Calculus question and answers for November 17, 2023
- Q Let f(x) = 2log4(x - 1) + 3. Find the domain, range, and equation of the asymptote.Domain: (1,?)Range: (-?, ?)Equation of asymptote: y = 1Domain: (1, ?)Range: (-?, ?)Equation of...
- Q State the domain of the function. Give your answer as an inequality.f(x) = ln (5-x)
- Q Use properties of exponents to find the x-intercepts of the function f(x) = log(x + 4x + 4) algebraically.
- Q Use a graphing calculator to approximate the solution to the equation. Round to three decimal places.2 ln (4x + 1) = 1 2In (-4x) + 1
- Q Solve the system of equations.x - 3y - z = -6-x + 8y-4z = 162x-15y +7z = -30Select the correct choice below and fill in any answer boxes within your...
- Q f(x) = log6 (x+6) ? 5What is the domain of the function?(-6,?)(-?, -6)(-?, ?)(6,?)What is the range?(5,?)(-?,?)(0,?)(-?, -5)At the x-intercept, x =At the y-intercept, y =
- Q Imagine the point (-?3 2, 1 2) on the terminal side of an angle.Find the value for the cosecant of this angle.negativepositive
- Q Solve the following system of equations.x + y + z = - 42x + 4y + 2z = - 18-x + 7y - 3z = -34Select the correct choice below...
- Q If the calculator gives us the following values for "a" and "b" in the form of y = ax + b, what should the regression equation (statistics form) look like?...
- Q Suppose that a polynomial function of degree 4 with rational coefficients has -2+5i, 5-sqrt5 as zeros. Find the other zeros.
- Q For the function f(x)=x +3, construct and simplify the difference quotient f(x+h)-f(x) hThe difference quotient is
- Q A silver dollar is tossed vertically from the roof of a building that is 57 meters tall. If the silver dollar impacts the ground after 6 seconds, determine the initial...
- Q Click on the equivalent radical form of the exponential expression.x7/27?x?x7?x(?x2)7
- Q A penny is tossed vertically from the roof of a building that is 126 feet tall. If the penny impacts the ground after 10 seconds, determine the initial velocity, v0,...
- Q Let g''(v) = 36vFind the particular solution to the above differential equation that satisfies the following initial conditions.g'(0) = 6g(5) = -2
- Q Let dh dz = e7zFind the particular solution to the above differential equation that satisfies the following initial conditions.h'(0) = -3h(0) = 1
- Q A particular cookie recipe calls for 1 6 cups of butter to make 3 dozen cookies. Giselle needs to make 24 dozen cookies for the bake sale. How many cups...
- Q In(1/200)Step 1Apply the logarithmic property, In(a/b) = In(a) In(b), to simplify. In(1/200)=ln ) - ln(200Write the factors of 200.In(1/200) = lnn(1) - In(8 )
- Q Use long division to find the quotient and remainder.(3x + 25x+28) = (x + 7)What is the quotient?What is the remainder?
- Q Find the mass and center of mass of the lamina that occupies the region D and has the given density function p.D = {(x, y) | 1 ? x ?...
- Q Write the factors of 40,In(40) = In(8 x )
- Q After the announcement of a sale, a bookstore sold % of all its books in stock. One thefollowing day, this bookstore sold 4,000 more books. Now only 1/10 of the...
- Q Use the given polynomial function to answer the questions.What is the degree of the polynomial? (x) = ?x (3x ? 2)What is the leading coefficient?Which describes the end behavior of...
- Q What kind of transformation converts the graph of f(x) = 2x + 9 into the graph of g(x) = 8x + 9?horizontal stretchvertical shrinkvertical stretchhorizontal shrink
- Q The pH of a solution ranges from 0 to 14. An acid solution has a pH less than 7. Pure water is neutral and has a pH of 7. The...
- Q Let v > 1. Show that8v - 8 v - 1 > 8 ln 8Justify your answer.Hint: Apply the Mean Value Theorem to f(x) = 8x on [1, v].
- Q Consider the equation below. (If an answer does not exist, enter DNE.)f(x) = 5 cos(x) - 10 sin(x), 0?x?2?(a) Find the interval on which f is increasing. (Enter your answer...
- Q Use Newton's method with initial approximation x1 = -1 to find x? the second approximation to the solution of the following equation.x + x + 7 = 0
- Q A radioactive material has a decay rate of 0.019% per year. Suppose that a nuclear accident causes this material to be released into the atmosphere perpetually at the rate of...
- Q For the probability density function, over the given interval, find E(x), E(x2), the mean, the variance, and the standard deviation.f(x) = 1 18x2, [-3,3]
- Q A number x is selected at random from the interval [4,20]. The probability density function for x is given by the following function. Find the probability that a number selected...
- Q Use the graph of f in the figure to the right to complete parts (A) through (M) (assume that f''(0) <0, f''(b)>0, and f''(g) > 0).(L) Find the horizontal asymptote(s)....
- Q Fill in the following blanks with the greatest digit that makes each statement true.a. 3 | 53_b. 9 | 809_7c. 11 | 54_9d. 5 | 347_e. 6 | 4_18f. 8...
- Q Of all numbers whose difference is 2, find the two that have the minimum product.What are the two numbers?
- Q A survey found that 10 out of 15 students like pizza. If four students are chosen at random what is the probability that all the four students like pizza?
- Q A group of researchers wanted to measure the impact of playing classical music at bedtime to infants. They choose 20 infants to play music from 6:30 - 7:30 pm at...
- Q Monthly sales of a particular computer are expected to decline at the following rate of S'(t) computers per month, where t is time in months and S(t) is the number...
- Q For the quadratic function f(x)=-(x+4)-3, determine the largest open interval of the domain (a) over which the function is increasing and (b) over which the function is decreasing.A) The largest...
