Calculus question and answers for August 19, 2023
- Q For the real-valued functions g(x)=x-5. and h(x)=?x-2, find the composition g h and specify its domain using interval notation.
- Q For the real-valued functions g(x) = 4x-1 and h(x)=?x+5, find the composition g h and specify its domain using interval notation.
- Q A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the firstmodel made, and let y represent the number (in millions) of the second...
- Q The point A(3, 9) lies on the curvey=x40If B is the point (x, x^2), find the slope of the secant line AB for the following valuesof x. Use all decimal...
- Q Write an inequality to describe the region.The region between the yz-plane and the vertical plane x = 3.00<x<30 < x + y + z < 30<z <30<y<3none of these
- Q If = 2 +33 + 12kland B-3+43-6are the two vectors, find the resultant vector.O 5+7+6O 5 73 +6O 573 6?>Osi+73-6
- Q For the real-valued functions g(x)=x +1. and h(x)=x-5, find the composition g h and specify Its domain using interval notation.
- Q f(x) = -3x+4g(x)=?4x-3Find f.g and f+g. Then, give their domains using interval notation.
- Q Find an equation of the sphere that passes through the point (1, 6, 3) and has center (3, 5, -5).
- Q Find the scalar and vector projections of b onto a.a = (6, 7, -6) b = (3,-1, 1)scalar projection of b onto avector projection of b onto a
- Q In a composite function, If f[g(x)] = x=g[f(x)] thenOf(x) and g(x) must be same functionsOf(x) and g(x) is not a functionOf(x) and g(x) are inversesOf(x) and g(x) must be different...
- Q Choose the best description of the normal line.a line parallel to a given line or curvea line with a zero slopeCCa line with an undefined slopeCa line perpendicular to a...
- Q Find the extreme values of the function on the given interval:16f(x) = x + 6; 1 ? x ?41 and 41 and 22 and 41, 2, and 4
- Q Find a + b, 9a + 7b, lal, and la - bl. (Simplify your vectors completely.)a = 9i - 8j + 7k, b = 7i - 9ka + b119a +...
- Q The conjugate of a complex number a + bi is 25+ 3i. What is a + bi?- 25 + 3iO25-3iO-25-3i25+ 3i
- Q Which of the following statements is the most correct statement regarding thecritical points of the following function.3y = ax + bx + cx+dthere can be any number of critical pointsthere...
- Q Describe the surface in R3 represented by the equation x + y = 4,This is the set {(x, 4-x, z)|x ER, ze Ry which is a horizontal plane that intersects...
- Q If k is positive in y = f(x) + k, then shift the graph of the parent functionby k units.upwarddownwardrightleft
- Q Find the slope of the tangent to the curvey = 1+ln zat the point (1, 1).0 FNO1O o1
- Q Let f(x)10x+12point (0,5) is given by ym =b-7e". Then the equation of the tangent line to the graph of f(x) at the= mx + b for
- Q -Determine the slope of the tangent to the graph of y = (x + 3x ? 2)(7 - 3x)at (1,8).
- Q Let s(t) = 6t - 27t - 180t be the equation of motion for a particle. Find a function for thevelocity.v(t) =-Where does the velocity equal zero? [Hint: factor out...
- Q Determine the equation of the tangent to y = (3x-2 - 2x)5 at (1, 1).
- Q Simplifysin (t)to an expression involving a single trig function with no fractions.1 sin(t)If needed, enter squared trigonometric expressions using the following notation.Example: Enter sin (t) as (sin(t)).
- Q Find x in the following equation.logbx+ logb(x-2) = log24X=
- Q What is - 2 x (8 - i)?- 16 + 2iO-16-2i16 + 2i- 10 + 2i
- Q Solve cos(x)There are two solutions, A and B, with A <BA =-0.25 on 0x< 2?B =Give your answers accurate to 3 decimal places
- Q A spherical balloon is inflated with gas at a rate of 700 cubic centimeters per minute.(a) Find the rates of change of the radius when r = 70 centimeters and...
- Q Determine the points on the curve y = x x - x + 1 where the tangent-is horizontal.
- Q Consider the following function.f(x) = (x + 6)2/3(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X =(b) Find the open intervals on which the function...
- Q Determinea. y =dydxfor each of the following functions:c. y =?+ ?-b. y = 6(2x - 9)52?x3x5 + 4?+XV3+ 6?3/xI
- Q Find the point where the tangent line to y = x at x = 0.3 crosses the x-axis.x-intercept =
- Q If f(x) = x + 3x + 4x + 5 and g(x) = 5, then g(f(x)) =O5x + 15x + 20x + 252255x + 15x + 25051125A
- Q Let h(x) = e-4Determine the equation of the tangent line to h at x = -1. Report the solution using slope-intercept form.Submit Question
- Q Find the slope of the tangent line to the curve-3x + xy + 2y = - 24at the point (4, 2).Slope
- Q Use the given information to answer the following questions.center (3, -2, 5), radius(a) Find an equation of the sphere with the given center and radius.(b) What is the intersection of...
- Q Solve sec(4a)-8= 0 for the four smallest positive solutionsB
- Q Solve 7 sin(1) = 2 for the four smallest positive solutions
- Q The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rate of change of the area whenr = 29 centimeters.
