Water is pumped into a sphere of radius R at a variable rate in such a way that the water level rises at a V (approximately, but 63. constant rate (Figure 21). Let V (t) be the volume of water in the tank at time t. Sketch the graph with the correct concavity). Where does the point of inflection occur? FIGURE 21

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 + 1 y = y 6 4 -1 1…

A: y=23x2+132 Differentiating with respect to x, we get dydx=23·32x2+132-1·dx2+1dx=x2+112·2x=2xx2+112

Q: A tennis player moves in a straight-line path as shown in the figure. On the vertical axis in the…

A: a) Starting from origin at t = 0, the position of the tennis player is 3.5 m at t = 1.0 s , so the…

Q: The slope of the tangent line to the curve x = t cost and y = t sin t at the point corresponding to…

A: The slope of tangent line

Q: In the given question , find the arc length of the graph of the function over the indicated…

A: Given: x = 13 y2+232,   0 ≤ y ≤ 4 To find: The arc length of the graph of the function over the…

Q: Find the arc length of the graph of the function over the indicated interval.

A: Using the power rule we find the derivative of y

Q: If a is a positive integer, then the slope of the tangent to the graph of y = + a ln(ax) at x = 1 is…

A:

Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

A:

Q: a² + y? – a*y³ f(r, y) x² + y?

A:

Q: Find the length L of the arc formed by y=e^4x/4,0≤x≤3

A: To find the length L of the arc formed by y=e^4x/4,0≤x≤3

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 speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

Q: A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at…

A:

Q: Suppose the velocity of a particle at time t is given by 3/19 (t+1) + VI+1 7(1) tan(t) %3D 1+ t2

A:

Q: It is known that at a distance of 1.5 metres from the siren, the sound intensity is 4 watts per…

A:

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: The tangent line to the graph of y = e² at æ = 0 is perpendicular to the tangent line to y = e at æ…

A:

Q: Find the arc length of the graph of the function over the indicated interval.

A:

Q: Find a > 0 such that the tangent line to the graph of f(x) = x?e=* at x = a passes through the…

A:

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 y 40 30 20 10 2 4…

A: For the function f(x)  defined in the  in the interval  [a,b]   the arc length is  given by…

Q: (a) Find the velocity at time t.

A:

Q: Find the arc length of the graph of the function over the indicated interval.

A: Differentiating with respect to x, we get

Q: The accompanying figures show the position versus time curves of four different particles moving on…

A: Suppose the position of the particle at any time t be s, then instantaneous velocity=dsdt This…

Q: The slope of the tangent line to the graph of z- y? = In(zy) at the point (1,1) is Select one: O a.…

A: Given the equation of the curve x2 -y2 =ln(xy) We have to find the slope at (1,1) So, the slope is…

Q: 2. Suppose s(t) is the position of an object moving along a line at time t > 0. Describe a process…

A:

Q: Find the arc length of the graph of the function over the indicated interval.

A:

Q: Find the arc length of the graph of the function over the indicated interval.

A:

Q: The radius of the first circle is modeled by w(t)=12-12e^-0.5t at what time t is the radius of the…

A: The given equation of circle is w(t)=12-12e-0.5tUpon differentiating: (As it is given rate, we…

Q: Find the arc length of the graph of the function f(x) = (4/5)x5/4 over the interval [0, 4].

A:

Q: Sketch the curve. And indicate the direction of increasing T at T =0

A:

Q: Find the arc length of the graph of the function over the indicated interval. =극v2 + 2)32, 0sys7 X =

A: Use length of curve formula about Y axis

Q: If an airplane is flying at 140 miles per hour East and turns in a smooth curve with a diameter of 3…

A: Given Velocity=140 miles per hour diameter=3 miles Centripital acceleration=v2r

Q: Which of the following is true about the net distance traveled by an object from time t = a to time…

A: Given,           The net distance traveled by an object from time t=a to time t=b where…

Q: Find the arc length of the graph of the function over the indicated interval. y = 3/2 + 1 y 40 30 20…

A: This is application of derivative problem

Q: Find the length of the arc of the curve y = ln x over the interval: 1, 7| . Round the answer to four…

A:

Q: The slope of the tangent line to the graph of y? = In(ry) at the polnt (e, 1) Is Select one: a.e=1…

A:

Q: Suppose that the radius r and area A = pai r2 of a circle are differentiable functions of t. Write…

A: Given, Radius = r Area = A= pi*r^2

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: Find the arc length of the graph of the function over the indicated interval. X = 3 Vyv - 3), 1<y s…

A:

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA in…

A:

Q: Find the arc length of the graph of the following function over the interval [2, 3]. 1 f(x) = 4x2

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

A:

Q: The graph of y = 2x (x+ 1) and y = 1 (x>0) intersect at one point, x=r, as shown to the right. Use…

A: Let the given functions be, hx=2x2x+1gx=1x Equate both the functions,…

Q: Ithe particle is at the point (1, ) at time t 0, how far is the particle from the origin at time t=…

A:

Q: 1.4 Using the graph in Figure 1.7 below, find Sº, f(t)dt and if the area of the shaded region is A,…

A:

Q: If the distance y from the origin at time t is given by y = -16t² + 3000t + 50,000, find the initial…

A: Given: The distance y from the origin at time t is given by  y = -16t2+3000t+50,000 To find: The…

Q: 2 Wite the equation of the tangent line. at point. (1/3っーん) y= tan (3x). %3D 3)Snow ball melts so…

A: