Calculus question and answers for November 16, 2023
- Q Perform the indicated operation and simplify the results. Assume that the denominator in each problem is not 0.a) Divide 6m + 2m by 2mb) Divide 8t?+ 4t by 4t c)...
- Q Solve for the variable P to two decimal places.60,900 = Pe^0.099(12)P = (Round to two decimal places as needed.)
- Q The range R of a projectile is related to the initial velocity v and projection angle by the equation R = v sin 2?/g, where g is a constant. How...
- Q The elasticity of a particular thermoplastic can be modeled approximately by the relation ? = 2.5x10?/T^2.3, where T is the Kelvin temperature. If the thermometer used to measure T is...
- Q Suppose that the dollar cost of producing x radios is c(x) = 200 + 10x - 0.2x. Find the average cost per radio of producing the first 30 radios.
- Q Given g(x)=x-9x, find the equation of the secant line passing through (-3, g (-3)) and (5, g (5)). Write your answer in the form y=mx+b.
- Q The one-to-one function g is defined below.g(x) = 9x/5x-6Find g?(x), where g? is the inverse of g.Also state the domain and range of g? in interval notation.g?(x) =Domain of g...
- Q Write 7 sinh(x) + 4 cosh(x) in terms of e^x and e^-x.
- Q Find the derivative of Fx)=2x-5 using limits
- Q Find all solutions of the equation.2 sin x + 1 = 0
- Q Find the exact value by using a sum or difference identity.sin 165
- Q For eac of functions f and g below, find f(g(x)) and g (f(x)). Then, determine whether fand g are inverses of each other.Simplify your answers as much as possible.(a) f(x)...
- Q Prove that k= 1/s , tau =0 s> o are the natural equations of the logarithmic spiral given by r= 1/?2 e^?
- Q Use sigma notation to write the sum.5/3+1 + 5/3+2 + 5/3+3 + ... + 5/3+14
- Q If you translate the graph of y = f(x) 4 units to the right, reflect it over the x-axis, stretch it vertically by a factor of 2, then translate it...
- Q Construct a variation of the Recaman sequence numerically and also with a picture and formula. This variation is that you do not increase by one, but by even numbers. Thus...
- Q Determine if the function y = x+1 / x^2 - 3x + 2 is continuous at the values x=0, x= 1, and x = 2.Is the function continuous at x...
- Q A football player punts a ball at an angle of 45 at 1.5 feet off the ground, with an initial velocity of 78 feet per second. How far away does...
- Q Given sin? = 8/17 and cos? = 15/17 which of the following can be proven using a Pythagorean identity?1 + (8/17)^2 = (15/17)^21 + (15/17)^2 = (8/17)^2(8/17)^2 + (15/17)^2 =...
- Q 1Which of the following is the simplified expression of 1+ 1/cot? tan??
- Q The concentration, C, of phenylbutazone, in micrograms per milliliter (g/mL), in the plasma of a calf injected with this anti-inflammatory agent is given approximately by C(t) = 42.06 e^ -0.01042t,...
- Q Given y=?x. Find dx/dt when y=7 and dy/dt = 1.55.
- Q Assume that x = x(t) and y=y(t). Let y = x +2 and dx/dt = 4Find dy/dt when x = 3.
- Q Let x = -16?/3Part A: Determine the reference angle of x.
- Q f(x) = 3x+12/x-4Findsa. relative maximum and minimumb. vertical and horisontal asymptotesc. Graph
- Q Use the two given functions to write y as a function of x.y = 4a-1, a = - 4x +3y =(Simplify your answer.)
- Q Graph the solution to the following inequality on the number line.(x+6) (x+1)>0
- Q Let f(x) = x/2 - sin ?x/6. Find all values of c in the interval (-1, 0) such that f'(c) =
- Q The count in a bacteria culture was 800 after 20 minutes and 1200 after 30 minutes. Assuming the count grows exponentially,What was the initial size of the culture?Find the doubling...
- Q Solve the equation |5x + 2| = 14The solutions are:
- Q Let f(x) = 1/x-6 and g(x) = 7/x + 6Find the following functions. Simplify your answers.f(g(x)) =g(f(x)) =
- Q Consider f(y) = -13y - 26 sin(y) on [0, 2?].Determine the intervals on which f is decreasing.f is decreasing on:f is decreasing nowhere.Determine the intervals on which f is increasing.f...
- Q Finding x- and y-intercepts given a polynomial functionFind all ercepts and y-intercepts of the graph of the function.f(x) = 3x +5x-12If there is more than one answer, separate them with...
- Q Find a polynomial f (x) of degree 4 with real coefficients and the following zeros.1 (multiplicity 2), -2+3i
- Q Determining the end behavior of the graph of a polynomial...(a) f(x)= = -2x + 2x - 7x + 4Falls to the left and rises to the rightRises to the left...
- Q Use thisto find all zeros of the function.f(x) = 5x+x2-20x-4If there is more than one zero, separate them with commas. Write exact values, not decimal approximations
- Q For the polynomial below, 2 is a zero.g(x)=x=x + 4xExpress g (x) as a product of linear factors.www.10x - 4
- Q For the polynomial below, -2 is a zero.f(x)=x + 3x - 4x - 12Express f(x) as a product of linear factors.
