# Z32

Most popular questions and responses by Z32-
## Calculus

The population of a region is growing exponentially. There were 40 million people in 1980 (when t=0) and 50 million people in 1990. Find an exponential model for the population (in millions of people) at any time t, in years after 1980. P(t)= Predicted

*asked on October 6, 2009* -
## Physics

One cubic meter (1.00 m^3) of aluminum has a mass of 2.70 multiplied by 10^3 kg, and the same volume of iron has a mass of 7.86 multiplied by 10^3 kg. Find the radius of a solid aluminum sphere that will balance a solid iron sphere of radius 1.40 cm on an

*asked on August 27, 2010* -
## Physics

A freezer has a coefficient of performance of 6.30. It is advertised as using 486 kWh/yr. Note: One kilowatt-hour (kWh) is an amount of energy equal to running a 1-kW appliance for one hour. a) On average, how much energy does it use in a single day? I got

*asked on February 16, 2011* -
## Physics

How much energy does it extract from the outside air with coefficient of performance 3.85? A heat pump has a coefficient of performance of 3.85 and operates with a power consumption of 6.91 x 10^3 W. The first part of the question asked How much energy

*asked on February 16, 2011* -
## Calculus

A plane flying with a constant speed of 5 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 35 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 10 minutes later? I got

*asked on September 25, 2009* -
## Calculus

[Exponential growth & decay] The half-life of radioactive strontium-90 is approximately 29 years. In 1965, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years

*asked on October 6, 2009* -
## Calculus

Air is being pumped into a spherical balloon so that its volume increases at a rate of 30 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 19 cm? V= 4/3*pi*r^3 S= 4 pi r^2

*asked on September 24, 2009* -
## Calculus

A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is her shadow lengthening when she is 30 ft from the base of the pole?

*asked on September 24, 2009* -
## Calculus

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 22 feet?

*asked on June 22, 2009* -
## Calculus

A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2. What are the dimensions of such a cylinder which has maximum volume? Radius? Height?

*asked on June 22, 2009* -
## Calculus

The velocity v(t)= -t^2 + 6t - 8, find the displacement and distance traveled during the time interval [-1,5]?

*asked on December 11, 2009* -
## Calculus

Find the linearization of f(x)= sqrtx at x=25 and use the linearization to approximate sqrt25.2 This is my math: 5+ 1/10 * (25.2-25) but it's wrong.

*asked on September 27, 2009* -
## Calculus

A rancher wants to fence in an area of 5189400 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

*asked on June 22, 2009* -
## Calculus

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 45.000 meters.

*asked on October 13, 2009* -
## Calculus

If 6075 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume=??? cubic cm

*asked on June 22, 2009* -
## Calculus

Newton's Law of Cooling states that the rate at which an object cools is proportional to the difference in temperature between the object and the surrounding medium. Thus, if an object is taken from an oven at 303 F and left to cool in a room at 74 F, it's

*asked on October 13, 2009* -
## Calculus

A fence 5 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? [Hint: Determine the length of a ladder

*asked on June 22, 2009* -
## Calculus

The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 370 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent.

*asked on June 22, 2009* -
## Calculus

Find an overestimate and underestimate that the bug crawls during an hour v= 1 / [2+t]? For time, t, in hours, 0

*asked on November 13, 2009* -
## Calculus

A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the length L and width W

*asked on November 2, 2009* -
## Calculus

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 16 cm.

*asked on September 24, 2009* -
## Calculus

[Implicit Differentiation] (5x-y)^4 + 2y^3 = 258 evaluate y' at the point (1,1)

*asked on September 22, 2009* -
## Calculus

A projectile is launched at an angle of 60 degrees to the horizontal from 6.5 ft above the ground at an initial speed of 150ft/sec. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the

*asked on March 9, 2011* -
## Calculus

[Integrals] h(x)= -4 to sin(x) (cos(t^5)+t)dt h'(x)=?

*asked on November 21, 2009* -
## Caluclus

[Mean Value Theorem] f(x)=-3x^3 - 4x^2 - 2x -3 on the closed interval [0,8]. Find the smallest value of c that satisfies the conclusion of the Mean Value Theorem for this function defined on the given interval. I got 8 - sqrt(5696) / -18 = 3.748436059 but

*asked on October 23, 2009* -
## Physics

An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km). The first question asks

*asked on February 26, 2011* -
## Calculus

Water is being pumped into an inverted conical tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 28 centimeters per minute when the height of the water is 3.5 meters,

*asked on September 25, 2009* -
## Calculus

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM? This is what I got but it's not right 28.727

*asked on September 25, 2009* -
## Calculus

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2-x^2 What are the dimensions of such a rectangle with the greatest possible area? Width=? Height=?

