Water is poured into a conical container at the rate of 10 cm3/sec. The cone points directly down, and it has a height of 25 cm and a base radius of 5 cm. How fast is the water level rising when the...

Water is poured into a conical container at the rate of 10 cm3/sec. The cone points directly down, and it has a height of 25 cm and a base radius of 5 cm. How fast is the water level rising when the...

f(x) = sinx Max f(t), 0≤t≤x for 0≤x≤π Please attach the graph and the explain the procedure

Could you walk under it without hitting your head?

I have been stuck on this integral for 3 hours. Here is what I have so far.. : https://ibb.co/mWAC7x

A car leaves an intersection traveling west. Its position 4 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position...

Hi, Rewrite integrals using indicated order of integration, then evaluate resulting integral. 1. ∫01 ∫-22 ∫0√(4-(y^2)) dzdydx in the order...

How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits? This is in relation to radioactive decay for those that are wondering, thank you for your help and time...

if F(x)=∫0x (t-1)/(t2+9)dt, then which of the following statements are true? I. function F has a minimum value at x=1 II. function F has increase on the (1,∞) III. F’’(x) is negative...

(a) Let f(x),g(y) be continuous functions deﬁned for a ≤ x ≤ b, c ≤ y ≤ d, resepctively. Let h(x,y) = f(x)g(y). Let R = {(x,y) : a ≤ x ≤ b,c ≤ y ≤ d}. Show that ∫R h(x,y)dA =(∫ab f(x)dx)(∫cd...

1. Sketch each region and use a double integral to find its area: The region inside both the cardioid r=1-cosθ and the circle r=1 2. Find the following average values The...

Find the second derivative d2y/dx2 of the function defined implicitly by the equation. x1/3 + y1/3 = 94 d2y/dx2 = ___________

a. Find the volume of the solid region. The solid above the parabolic region R={(x,y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x2} and between the planes z = 1 and z = 2-y b...

Let f be the function defined as follows. y = f(x) = √(9x+5) (a) Find the differential of f. Answer: dy = (9/2√(9x+5))dx (b) Use your result from part (a)...

Please help me with this question please

Suppose R1,R2 are real numbers satisfying 0 < R1 < R2. A function is deﬁned in terms of polar coordinates by f(r,θ) =√(R1 + R2)r−r2 −R1R2. (a) Show that the domain of...

Evaluate the following integrals: a. ∫∫R (x+y) dA; R is the region in the first quadrant bounded by x=0, y=x2 , and y=8-x2 b. The solid in the first octant...

The cost of manufacturing stuffed yellow cats is C(x)= 1/3x2 + 4x + 53 where x is the number of cats produced in thousands. The production level for the number of stuffed cats produced after...

Need help to sold the Calculus problem find an equation of the tangent line to the curve y=x√x that is parallel to the line y=3+6x

The surface area of a sphere is decreasing at the constant rate of 5π cm2/s. At what rate is the volume of the sphere decreasing at the instant its radius is 4 cm?

A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.5 m/sec. How fast is the top sliding down...