- Q Find amla-4, 3, 2-if(x) = 11degree 4 with real coerricleand the following zeros0x5U
- Q For theomial below, 2 and 1 are zeros.43f(x)=x-x-8x +16x-8Express f(x) as a product of linear factors.2
- Q Consider f(x) = -12 arcsin (625)Determine the intervals on which f is decreasing.Of is decreasing on:Of is decreasing nowhere.Determine the intervals on which f is increasing.Of is increasing on:Of is...
- Q f(x)=2x+8x+7 Identify the transformations for the given parabolic function, click all that apply.Hide answer choicesA shifts left 2B) vertical shrink by 2vertical stretch by 2D) shifts up 1E shifts right...
- Q Question 6 of 10 (1 point) | Attempt 1 of Unlimited View question in a popupCar inspection: Of all the registered automobiles in a city, 11% fail the emissions test....
- Q (a) Find the largest number 6 such that if Ix - 3| < 6, then [5x - 15| < &, where & = 0.5.d?(b) Repeat part (a) and determine &...
- Q Find a function that has derivative f'(x) = -6x-6 and with graph passing through the point (-6, 1).
- Q Locate the absolute extrema of the function g(x)=3x +5on the closed interval [0, 5]
- Q Determine the value of k5,f(x) = {kx + 5?Ak=4B. k=1C. k=2D. k=5IN2for which f(x) is continuous.x <3(x + k, x ? 3K
- Q Find c> 0 such that the area of the region enclosed by the parabolas y = x - c andy = c - x is 190.C =
- Q Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.Area: 25 square feetft (smaller value)ft (larger value)
- Q Use - ?o or ?o where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.f(x) = 2x/x+8Identify all vertical asymptotes. Select the correct...
- Q Use - ? or ? where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.f(x) = 2x/x+8Locate all zeros of the denominator and...
- Q Find the limit if it exists.lim 4xX?8Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. lim 4x =X?8(Simplify your answer.)B. The limit...
- Q Find lim f(6 +h)-f(6)/h if f(x) = 4x - 1. h?0lim f(6 +h)-f(6)/h if f(x) = 4x - 1. h?0(Simplify your answer.)
- Q Find the limits in a) through c) below for the function f(x) =x-9x+8/ x+8 Use ? and ? when appropriate.a) Select the correct choice below and fill in any answer...
- Q For the given function f, evaluate f(-4), (-3), (-2), and f(-1).f(x) = 2 if x?-4 -4 if x>-4
- Q For the given function f. evaluate f(-3), f(-2). f(-1), and f (0).f(x) =-2x+3 if x < -1 4x-2 if x>-1f(-3) =f(-2)=f(-1) =f(0) =
- Q Find (A) the leading term of the polynomial, (B) the limit as x approaches ?o, and (C) the limit as x approaches - ?p(x) = 5x + x - 6x6(A)...
- Q What is the area of the sector of a circle who's radius is 43.5 cm and is bounded by an arc of ?/12 radians?A. 247.7 cm2B. 5.69 cmC. 946.13 cmD....
- Q The position of an object is given by s(t) = In(t).What is the displacement of the object between t = 1 and t = 4?A. 3B. 4.159C. 4.328D. 16.87
- Q Find each function value and limit. Use - ?o or co where appropriate.f(x) = 3x - 6x / 10x? + 5(A) f(-6)(B) f(-12)(C) lim f(x)(A) f(-6)=(Round the nearest thousandth as...
- Q For the polynomial below, -3 is a zero.h(x)=x + 9x + 25x + 21Express h (x) as a product of linear factors.
- Q Let f(y) = -4-3y + 8yDetermine the critical values of f. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Use the Factor Theorem to determine whether x + 3 is a factor of P(x) = x + 2x +7.Specifically, evaluate P at the proper value, and then determine whether...
- Q Use the Factor Theorem to determine whether x +2 is a factor of P(x) = -2x?-2x+4x+24.Specifically, evaluate P at the proper value, and then determine whether x + 2 is...
- Q For f(x) = 1/6+x, the slope of the graph of y = f(x) is known to be -2/49 at the point with x-coordinate 1. Find the equation of the tangent...
- Q For the polynomial below, 2 is a zero.g(x)=x - 8x + 16x - 8Express g (x) as a product of linear factors.
- Q Find all asymptotes (vertical, horizontal, and/or slant) for y = x / (x-16 )
- Q Find the limit, if it exists. (If an answer does not exist, enter DNE.)lim x-6 / x + 3x?-?
- Q Use the remainder theorem to find P (3) for P(x) = -2x +6x-x-5.Specifically, give the quotient and the remainder for the associated division and the value of P (3).
- Q (-4x+9x-20x4+5-8x) (-4x+1)Write your answer in the following form: Quotient +
- Q Use the remainder theorem to find P (1) for P(x)=x+-4x-4x +9.Specifically, give the quotient and the remainder for the associated division and the value of P (1).
- Q A boat travels 26 miles east from a lighthouse then changes direction traveling 15 south of west for 13 miles. How far is the ship from the lighthouse? [?] miles
- Q For the polynomial below, 2 is a zero.h(x)=x - 8x + 14x - 4Express h (x) as a product of linear factors.
- Q For the polynomial below, 1 is a zero.f(x)=x + 4x + x - 6Express f(x) as a product of linear factors.
- Q Divide.(-3-14x+10x): (5x-4)Write your answer in the following form: Quotient +
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