Water flows from a tank of constant cross-sectional area 60 ft2 through an orifice of constant cross-sectional area 1/4 ft2 located at the bottom of the tank. Initially, the height...

Water flows from a tank of constant cross-sectional area 60 ft2 through an orifice of constant cross-sectional area 1/4 ft2 located at the bottom of the tank. Initially, the height...

Use differentials to approximate the quantity a. √101 b. 4√81.6

A 15-ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding down the wall at the instant of time when the bottom of the ladder is 9 ft from the wall and sliding...

The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 3 in. long and increasing at the rate of 0.4 in./sec. How...

Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. $ 625p^2 - x^2...

Let h(c)=c(square root((c^2/g^2) + 1/4) - (c^2/g) (square root is only over (c^2/g^2) + 1/4) show that Lim of h(c) = g/8 as c approaches infinity

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...

(i) If we call the first number x, and the second z, write an equation that relates these numbers. (ii) Use (i) to write an equation that gives the second in terms of the first. (iii)...

(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...

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

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...

log base(ab) [2log base(ab)(√a)-1/2log base(ab)√ab(b)]=(log base(ab) (a))^2-(log base(ab)(b))^2 I do not know

The demand function for a certain make of ink-jet cartridge is the following where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. p =...

A balloon is at a height of 20 meters, and is rising at the constant rate of 5 m/sec. A bicyclist passes beneath it, traveling in a straight line at the constant speed of 10 m/sec. How fast is...

A rocket's path is graphed by the function f(x) = x^3 - 8x, where x refers to time after launch (s). At what point after its launch would you release its thrusters in order for its tangent...

What is the arclength of r=6sin(3θ)? Given the formula Lpolar= ∫√[r^2+(dr/dθ)^2]dθ I can find the arc length using the r stated above and r'=18cos(3θ) Given that one petal is...

The distance S covered by a car after t sec is given by: s=-t3 + 8t2 +20t (0≤t≤6) Find the general expression for the car's acceleration at any time t (0≤t≤6)...

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