A boat at anchor is bobbing up and down in the sea. The vertical distance, y, in feet, between the sea floor and the boat is given as a function of time, t, in minutes, by y = 11 + cos(2nt) ft. Find the vertical velocity, v, of the boat at time t. v = ft/min

Q: find the equation of the tangent line at x=-6 for f(x)=x^3/2. write the answer in the form y=mx+b

A:

Q: A rope passing through a capstan on a dock is attached to a boat offshore. The rope is pulled in at…

A:

Q: 1 R(t) = 2 sin(t) – 4 cos(1)

A:

Q: Write the function f(t) in terms of unit step functions and then find L {f(t)}: f(t) = { sin 3t 0st<…

A: For (a), We need to compute, L{t cos (5t)}.

Q: Function Point h(t) sin t + et %D 7 7

A:

Q: Given f(x) = 6xe® csc(x), answer the following: a) f'(x) = b) The equation of the tangent line to…

A: A function f(x)=6xexcsc(x), we have to find the derivative of the given function i.e. f'(x) also…

Q: The velocity of a particle moving along the a-axis is given by f(t) = 12 – 4t cm/sec. Use a graph of…

A: Here we have to use the graph of the f(t).

Q: Consider the function y = x(In x)². At which point the tangent line to the graph of this function is…

A:

Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3,5).…

A:

Q: A ball is thrown vertically upward from a height of 5 feet with an initial velocity of 40 feet per…

A: Given , initial speed u=40ftsec           Final speed v=0 ftsec          acceleration=-32 fts2From…

Q: Carry out the following steps. a. Use implicit differentiation to find dy/dx .b. Find the slope of…

A: a. Use implicit differentiation to find dydx. ddxx-2y=ddx012x-2×12ydydx=012x=1ydydxdydx=y2xdydx=xy2x

Q: The shape of f (x) = ln x, but shifted three units upward andreflected in the y-axis

A: Given: f(x)=ln(x) Let the function be y=ln(x) The graph is shifted 3 units upward. y+3=lnx

Q: d. To simplify calculations, a student uses a tangent line approximation to P(t) at 1=0 as a model…

A: (d)

Q: 1. If friction is ignored, the time, t (in seconds) required for a block to slide down an inclined…

A:

Q: Determine the number(s), x, between 0 and 2T where the line tangent to the function f(x) = 5 3…

A:

Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

A: Differentiate the distance function, s(t) with respect to t to calculate the velocity function,…

Q: r = -1 + cos 0 0=t/2

A: In the question we have to find the slope of function -…

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: b) Find f(1) and find the equation of the tangent line at the point (1, f(1). c) Graph y = f(x) and…

A:

Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

A:

Q: The distance (in km) of an airplane departing from Toronto Pearson Airport t seconds into flight is…

A:

Q: The depth d of the water in a harbour, measured in meters, t hours after midnight, can be…

A: Form an inequality representing this scenario. Solve that inequality to yield the result.

Q: Carry out the following steps. a. Use implicit differentiation to find dy/dx .b. Find the slope of…

A: Given curve is cosy=x. Chain rule of differentiation states that: ddxfgx=f'gx·g'x Differentiating…

Q: The amount of daylight in a town can be modelled by the sinusoidal function d(t)= 4.37 cos 0.017t +…

A: Solution of given question is written in below steps.

Q: For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs…

A: Explained below

Q: Find the derivative of the trigonometric function. f(t) = 3 sec ( t − 1)2

A: To find the derivative of ft=3 sect-12

Q: Given f(x)=cos(3x) write the equation of the line tangent to y=f(x) when x=π/18

A:

Q: For what value(s) of t will the slope of a line tangent to x = 6 sin t, y = t² + t be undefined, for…

A: Here we have to find the slope of the tangent line.

Q: Find the differential of each function.

A: (a) Differentiating with respect to t, we get

Q: On a particular summer day the temperature function in Celsius is given by (T(t +7) T(t) = 20 + 8…

A: Note : As per our guidelines we are supposed to answer only one question. Since you have asked…

Q: If T(æ) = + is the temperature of a runner (in Fahrenheit) at a distance x from the start line (in…

A: Given: The function of temperature of a runner at a distance x is given as T(x)=1x+1x9. The…

Q: Determine the derivative of the function f = log, | tan 5m + sec 5m| with respect to m. O cot (5m)…

A:

Q: The productivity of a person at work is modelled by a cosine function: y = 5 cos s(t) +5, where t is…

A:

Q: For the graph of g(x) = 3* cos(x), which of the following numbers is closest to the slope of the…

A:

Q: Express the hupotenuse of h of a night triangle with an area of 25 m a function of its peri meter P.…

A: This question is based on Triangle.

Q: Find the equation of the tangent line at x =7 for f(x) = 6 – x. Write the answer in the form y= mx…

A: Equation of the tangent at x=7 is y=mx+b where m is slope

Q: Consider the function f(x) = e^x2−6x+5 . Find the value(s) of x at which the tangent line is…

A: Given thatf(x)=ex2−6x+5ddx(f(x))=ddx(ex2−6x+5)               =ex2ddx(x2) −6               =2xex2-6

Q: Draw the following function (y = t * sin (t). * Sin (t) if you know that the t-values range from…

A: given function is                                                 y=t sint,    0≤t≤2π graph is

Q: The motion of a cam is defined by the relation @=0.30t(12-t2) where @ is expressed in radians and t…

A: We are given : θ=0.30t(12-t2)=3.6t-0.30t3 Angular Displacement at t=4 : θ(t=4) =0.30(4)(12-16)=-4.8…

Q: During the time interval 3 <t < 8, the rate at which the number of bears in a forest is changing, in…

A:

Q: x = 6 sin t, y = t +t at t = 0.

A: Let's find.

Q: Find dy Idx for the following implicit functions : y2.cot x = [sin(x. y)]-1

A: Given y2cot(x)=[sin(xy)]-1            =1sin(xy)            =cosec(xy)          ∵1sin(x)=cosec(x)By…

Q: . The velocity, v, of an object in a medium at -80 dv time t seconds is given by: t = 20 v(2v – 1) -…

A:

Q: Let a function y(x) be given implicitly by the formula: y3 − 3xy2 + y cos(x) − x4 = 10. Find the…

A:

Q: Find the derivative of the trigonometric function. Re) = e® sin(e) f (e) = -1

A:

Q: Find the derivatives of the functions q = cot (sin t/t)

A:

Q: C-the derivative is y = 0³ e 28 cos 50

A:

Q: Consider the function -3t h (t) = e cos (2t) . Compute h' (T/3) ~ Number FORMATTING: Give the value…

A:

Q: Given position s (in ft.) as a function of time t (in sec.): s=ť – 6t + 1, find the acceleration…

A: Given S(t)=t3-6t+1 is the equation for positionWe know that we get velocity upon differentiating the…

Q: The velocity, v of a body as a function of time, t is given as v(t) = 5e4+4, where t is in seconds,…

A: Since, we have been given that v(t)=5e-2t+4-(i), where t is in secondsand v is in m/s.Our Aim is to…