- Q Determine an angle that is a coterminal angle of the angle 0. Use degree measure. (Answers may vary.)-1.0-0.5y1.00.5-0.51.00=117120.51/0X
- Q A car travels 13 km southeast andthen 16 km in a direction 40north of east. Find the direction ofthe car's resultant vector.[?]
- Q Consider- 10 In (y) = 6y sin Determine the equation of the tangent line at (0, 1). Report the solution using slope-intercept form.
- Q ConsiderDetermine the derivative of y with respect to x.=5x + yx - 2y= x7
- Q The radius r of a sphere is increasing at a rate of 3 inches per minute.(a) Find the rate of change of the volume when r = 12 inches.in./min(b) Find...
- Q Let f(x) = x?3+xDetermine the equation of the tangent line to f at (1, 2). Report the solution using slope-intercept form.
- Q Find the equation of the line tangent to the graph of x + y = 5xy 11 at (1, ? 3).The equation of the tangent line is
- Q 1(5 - 8x) Determine the derivative of h.Let h(x)=h'(x) =Determine the slope of h at x = -6.h'(- 6) =
- Q Problem 8. A baseball is launched into the air with an upward velocity of 106 feet per second.The height of the baseball after t seconds can be represented by the...
- Q DShrives Publishing recently reported $13,000 of sales, $5,500 of operating costs other than depreciation, and $1,250 of depreciation. The company had $3,500of bonds that carry a 6.25% interest rate, and...
- Q Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month payments. What percentage ofthe 2nd monthly payment will...
- Q You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month,how many months...
- Q Sean gets an average of 20 calls during his 8 hour work day. What is the probability that Sean will get at most 9 calls in a 4hour portion of...
- Q Find an equation to the tangent time for the graph of/ at the given pointf(x)=(2x + 8), (1, 100)
- Q After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for thefirst 6...
- Q An office copier has an initial price of $2,300. A service contract costs $200 for the first year and increases $60 per year thereafter. It can be shown that the...
- Q Use the Principle of Mathematical Induction to show that the following statement is true for all natural numbers n.19+8+7+...+(10-n) = n(19-n)What two conditions must the given statement satisfy to prove...
- Q Prezas Company's balance sheet showed total current assets of $2,500, all of which were required in operations. Its current liabilities consisted of $975 ofaccounts payable, $600 of 6% short-term notes...
- Q Problem 5. Find the standard form of the equation of the circle x + y - 2x +12y + 12 = 0.Then, state the center and radius of the circle.
- Q Problem 1. If f(x) has an inverse function f-(x), could either the graph of f(x) or the graphof f(x) be symmetric with respect to the y-axis? Explain your reasoning or...
- Q Your Aunt Ruth has $540,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately.How many years will it...
- Q A survey team is trying to estimate the height of a mountain above a level plain. From one point on theplain, they observe that the angle of elevation to the...
- Q A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5.3mi apart, to be 35 and 51, as shown in the figure.ANOTE: The...
- Q Graph the following function over the indicated interval.y=2*; [-3,3]Choose the correct graph below.O A.AyO B.-4Ay10-Q?OQC...O C.AyQKLAQ-4O D.AyO
- Q Assume Za is opposite side a, ZB is opposite side b, and Zy is opposite side c.Solve triangle ABC if ZA = a = 36.9, b = 12.6 mi, and...
- Q A water tower is located 412 feet from a building. From a window in the building, an observer notesthat the angle of elevation to the top of the tower is...
- Q 5. Let C be the curve of intersection of the hyperbolic paraboloidz=x-y and the cylinder x + y = 1.(1) Find the curvature of C at the point P(1,0,1).(2) Find...
- Q The function f(x) = (7x - 9)e(7x - 9)e-2 has one critical number. Find it.
- Q we know barycentric coordinates is definedas :(ao +...+an)OP = ao OA++ an OAn,below is two results of the coordinates,please point out OP and OAO OA1 -- OAnBarycentric coordinates ...(1,0,0)(1,0,0)(1/2,1/2,0)(1/2,1/4,1/4) (1/4,...
- Q Susan is six years older thanBeth. In four years, Susan willbe twice as old as Beth. Howold is Susan now?
- Q Using the information from the tablebelow, draw the graph for a function f.Label all intercepts, horizontal andvertical asymptote(s), inflection point(s)for full credit.Domain of fI and y coordinates of r- intercepts...
- Q Consider the curve given by y5 + 1 = ln(x + 5).a. [2 pts] Use a computer to graph the curve. Make sure to include most interestinfeatures in your graph.b....
- Q Consider the function f(x) = x - 50x +11, -4? x ? 11.The absolute maximum of f(x) (on the given interval) is atx=and the absolute maximum of f(x) (on the...
- Q Find the coordinates of the ordered pair where the minimum value occursfor the equation Q = 9x + 2y + 12, given these constraints:x ?-1-2x+y 202x + y ? 4O...
- Q MY NOTES PRACTICE AA tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume...
- Q Determine the equation of the tangent line to the curvezy = IngIat x = 1:Oy=-x+1Oy=-x-1Oy=x-1Oy=x+1
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
- Unlimited Question Access with detailed Answers
- Zin AI - 3 Million Words
- 10 Dall-E 3 Images
- 20 Plot Generations
- Conversation with Dialogue Memory
- No Ads, Ever!
- Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!