- Q Find the following product, and write the result in rectangular form using exact values.(8 cis 30)(3 cis 195)
- Q Consider the exponential function f(x) = 10.8(0.65)x. Using a graphing calculator, determine the function's half-life (the change in z for the output value to cut in half).
- Q Solve the following system of equations using the substitution method.2x - y = 4 (1)2y = 4x-8 (2)What is the solution of the system? Select the correct choice below and,...
- Q Solve by the elimination method. Also, determine whether the system is consistentor inconsistent, and whether the equations are dependent or independent.7/2x + 7/3y = 259/61/4x+1/3y=47/12(Hint: First multiply by the least...
- Q For the graph of y = f(x) shown to the right, find the absolute minimum and the absolute maximum over the interval [1,11].Identify the absolute minimum. Select the correct choice...
- Q Solve using the elimination method.0.2x-0.3y = -0.40.3x-0.2y = -0.6(Hint: Since each coefficient has one decimal place, first multiply each equation by 10 to clear the decimals.)Select the correct choice below...
- Q Write the function as a sum of terms of the form axn, where a is a constant.f(x)=10/x4
- Q Suppose f(x) = -1/2 Determine and graph four distinct antiderivatives of f.
- Q A study of consumer smoking habits includes 193 people in the 18-22 age bracket (60 of whom smoke), 127 people in the 23-30 age bracket (35 of whom smoke), and...
- Q The Topology Taxi Company charges 2.50 for the first quarter of a mile and 0.45 for each additional quarter of a mile. Find a linear function which models the taxi...
- Q The following involves a trigonmetric equation in quadratic form. Solve the equation on the interval [0,2?).6 tan2 x-18=0
- Q Solve the inequality and enter the solution set in interval notation. Type infinity for and negative infinity for -?. Do not enter blank spaces in your answer.12x - 48 ?...
- Q Find the exact value of cos ?.sin ?= -12/13, ?<?<3?/2
- Q Let f (x) = 3 (1/2) .Evaluate the following:f(-1) =f(0) =f(2)=Is f(x) increasing or decreasing? (Hint: Type in "inc" for increasing and "dec" for decreasing.)
- Q Let f(x) = 2(3)x.Evaluate the following:f(-1) =f(0) =f(2)=Is f(x) increasing or decreasing? (Hint: Type in "inc" for increasing and "dec" for decreasing.)
- Q An investment of $45,000 earns 6% annual interest and is compounded semiannually. If no funds are added or removed from this account, what is the future value of the investment...
- Q Graphical Behavior of the Log to the Base 10 (Common Log) Function:a. Plot both the exponential function f(x) = 10 * and the logarithmic function g(x) = log10 x in...
- Q Suppose you have a non-right triangle such that angle A is opposite of side a, angle B is opposite of side b, and angle C is opposite of side c....
- Q Find the domain and intercepts.f(x) =42/x-3A. The x-intercept(s) of the graph is (are) x =(Simplify your answer. Type an integer or a decimal. Use a comma to separate answers as...
- Q Find all real solutions of the equation (x - 5) = 36. x1 = and x2 = with x1<x2
- Q The temperature of a pond has been fluctuating abnormally over the past three days. A computer program has calculated the deviation from the normal temperature to follow the function ?(t)=t-1...
- Q The polynomial function fis defined by f(x) = ?2x-3x+4x+5x+2.Use the ALEKS graphing calculator to find all the points (x, f(x)) where there is a local minimumRound to the nearest hundredth.If...
- Q Suppose that the supply and demand equations for printed T-shirts for a particular week are given as follows, where p is the price in dollars and q is the quantity...
- Q Below is the graph of y = 3xTranslate it to become the graph of y=3x-4 +2.
- Q A principal of $3000 is invested at 6.5% interest, compounded annually. How much will the investment be worth after 13 years? Use the calculator provided and round your answer to...
- Q The student council at a college is made up of five freshmen, six sophomores, seven juniors, and eight seniors. A yearbook photographer would like to line up two council members...
- Q For z = 3-4 i and w = 3+2 i calculate a 10 significant figure approximation to the argument of(w13+z11) / (z18+w17)
- Q Verify the following identity.-tan ?/2 = tan ? / sec ? + 1
- Q Write the polynomial inequality in the form p(x)<0(x)<0, p(x)?0(x)?0, p(x)>0(x)>0, or p(x)?0(x)?0; then find the real zeros of p(x) (x).
- Q Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = (x+3) exCompute the derivative of f(x).f'(x) =Select the correct choice...
- Q Find the consumer surplus at the equilibrium point. Round to the nearest cent.D(x)=(x-3); x =3/2A. $7.28B. $3.25C. $4.33D. $4.50
- Q Find the present value of $11,700 due 7 yr later at 12.5% compounded continuously. Round the answer to the nearest cent.A. $3,707.29B. $4,877.29C. $28,066.82D. $26,896.82
- Q Find the equilibrium point.D(x)=9-6x, S(x) = 4 + 6xA. (5/12, $19)B. (-5/12, $1.5)C. (5/12, $6.5)D. (5/2, $19)
- Q Find the absolute maximum and absolute minimum values of f on the given interval.f(t) = 2 cos(t) + sin(2t), [0,?/2]
- Q 1000 dollars grows to 1 million dollars after 60 years in a bank. If interest is compoundedcontinuously, what is the rate of interest per year?a 1.83%b. 11.51%c. 28.13%d. 3.84%e 0.12%
- Q Bob and Doris Mackenzie have a new grandchild, Brenda. They want to create a trust fund for her that will yield $250,000 on her 24th birthday. a) What lump sum...
- Q At age 35, Clarence earns his MBA and accepts a position as a vice president of an asphalt company. Assume that he will retire at the age of 65, having...
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