*asked on June 22, 2009* -
## Physics

If the stone strikes the ground 65 m away, find the time of flight and initial speed? Vxi = 17.7 m/s Vyi = 8.636 m/s xi = yi = 0, yf = -65.0 m, ay = -g, and vi = 19.7 m/s This is my work so far: trying to find t: 4.9t^2 - 8.636 -65=0 Then I used the

*asked on September 9, 2010* -
## Calculus

f(x) = 6e^(-5x) ln(x), find f'(3)?

*asked on December 7, 2009* -
## Calculus

Find the inflection points for f(x) = 12x^5 + 45x^4 - 360x^3 + 7

*asked on October 26, 2009* -
## Calculus

Evaluate the following limits. lim as x approaches infinity 6/e^x + 7=____? lim as x approaches negative infinity 6/e^x+7=____?

*asked on September 29, 2009* -
## Engineering C source code

Prompt the user for the inner and outer diameter and thickness of the washer to be entered in cm. Then prompt for the material density in grams per cubic cm (g/cm^3) and the number of washers in the batch. Finally, print out the expected weight in kg. Make

*asked on September 16, 2009* -
## Physics/Engineering

1. The problem statement, all variables and given/known data I am using a Vishay strain indicator with it hooked up to a strain gage hooked up 1" away from the wall on the solid beam. The beam is .5" by .5", and it is solid. The beam is 16" long and I am

*asked on November 17, 2011* -
## Calculus 3

Compute the average value of following !@#$%^&tion over the region R? f(x,y)= sinxsiny R= { (x,y): 0 ≤ x ≤pi, 0 ≤ y ≤pi}

*asked on April 15, 2011* -
## Calculus

Can two level curves of a function intersect; explain?

*asked on March 4, 2011* -
## Philosophy

Does Bonnie Steinbock think committing adultery is okay or not okay?

*asked on April 29, 2010* -
## Calculus

Suppose that f(x) = (5x + -2)^(1/2) Find an equation for the tangent line to the graph of f(x) at x=1. Tangent line: y=?

*asked on February 16, 2010* -
## Calculus

Reflecting the graph calculus problem f(x) = 5^x? reflecting the graph about the x-axis and the y-axis: y=___________ reflecting the graph about the line y = 3. y=__________

*asked on January 27, 2010* -
## Calculus

Evaluate the integral by interpreting it in terms of areas as 0 goes to 12 |2x - 7|dx? This is my work so far: 2x-7=0 x=7/2 slope = 2; y-int = (0, -7) Area of a triangle is 1/2BH.

*asked on November 15, 2009* -
## Calculus

What is the absolute max and absolute min of 3+13 |t-8| for -1

*asked on October 20, 2009* -
## Calculus

What is the derivative of f(x)=5^x log6(x)?

*asked on October 15, 2009* -
## Calculus

The limit below represents the derivative of some function f at some number a. State such an f and a. lim x-->2 2^x-4/x-2 f(x)=_______ a=_______

*asked on October 2, 2009* -
## Calculus

Use linear approximation, i.e. the tangent line, to approximate (the 3 is inside the v part if you know what I mean, it's not 3 times sqrt) 3√125.2 as follows: Let f(x) = 3√x. The equation of the tangent line to f(x) at x=125 can be written in the form

*asked on September 28, 2009* -
## Calculus

Evaluate y' at (2,1) [Implicit differentiation] 5xy-3x-4=0 I got 3/10 and 2/10 but both were wrong.

*asked on September 22, 2009* -
## Calculus

I wanted to know how you would know that -4x^2 + 2x +90 / x-5 would be able to factor down to (x-5)(-4x-18)/x-5 By looking at -4x^2 + 2x +90 / x-5 , I would never think that it could be factored down to (x-5)(-4x-18)/x-5 How should I approach it so I know

*asked on September 17, 2009* -
## Calculus

Find the domain of the following function h(x,y) = sqrt(x-9y+5)?

*asked on March 9, 2011* -
## Calculus

Consider the parabola r(t)=, does the principal unit normal vector point in the + or - y-direction along the curve?

