Calculus question and answers for August 18, 2023
- Q A 1000 L tank is draining such that the volume V of water remaining in the tank after t minutes is V = 1000[1 - t/60] Find the rate at...
- Q The population density of a city is given by P(x, y) = - 20x - 25y + 200x + 250y + 170, where x and y are miles from the...
- Q Which of the following shows the graph of g(x)= sec(x+?/2)-1?
- Q A sine function has an amplitude of 2, a period of ?, and a phase shift of -?/4.What is the y-intercept of the function?(a)2(b)0(c)-2(d)?/4
- Q A closed rectangular box is to be made with a volume of 0.9 m. In addition,1. the box must have a square base;2. the area of the base must not...
- Q The amount of daylight a particular location on Earth receives on a given day of the year can be modelled by asinusoidal function. The amount of daylight that Windsor, Ontario...
- Q If cos ? = sin ?, which of the following could be true of ? and ??I. ? + ? = 90II. ? and ? lie in different quadrantsIII. ?...
- Q Let g(x) = 7 sin x on [0, 2?].Determine the value(s) of x, if any, for which g has a horizontal tangent line.A. g has a horizontal tangent line at...
- Q Question 1(domain & range: 1, intercepts - 2 marks, asymptotes - 1, intervals ofincrease/decrease - 2, min/max - 2, points of inflection - 2, sketch 2)y = x - 16x...
- Q Let g(x)=(x-3)^(1/2)Determine the equation of the tangent line to g at (28, 5). Report the solution using slope-intercept form_____
- Q Let d(t) = 30t feet continue to be the distance function with respect to time (in seconds) of the car. We are going to compute the average velocity of d...
- Q Prove it;(secsec x-1)/ (secsec x+1) + (coscos x-1)/ (coscos x+1) = 23
- Q The formula t= 1/c in (A/A-N) is called the learning curve, since the formula relates time t passed, in weeks, to a measure N of learning achieved, to al earning...
- Q Find two linearly independent solutions of 2xy" - x y' + (5x+1)y=0, x >0 of the formy? = x^r1(1+ a? x + a? x + a? x + ...).y?= x^r2(1+b?x...
- Q An individual is 45 years old. At the end of each month, he deposits $270 in a retirement account that pays 5.11% interestcompounded monthly.(a) After 9 years, what is the...
- Q If a ball is thrown vertically upward with an initial velocity of 96 ft/s, then its height after t seconds is s = 96t -16t(consider up to the positive direction)(a)...
- Q a. For the plane with equation ? : 2x - y + 5z = 0, determine i. the coordinates of three points on this plane ii. the equation...
- Q Determine the equation of the tangent line to the curve f(x) = ?(6x +4) at x = 2. Write your equation in standard form.
- Q Charlotte invested $33,000 in an account paying an interest rate of 7(3/4)%compounded continuously. Alyssa invested $33,000 in an account paying an interest rate of 7(1/4)% compounded daily. After 19 years,...
- Q Let f(x) = -(1/2)x + 4Determine the equation of the line that is perpendicular to f at (-4, -4 ) .Report the solution using slope-intercept form .
- Q Let h(x) = 3x + 6x - 6Determine the equation of the tangent line to h at x = 9. Report the solution using slope-intercept form.
- Q Bella invested $7,400 in an account paying an interest rate of 5(3/8)% compounded continuously. Lily invested $7,400 in an account paying an interest rate of 5(3/4)% compounded quarterly. After 17...
- Q Find the arclength of y = 1 + 2x/ between x = 0 and x = 1.
- Q Let f(x) = (x+7) / (x-7) Determine the equation of the tangent line to f at (5, 6). Report the solution using slope-intercept form.
- Q Nevaeh invested $80,000 in an account paying an interest rate of 5 1/8% compounded continuously. Aaliyah invested $80,000 in an account paying an interest rate of 5 3/8% compounded monthly....
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