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Find the area under the curve : y=e^-2x from x=0 and x=1

Solve the following equation for all possible values of x:

x^2=1+j

A car traveling on the highway at a speed of 75 mph when the driver sees a wreck occur ahead and slams on the brakes. If the coefficient of the kinetic friction between the wheels and the ground is 0.60, a) How far will the car travel before it comes to rest? b) How long does this take? c) What acceleration does the car experience in the time that causes the car to come to rest?

A cue ball of mass 0.17 kg hits a nine ball with mass 0.16 kg that is initially at rest. If the nine ball is cut in such a way that both balls leave the impact with a 25 degree angle, what are their velocities after impact? Assume the cue ball has an initial velocity of 15 m/s.

How much work does friction do on a car that has a mass of 1500 kg and an initial velocity of 60 mi/h, if the driver slams on his brakes and skids to rest over a distance of 80m ? If it takes 3.0s for the car to come to rest, how much power was generated?

Find the equation of the line tangent to the curve y=x^2-6/x at the point (3,7)

The function y=x^4-18x^2+40 has the following points of inflection:

The derivative (dy/dx) of function

y= 2x2(3-x2)5

is:

The slope of the line tangent to the function y=2/(x2+1) at the point (-1,1) is:

The radii of 4 different-size ball bearings differ by 1.00 mm in radius from 0ne size to the next. If the volume of the largest equals the volumes of the other 3 combined, find the radii.

The Center (or Vertex if is a Parabola) of the given curve 2x2 + y2 + 8x = 8y is:

The stream from a fire hose follows a parabolic curve and reaches a maximum height of 60 ft at a horizontal distance of 95 ft from the nozzle. The equation that represents the stream with the origin at nozzle is:

A road passes through a tunnel with a semi-elliptical cross section 64 ft wide and 18 ft high at the center. what is the height of the tallest vehicle that can pass through the tunnel at a point 22 ft from the center?

An architect designs a Norman window, which has the form of a semicircle surmounted on a rectangle. Find the area (in m^2) of the window if the circular part is on the circle x^2+y^2-3y+1.25=0

Find the standard equation of the parabola with a vertex (0,0) and that passes through (2,2) and (8,4).

A square is inscribed in the circle x^2+y^2=32. Find the area of the square.

An airplane wing is designed such that a certain cross section is an ellipse 8.4 ft wide and 1.2 ft thick. Find the equation that can be used to describe the perimeter of the cross section.

A spotlight with a parabolic reflector is 15.0 cm wide and is 6.5 cm deep. Where should the filament of the bulb be located so as to produce a beam of light?

Find the equation of the hyperbola with vertices (-2,4) and (-2,-2) and a conjugate axis of 4, by use of definition.

Find the Locus of a point P(x,y) that moves so that the line joining it and (2,0) is always perpendicular to the line joiming it and (-2,0). Describe the Locus.