*asked on February 25, 2011* -
## Calculus 3

Determine whether the lines intersect(have a common point) and if so, find the coordinates of that point? r(t) = < 4t+3, 4t + 2, 6t + 6>, for -infinity < t < infinity R(s) = < s + 2, 3s - 1, -4s + 10>, for -infinity < t < infinity And if r and R describe

*asked on February 18, 2011* -
## Physics

A crow flies in two successive displacements to a point that is 80 m to the west. Its first displacement is 80 m in a direction θ = 50° west of north. What is the magnitude of its second displacement? What is its direction as measured by the angle θ

*asked on September 2, 2010* -
## Physics

Junes Verne in 1865 suggested sending people to the Moon by firing a space capsule from a 195 m long cannon with a launch speed of 12.78 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during launch?

*asked on September 1, 2010* -
## Calculus

What's the derivative of x^2(1- x/6)?

*asked on February 9, 2010* -
## Calculus

What is the antiderivative of f(x)= 2x^8 + 10x^5 - 8x^4 - 4? I got (2/9)^9 + (10/6)^6 - (8/5)^5 - 4x but it's not right.

*asked on November 5, 2009* -
## Calculus

Help me simplify this down some more so I can set it to zero and find my critical points. f(x) = x^3 (x+2)^6 f'(x) = x^3 * 6(x+2)^5 + 3x^2 * (x+2)^6

*asked on October 23, 2009* -
## Calculus

A 25 foot ladder is leaning on a 9 foot fence. The base of the ladder is being pulled away from the fence at the rate of 10 feet/minute. How fast is the top of the ladder approaching the ground when the base is 9 from the fence? [Note: The ladder is

*asked on October 13, 2009* -
## Engineering Materials

Using mechanics of materials principles (ie. equations of mechanical equilibrium applied to a free-body diagram), derive the following equations. sigma' = sigma cos^2 θ = sigma(1+cos 2θ / 2) and tau = sigma sin θ cos θ = sigma( sin2θ / 2)

*asked on October 8, 2009* -
## Calculus

If xy=4 and dy/dy=3 then find dx/dt when x=4?

*asked on September 24, 2009* -
## C programming

The task is to create a c source code program that will name a quadrant when a given coordinate is given. Example: Input Coordinate Pair: 0 5.3 Positive y Axis I just need help on how to start this. I know I have to use if else statements but I'm not sure

*asked on September 23, 2009* -
## Calculus

[Implicit Differentiation] (6+y)^3 + 4y = x + 55 with y' at (1, -2) y' at (1,-2) =? I got this far but I'm not sure if I'm doing it right: 3(6+y)^2(1dy/dx)+4dy/dx=1

*asked on September 22, 2009* -
## Calculus

Find the derivative of cos(sqrt(e^(x^3)cos(x)) I got -sin(sqrt(e^(x^3)cos(x))*((sqrt(e^(x^3)cos(x)) Do I just leave the e^(x^3)cosx alone since it's "e" or do I still have the find the derivative for it?

*asked on September 15, 2009* -
## Calculus

Given that f(x)=x^6h(x) h(-1)=3 h'(-1)=6 Calculate f'(-1).

*asked on September 4, 2009* -
## Calculus

Evaluate the integral. -2 at the bottom of the integral sign and 7 at the top. f(x)dx f(x)={x if x or equal to 1 I'm not sure how you would apply these two concepts together?

*asked on June 24, 2009* -
## Calculus

Express the region inside the leaf of the rose r=2sin2? in the first quadrant as an iterated integral over R?

*asked on April 29, 2011* -
## Physics

(Vectors) If |A x B| = 6.45AB, what is the angle between A and B?

*asked on September 3, 2010* -
## Calculus

Evaluate the integral from 2/sqrt2 to 4; 1/(t^3 sqrt(t^2-4))?

*asked on September 3, 2010* -
## Calculus

Estimate the area under the graph f(x)=3x^3 + 5 from x=-1 to x=5 using 12 mid points? I got the right answer for using 6 mid points but what mid points would I use for 12?

*asked on April 20, 2010* -
## Calculus

Determine the y-coordinate of the critical point for the function where 0

*asked on April 13, 2010* -
## Calculus

Evaluate the indefinite integral: x^2 / (3-4x^3)^6 I got -1/(60(4x^3-3))^5 but it's not right.

*asked on December 9, 2009* -
## Calculus

Find the concavity and min and max for f(x) = x*sqrt(x^2+36) defined on the interval [-4, 7]?

*asked on December 8, 2009* -
## Calculus

f(x) = [3/x^2] - [5/x^7], F(x) is the antiderivative of f(x) with F(1)=0. F(x) = ? I have no idea how to approach this problem. The fractions are scaring me.

*asked on November 6, 2009* -
## Calculus

F(x) = x^3 / (x-16) is concave up and down on what intervals? I got the derivative to be f' = (x^4 - 48) / (x^2-16)^2 and I found the local min and max but now I need to find where it concaves up and down.

