terms of x and replace y…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: given: f(x)={(x^(2)+1 if x>-1),(2x if x<=-2)} a) draw an accurate graph of f(x). b) f(1) c)…

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Q: 1. A state charges polluters an annual fee of $20 per ton, for each ton of pollutant emitted into…

A: Given, A state charges polluters an annual fee of $20 per ton, up to a maximum of 4,000 tons. No…

Q: (a) f is an odd function. (b) g is an even function. (c) h = g(f(x)). -3 -2 -1 1 2 3 f(x) =| 2 3 2…

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Q: etermine the values of x for which the function f(x)={2x2−4        x<2…

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Q: 33-38 Find the functions (a) f o g, (b) g º f, (c) f•f, and (d) g o g nd their domains.

A: . as we know, the square root of any negative real number is a complex number so the value of…

Q: -4 -4 At the point shown on the function above, which of the following is true? Of' 0 O f' > 0, f''…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 5. A fence is to be built against a concrete wall to form a rectangular lot. Only three sides of the…

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Q: - x (a) Determine whether f(x) is even or odd or neither. x2 + 1 (b) Determine whether g(x) = x° –…

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Q: g(x) = f(x + 1) - 2 Two functions, f and g, are related by the given equation. Use the numerical…

A: Given that g(x) = f(x + 1) - 2 This means f(x) moves 1 unit left and 2 units down to produce g

Q: FUNCTION INTERVAL a) f(x) = x* – 3x³ + 2x² – x + 6 [-4,3] b) f(x) = x2+9 [0, 2] 2x-3 c) f(x) = [-6,…

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Q: -3 -2 -2 -6 At the point shown on the function above, which of the following is true? Of' > 0, f'' >…

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Q: 4-3x Let f(x) be a one to one function and f-(x) = then the function 2x+1 f(x) can be 4-x a) f(x) =…

A: We have to find f(x).

Q: c) Determine the values of x for which the function f(x) = 2x2 −4      x<2           x + 2        2…

A: Given: Piecewise function: fx=2x2-4, x&lt;2x+2, 2&lt;x&lt;57, x≥5 For function to be continuous at…

Q: x+6 and (h o f)(x)= 4x -7 Let f(x)= Зх-8 5х-6 Then h(-4)= 1 4 1 15 97 168 2 9 | 8 32 51

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Q: Therefore, we have 3w?- 7w + 5 - 3w2 7w/2, sw 1/2 Now, since the function Is a sum of power…

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Q: x2,   x≥0       -x2,  x<0   Find f'(0)

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Q: 1. Jamal's latte shop finds that its weekly profit (measured in dollars) is given by the function p,…

A: topic - functions

Q: 1-35. Consider the functions f(x)= 3x² – 5 and g(x) = Jx-5+2. %3D a. Find f(5). Find g(5). b. C.…

A: To find the function value at a given point substitute the particular point in the given  function.

Q: 24 18 12 -4 to %3D %3D a. Write a function formula for g using the function f. 9(z) = x+c Preview b.…

A: a. From the given graph observe that, the graph of g is obtained by reflecting the graph of f with…

Q: 1-35. Consider the functions f(x)= 3x2 – 5 and g(x)= Jx-5+2. %3D Find f(5). b. Find g(5). a. Find…

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Q: 1. f(x) = x* – 2x² – 8 a. f(-x) = b. Is the function even, odd, or neither? 2. f(x) = -3x +x³ + 2x…

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Q: Two functions are defined by f: x ax + I andg:x 4b **1, where a and b are constants. Given that f(a)…

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Q: 7 A linear function f is such that f(1) = 5 and f(5) = 1. a Find the formula for the function f. b…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.