169 Answered Questions for the topic calc

#### the area of the region bounded by y=x^2 and y=x is________.

a. 1/6
b. 1/3
c. 1/2
d. 5/6
e. 1

#### Consider the region, R, bounded by the x-axis, the y-axis, and the graphs of the equations y=1/(x^2+1) and y=lnx

Find the area of the region R. a. 5.497 b. 1.483 c. 0.879 d. 0.013

#### Suppose we have a rod that is 6 meters long, with density function p(x)=2x+3. What is the center of the mass of the rod?

¯x= 11/3
¯x= 8/3
¯x= 14/3
¯x= 4/3
none of these

#### probability and integrals

Suppose that f(x) is the probability density function describing the distribution for the number of minutes it takes to solve a puzzle. Which of the following represents the probability that you...
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#### Given the cost function C(x), the marginal cost is given by which of the following?

a. ∫C(x)dx
b. ∫xC(x)dx
c. C'(x)
d. ( C'(x) )/x
e. none of these

#### center of mass

Particles A and B are located on the x-axis. The masses and positions of the particles are: mA = 12 grams xA = 2 mB= 8 grams xB = 10 What...
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#### stretching a spring

Suppose that a force of 20N stretches a spring 0.4 m beyond its natural length. How far will a 40N force stretch the spring? a. 1.0 b. 0.4 c. 0.2 d. 0.8

#### . A spaceship weighs 50 tons on the launch pad. As it ascends, it burns fuel so that it weighs 20 tons by the time it reaches an altitude of 70 miles.

How much work is done in lifting the spaceship to an altitude of 70 miles? a. 2450 mi-tons b. 2100 mi-tons c. 3500 mi-tons d. none of these

#### Suppose that a slice of pizza at a temperature of 80°F has been placed inside a freezer, where the temperature is 2°F.

I know that the equation, dT(t)/td = k(T(t)-2º) would represent the rate at which the temperature, T is decreasing.
If the pizza cools to 45° in 1 hour, then its temperature after t hours...
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#### newtons law of cooling

A cup of coffee at 160° is placed in a room where the temperature is 70°. After 5 minutes, the coffee’s temperature is 112.5°.
Find the temperature of the coffee 10 minutes after it was placed...
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#### newtons law of cooling

You are making pudding for a dinner party, and you put it in the refrigerator at 5 p.m. Your refrigerator maintains a constant temperature of 40 degrees. The pudding will be ready to serve when it...
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#### A solid has a flat base, which is bounded by the graph of y=x^3 and y=vx in the first quadrant only.

Each cross section of the solid perpendicular to the x-axis is the shape of a square. Find the volume of this solid. a. 5/14 b. 25/126 c. 5/12 d. 47/125

#### a particle moves along the x-axis with its x coordinate given by the function s(t)=2t^3-21t^2+60t for t=0

what would be the speed when t=3 and how do you find the exact time the particle changes direction?

#### If an object is displaced a distance d by a constant force F, the amount of work done is given by _____.

a. W=F+d
b. W=F-d
c. W=Fd
d. W=F/d

#### Find the solution of the differential equation

equation: dy/dx=(x+1)/y2 that passes through the point (-2, 2).
a. y=√(1/2 x2+x+4) b. y=3√(3/2 x2 +2)
c. y=3√(3/2 x2+3x+8)
d. y=3√(1/2 x2+x+8)
e. none of these

#### Equation to find the amount left after t years

Suppose that a sample initially contains N0 grams of a radioactive substance. If this substance has a half-life of 32 years, then which of the following equations can be used to find the amount...
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#### Which of these differential equations is NOT seperable?

dy/dy=x+y
dy/dy=xy
dy/dy=x/y
dy/dy=2xy

#### A tank is formed by revolving the graph of y=x^4 around the y-axis. The tank has a height of 16.

Find the value of m such that the line y = m represents the height at which the tank is half full.

#### Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?

V=2Π∫ xf(x)dx
V=Π∫ xf(x)dx
V=2Πx2f(x)dx
V=Π2∫ xf(x)dx

#### looking at a velocity time graph

when looking at a velocity vs. time graph, how can one determine the total distance traveled as well as the displacement?

#### which of the following integrals is INCORRECT?...

A) ∫tanxdx=sec2x+C
B) ∫cscxdx=ln[cscx-cotx]+C
C) ∫cotxdx=ln[sinx]+C

#### true or false?

y=e-x satisfies the differential equation, ( (d2y)/(dt2) )+y=0
true or false?

#### solution to differential equation

which of the following is a solution to the differential equation y''+2y'+y=0
a) y=cos2x
b) y=x2
c) y=xe-x

#### true or false?

y=sinx+cosx satisfies the differential equation ( (d2y)/(dt2) )+y=0
true or false?

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