*asked on October 27, 2009* -
## Calculus

What's the derivative of (x-1)(x-7)^3+10?

*asked on October 20, 2009* -
## Calculus

Find the derivative of tanh(e^t)

*asked on October 9, 2009* -
## Calculus

[Linear Approximations and Differentials] I tripled checked my work but I'm still not getting the correct answer. y=3x^2 x=3 & delta x =0.2 I get 3(3.2)^2 - 3(3) = 21.72

*asked on September 27, 2009* -
## Calculus

Find the Derivative of (7x^2-6)^8(-4x^2-3)^9

*asked on September 15, 2009* -
## Calculus

Evaluate the definite integral The S thingy has 1 at the bottom and 9 at the top. 4x^2+5 divided by the sqrt of x.

*asked on June 23, 2009* -
## Calculus

f"(x)=5x+3 and f'(-2)=-3 and f(2)=-5 Find f'(x) and find f(2).

*asked on June 23, 2009* -
## Calculus

Find the point on the line -5sx+y+3=0 which is the closest to the point (2, 5) (___,___)

*asked on June 22, 2009* -
## Calculus

f(x)=x*sqrt(x^2+2x+10) + 1*sqrt(x^2+2x+10 defined at the interval [-7,5]. A. f(x) is concave down on the region _,_. B. f(x) is concave up on the region _,_. C. The inflection point for this function is at ____? D. The minimum for this function occurs at

*asked on June 18, 2009* -
## Calculus

Use logarithmic differentiation to determine the derivative of the function defined by f(x)=x^5(x-3)^9/(x^2+2)^4

*asked on June 15, 2009* -
## Calculus

What does the arc length formula give for the length of the line r(t)= for 0 ≤ t ≤ 1?

*asked on February 22, 2011* -
## Math

Solve for t. -45.0 m = (8.636 m/s)t + ½(-9.80 m/s^2)t^2 ?

*asked on September 9, 2010* -
## Calculus

3 ⌠ 2⌡ (2x^2+5) / x^2 dx =? I got 1.66 but it was wrong.

*asked on November 18, 2009* -
## Calculus

Estimate the area under the graph of f(x) = 2x^3 + 3 from x= -1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the left and right

*asked on November 10, 2009* -
## Calculus

What are the critical points of f(x)= e^x / 3+e^x?

*asked on October 27, 2009* -
## Calculus

What is the x coordinate of the absolute minimum of 6x + [12/x] when x > 0?

*asked on October 22, 2009* -
## Calculus

Can someone break this down for me step by step? I'm reviewing for a midterm and got stuck on this problem. 5xy - 3x - 4 = 0 y' at (2,1) I'm not sure where the 5 goes when you apply the product rule to the xy.

*asked on October 15, 2009* -
## Calculus

Find the derivative of 1/8tan^(-1)(x/8) & (x/2)(sqrt(64-x^2) + 32sin^(-1)(x/8)?

*asked on October 14, 2009* -
## Calculus

Find the derivative of f(x)=x^2sinh^(-1)(3x)?

*asked on October 13, 2009* -
## Calculus

[Inverse Functions] f(x)= 5cos(x)sin^(-1)(x) f'(x)=?

*asked on October 7, 2009* -
## Calculus

F(x)=5e^x - 10 / 24e^x + 12 f^(-1)(x)=? a=? b=?

*asked on October 1, 2009* -
## Calculus

The expression e^x / e^(4+x) can be written as e^f(x), where f(x) is a function of x, find f(x)?

*asked on September 29, 2009* -
## Science/math

BCC crystal structure, atomic radius of .1363, and an atomic weight of 95.94g/mol. How would you compute the theoretical density?

*asked on September 15, 2009* -
## Calculus

If the equation of the tangent line to the curve y=9cosx at the point on the curve with x-coordinate 3pi/4 is written in the form y=mx+b then m=? and b=?

*asked on September 4, 2009* -
## Calculus

Using the first of these limits, find f'(3) if f(x)=4x^2+4x-2

*asked on September 3, 2009* -
## Calculus

f(t)=5^x sechx f'(x)=?

*asked on June 15, 2009* -
## Calculus

If f(x)=6arcsin(x^3) find f'(x)

*asked on June 15, 2009* -
## Calculus

If f(x)=4-coshx/3+coshx, f'(x)=?

*asked on June 15, 2009* -
## Calculus

Let f be the function defined by f(x)=2x+11-3e^x If the equation of the tangent line to the graph of f at the point (0,8) is given by y=mx+b then: m=? and b=?

*asked on June 12, 2009*