Basic Math question and answers for August 02, 2023
- Q (use graphing calculator)find all the solution of the systemx^2+y^2=25 , x+3y=2
- Q A bag contains 5 ​batteries, all of which are the same sizeand are equally likely to be selected. Each battery is a differentbrand. If you select 2 batteries at​ random,...
- Q For the given function  use either the 1stor 2nd derivative test to calculate thefollowing:  (Show all work!!) (must show test used)      a).  all criticalpoints      b).  draw the signdiagram      c).  find allrelative extreme points.      d).  list theintervals where the function increases...
- Q Use the Divergence Theorem to calculate the surface integral S F· dS; that is, calculate the flux of F across S. F(x, y, z) = x4i −x3z2j + 4xy2zk, S...
- Q 1. Change from rectangular to spherical coordinates.(1,0,sqrt3)2. Change from rectangular to spherical coordinates.(sqrt3,-1,2sqrt3)
- Q Find intervals of increase/decrease, max/min values, intervalsof concavitiy.f(x)=x^3 -3x^2 +2
- Q A model for the average price of a pound of white sugar in acertain country from August 1993 to August 2003 is given by thefunctionS(t) = −0.00003237t5 + 0.0009037t4 −...
- Q The Cartesian coordinates of a point are given.(a)    (−3, 3)(i) Find polar coordinates (r, θ) of the point, where r > 0and 0 ≤ θ < 2π.(r, θ) =(ii) Find polar...
- Q The hydraulic oil in a car lift has a density of 8.10 x 102kg/m3. The weight of the input piston is negligible. The radii ofthe input piston and output plunger...
- Q 2) A ball is dropped from rest at the top of a high cliff. Ittakes 10.00 seconds for the ball to reach the ground below. Find:a) the height of the...
- Q Why is the basic purpose of Calculus?
- Q Find the slope of the tangent line to the polar curve r=1-2sintat t=pi/3.
- Q The body removes antibacterial drugs at a rate in proportion tothe amount present. Your task is to:Express this as a differential equation.Assume the initial dosage is 450 milligrams. 7 hours...
- Q Deriving the Area of an Obtuse Triangle You just derived theformula for the area of an acute triangle using trigonometricratios. Now extend the idea to finding the area of an...
- Q Suppose that at the certain factory setup cost is directlyproportional to the number of machines used, and operating cost isinversely proportional to the number of machines used. Show thatwhen the...
- Q The​ cross-section of a nuclear power​ plant's cooling tower isin the shape of a hyperbola. Suppose the tower has a base diameterof156 meters and the diameter at its narrowest​ point,...
- Q Describe how the formula for arc length is derived.Please provide diagrams and example.
- Q 1. Determine the following limits, if they exist. If you applyL’Hˆopital’s Rule, you must indicate the type of indeterminate formand each step you apply it.(a) (3 points) lim x→0+ √...
- Q Use spherical coordinates.EvaluateTriple Integral(1 − x2 − y2) dV, where H isthe solid hemisphere x2 + y2 + z2≤ 9, z ≥ 0.
- Q At what point is the function f(x)= |3-x| notdifferentiable.
- Q Determine whether the statement is true or false.1−937x2 sin (x − y) dx dy0=3017x2 sin (x − y) dy dx−9
- Q The boundary of a lamina consists of thesemicirclesy =1 − x2and y =25 − x2together with the portions of the x-axis that jointhem. Find the center of mass of the...
- Q verify the identitiesa.) (cos 8x + cos 4x) / (sin 8x - sin 4x) = Cot(2x)b.) tan^2(x/2) = 1 - 2cot(x)csc(x) + 2Cot^2x
- Q How can you give someone $83 using exactly 7 bills, without using any one dollar bills?
- Q The concentration of a drug in the body decreases exponentiallyafter a dosage is given. In one clinical​ study, adult subjectsaveraged 14 ​micrograms/milliliter (mcg/mL) of the drug in theirblood plasma 1...
- Q Let R(x), C(x), and P(x) be, respectively, the revenue, cost,and profit, in dollars, from the production and sales of x items.If R(x) = 6x and C(x) = 0.004x^2+2.7x+70, find each...
- Q A submerged circular disk with a radius of 8 meters isoriented vertically such that the topis 4 meter beneath the surface of the water. Find the hydrostaticforce on one side...
- Q initial value problemy'=ty(4-y)/3, y(0)=y_0determine the behavior of solution as t increases depends on theinitial value y_0The answer says that y->-infinite when y_0<0. but i cannotunderstand. please explain it
- Q Find the parametric equations of the line of intersection of theplanes x − z = 1 and y + 2z = 3. (b) Find an equation of the planethat contains...
- Q r4s2 + cos(rs)2+ sec (r + s) =5Suppose that s is a function of r.1)Find d/dr s of the following function:2)Suppose further that r is a function of q. Find...
- Q Choose ALL the statements that are true forf(x)=12x-x3a. The graph of f(x) is increasing on (-2,2)b. f(x) has no inflection pointc. The graph of f(x) is concave downward on (-...
- Q Assume that the height of a ball in feet off of the ground aftert seconds is given by the function h(t).If you know the following about the function h and...
- Q solve the following in detailed1. Considerthe curve 3x+y-5xy=2 andfind an expression for dy/dx2. A15 foot ladder is leaning against a wall. If the bottom of theladder is sliding away from...
- Q A piece of wire 10 meters long is cut into two pieces. One pieceis bent into a square and the other is bent into an equilateraltriangle. How should the wire...
- Q 1. If you only had a graph of the second derivative, how couldyou tell where the original function is concave down?2. If you only had a graph of the second...
