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...

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...

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 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...

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

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...

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...

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...

The supply equation for a certain brand of radio is given as follows where x is the quantity supplied and p is the unit price in dollars. p = s(x) = 0.3√x + 15 Use differentials to approximate...

A coat of paint of thickness 0.06 cm is to be applied uniformly to the faces of a cube of edge 32 cm. Use differentials to find the approximate amount of paint required for the job, correct to the...

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

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

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...

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...

1. Sketch each region and used 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...

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

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...

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?

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