A utility company charges a base rate of 10 cents per kilowatt hour (kWh) for the first 350 kWh and 15 cents per kilowatt hour for all additional electricity usage. The amount E(in dollars) that the utility company charges is a function of the number x of kilowatt hours used. (a) Express E as a piecewise defined function if 0 ≤ x ≤ 350. E(x) = ______       if 0 < x ≤ 350     if 350 < x (b) Find E(100). $ What does this value represent? ____

Q: 1. Consider the function. f(x)=-3x³3 + 18x² 27x Step 1. Find all values of x that correspond to…

A:

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Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) > 0 and f"(x) <…

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Q: 3. Determine algebraically whether the function is even, odd or neither: g(x) = %3D .2 X< +3

A:

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A: Area of pasture is given by : A = x ( y + y ) = 2xy ………. (i) Fence total is given by : 3x + 4y = 280…

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A: see below the answer

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Q: a) Sketch the graph of a function f for which f(x)>0 and f'(x)>0 for all x. b) Sketch the graph of a…

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Q: 1 Find the domain of the function f(x) 2 - 25 (pp. 52-54)

A: To evaluate The domain of a function f(x)=x2-1x2-25 Let y=f(x)=x2-1x2-25

Q: 20. Determine algebraically whether the function 5x f(x) = x - 9 is even, odd, or neither.

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Q: True or False? For a function g(x). g"(3) = -8 indicates that g(x) is at x=3.

A: Given that for a function g(x), g"(3)=-8 indicates that g(x) is................ at x=3

Q: f (х) — (х — 1) (х — 3) 12

A:

Q: Sketch the graph of a function that satisfies all of the given conditions. f '(0)  =  f '(2) =…

A: f'(0)=f'(2)=f'(4)=0 means x=0,2,4 are critical points. f'(x)&gt;0 means f(x) is increasing…

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Q: If f and g are functions such that f (x) = (4x + 6)g(x), which of the following statements must be…

A: Given : f(x) = (4x+6)g(x)

Q: 40. a. Show that f(x) = 4x + 4 defines a one-to-one function. b. Write an equation for f(x). c.…

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Q: sketch a possible graph of a function f that satisfies the following conditions: i) f'(x) > 0 for x…

A: topic - functions

Q: Determine (algebraically) whether the given function is even, odd, or neither. G(x) = 1 - x + x3

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A: We know that increasing and decreasing both functions are one-one

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A: Given the characteristics of the graph of a function:

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A: Left hand Limit(LHL):

Q: 1. Use the graph of the function f below as the first step toward graphing-f(x + 2) +1. Show all…

A: topic - functions

Q: 8. Find f-1 of the one-to-one function f (x) =and state the domain and the range of f and f-1. x-3

A:

Q: a. Show that f(x) = 2x − 3 defines a one-to-one function.  b. Write an equation for f−1(x).  c.…

A: (a)The given function is

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A: Given that:                       Graph of g is obtained by reflecting graph of f about x-axis and…

Q: a) Find the domain and sketch the graph of the function. f(x) 5 , G(x) = (1-x 12-x o's xS1 0sxS1 1<…

A: Since you are asking multiple questions. We are answering only the first question for you as per our…

Q: 70 x'-6x The function f(x) = has a removable discontinuity at x = 0. To remove the 10+x2 x3+2x…

A: to see 2nd step

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A: Given that during a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 4…

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: 15. Test algebraically whether the function is EVEN, ODD, or NEITHER. a) f(x) = 5 + In]x| b) f(x) =…

A: To check whether a function is even. Odd or neither of two

Q: A school wishes to form three sides of a rectangular playground using 320 meters of fencing. The…

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Q: (a) Sketch a graph of a function f such that: f' > 0 and f" 0 and f" > 0, for x > 3. (b) Does the…

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Q: Describe a function g() in terms of f(x) if the graph of g is obtained by reflecting the graph of f…

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Q: Sketch the graph of a function that satisfies all of the given conditions. vertical asymptote x = 0,…

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Q: A library has 50,000 books and is adding 500 books every year. Write a function f(x) for the number…

A: Let x be the number of years. At x = 1, the number of books is 50,500 At x = 2, the number of books…

Q: Determine (algebraically) whether the given function is even, odd, or neither. f(x) = (4 + x2) / (1…

A: Given function is fx=4+x21+x4. We have to check that given function is even, odd or neither. As we…

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A:

Q: 13. Determine algebraically whether g(x)= is an even function, an odd function, or neither.

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Q: A. (a) Sketch the graph of the function given (b) Determine if it is continuous at x, (c) Identify…

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Q: Consider the function. x - 8 f(x) x + 3 Step 1 of 2: Find all values of x that correspond to…

A: The given rational function is: f(x)=x-8x+3      =x+3-11x+3…

Q: 11. Determine algebraically whether the function is even, odd or neith g(x) = x2 +3

A:

Q: Find the x- and y-intercepts of the graph of the function f(x)=−3|x−1|+6. Enter your answers as…

A: We have to find x-intercept and y-intercept for the given function f(x) = −3|x−1|+6

Q: Determine (algebraically) whether the given function is even, odd, or neither. G(x) = x/(1 + x2)

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Q: A tortoise and a hare are competing in a 1600-meter race. The arrogant hare decides to let the…

A: According to guidelines I have answered first 3 parts. Total distance = 1600m Speed of hare= 8 m/s…

Q: 7. Sketch the graph of a function f that satisfies the given conditions: f(0) = 3; f(-2) = f(2) = -4…

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Q: Analyze the graph of the function f (x) 2 a+9|+12 compared to the graph of the absolute value…

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Q: Scetch the graph of f   f(x) = 2-x    if x1

A: Given, f(x) = 2-x    if x ≤ 1 f(x) = x2-2x+2   if  x &gt;1

Q: Lumber that is used to frame walls of houses is frequently sold in multiples of 2 ft. If the length…

A: To express f(x) explicitly as an expression and use it for computing the required values

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.