- Q .If it has the following solution:y= c1 + c2 cos (2x) + c3 sin(2x) + c4 e3xThen:
- Q Suppose f(x) is a very well behaved function in that it iscontinuous and differential everywhere, and that f(2) = 6 and f(6)= 34.a. Find the slope of the line between...
- Q what is the derivative of y=e^x/(3x+1)^4(x+1)^3
- Q If I have the graph f(x)= 4x5 - 5x4 + 9 isit only possible to have a local max and min since the graph goesto +/- infinity?
- Q What are the different methods used to show a function is equalto its Taylor series near its center. In particular discussTaylor’s inequality and how it can be used. Give a...
- Q I Integrate x^2 e^(-.5(x+1))^2 dx from -infinity to+infinity
- Q (a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) isconcave up, and the intervals where f(x) is concave down, and theinflection points of...
- Q Recall that given a line L1 in the plane with slope m, a secondline L2 is perpendicular to L1 if and only if the slope of L2 is −1 m...
- Q find the area under the function f(x)=x^2 +5 from x=2 to x=4 taken=8
- Q Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curve aboutthe specified axis.1.y=sqrt(x-1) y=0 x=5;about the line y=32. y=5, y=x+4/x ;about...
- Q You have been contracted to design a walkway from a beachsidecottage to a scenic vista which is 50 meters down the beach and 30meters out into the ocean. Building a...
- Q Use the Integral Test to determine whether the infinite seriesis convergent.Sum from n=1 to infinity of5/(n(n+1))
- Q 1) Find the intervals on which f is increasing and the intervalson which it is decreasing. f(x)= -x^3-6x2) Find the intervals on which f is increasing and the intervalson which...
- Q There is 540 peoplein attendance at a high school basketballgame. The admission prices are $5 for students, $7 for parents, and$10 for faculty. The total revenue for the game is$3000....
- Q f(x) = -3x2+16x-5e) Find (in y=mx+b form) the equation of the line that containsthe vertex and the largest of the x-axis intercepts. If there aredecimals round to the tenths place.f)...
- Q The plane x+y+z= 24 intersects the conex2+y2= z2 in an ellipse. The goalof this exercise is to find the two points on this ellipse that areclosest to and furthest away...
- Q f(x) = x ln x(a) Write the Taylor polynomial T3(x) for f(x) at center a =1.(b) Use Taylor’s inequality to give an upper bound for |R3| =|f(x) − T3(x)| for...
- Q Find all horizontal and vertical tangent lines for theparametric curve defined by x(t) = t^3 - 3t +1, y(t) = 4t^2 +5.then write our the equations for the tangent lines
- Q Solve the following equation, giving the exact solutions whichlie in [0, 2Ï€). (Enter your answers as a comma-separated list.)cos(4x) = cos(2x)
- Q sketch the curve with the given polar equation by firstsketching the graph of r as a function of theta in Cartesiancoordinates.1) r = 3cos(3theta)2) r = 1 + 3cos(theta)3) r...
- Q Find an equation for the plane that is parallel to the plane3x−2y+z=1 and contains the point (2,0,−1). Write the equation inthe form ax+by+cz=d.
- Q Let C1 be the part of the exponential curve y = πe^x where 0 ≤ x≤ 1. Let C2 be the line segment between (1, πe) and (π, 2π). If...
- Q Approximate the area under the curve y=x^3+4 from x=2 to x=5using a left sum with 6 subdivisions.The area is approximately
- Q The plane curve represented by x(t) = t − sin(t), y(t) = 7 −cos(t), is a cycloid.(a) Find the slope of the tangent line to the cycloid for 0 <t...
- Q Calculus is closely associated with the idea of zero andinfinity and, to deal with these concepts, sophisticatedinstruments and themes are often used. The limit itself is one ofthose referenced concepts,...
- Q 3sin(t)+3sin(t)sin(2t)=3cos(t)-cos(3t).I'm trying to solve for t.
- Q Find the directional derivative of the function at the givenpoint in the direction of the vector v. ? = (2? + 3?)2, ? ⃑ = 1 2 ?⃑+ √3 2...
- Q The cost of producing x units of a product is given by C(x)=700+ 90 x - 90 ln(x), where x>=1Find the minimum average cost
- Q Approximate the sum of the series correct to four decimalplaces.∞(−1)n − 1n26nn = 1
- Q A zoo exhibit is to be made by: enclosing a rectangular area,and then divided horizontally down the middle perpendicular to oneside, then finally dividing it vertically 4 times perpendicular tothe...
- Q y''-5y'+4y=ety(0)=3y'(0)=1/3
- Q Let R be the region enclosed by the x-axis, the y-axis, the linex = 2 , and the curve ? = 2?? +3?(1) Find the area of R by setting...
- Q How to calculate the distance between trianglesIf you have two equilateral triangles and a different area andone inside the otherplease simple anwser
- Q Find the absolute minimum of the function f(x) = 2x^6 - 3x^4 onthe interval. (negative Infiniti, positive Infiniti)thank you
- Q Evaluate the integral by making an appropriate change ofvariables.7(x + y) ex2 − y2dA,Rwhere R is the rectangle enclosed by the linesx − y = 0,x − y = 3,x...
- Q Find the equation of the tangent line of the curve given by: ysin(6x) = x cos(6y)at the point (pi/6 , pi/12).
- Q by using double integral find the volume of the region thatbounded between two cylinder x^2+y^2=4 and x^2+z^2=4
- Q 1) A rectangular window is built with 12 meters of framingmaterials. What must the dimensions of the window be to let in themost light? Use calculus to solve2) What are...
- Q What is the difference between and definite and indefiniteintegral, the graphical interpretation of the definite integral andthe connection between the summation approximations. (left, right,trapezoid) with the definite integral.
- Q Find the volume of the solid region inside of the surface givenby ? 2 + ? 2 + ? 2 = 8 and between the upper and lower halves ofthe...
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