A series of swells passes through a group of surfers. They notice that for a few minutes, the waves pass through at regular intervals: every 14 seconds. Let t=0 be the time when the wave is at its lowest point. The maximum instantaneous increase in height of the wave is 2.25 feet per second. a. Find r(t), the rate of chang
Find the sum: 1/8+1/4+1/2+1+........64
What is the square root of the ln of x?
What are Gerhard Gentzen's mathematical accomplishments?
Prove that the point p is a limit point of the point set X if and only if each open point set containing p contains a point in X which is different from p. Prove without using sequences. Only use the def. of open set, open interval, and that the point p is a limit point of the point set X means that each open interval containing
A movie theater has a screen that is positioned 10 feet off the floor and is 25 feet high. The first row of seats is placed 9 feet from the screen and the rows are 3 feet apart. The floor of the seating area is inclined at an angle above the horizontal and the distance up the incline that you sit is x. The theater has 21 ro
1) The area of a circle is decreasing at the rate of 2 pie cm^2/s. At what rate is the radius of the circle decreasing when its area is 75 pie cm^2? 2)Find f'(-1), given f(y)=h(g(y)), h(2)=55, g(-1)=2, h'(2)=-1, and g'(-1)=7
Solve (1-x^2)^(1/2)y'+1+y^2=0 xy(1+x^2)y'-(1+y^2)=0 xyy'=1+x^2+y^2+x^2y^2 sinx(e^y + 1)dx=e^y(1+cosx)dy, Y(0)=0
At 2:00 pm a car's speedometer reads 30 mi/h. At 2:10 pm it reads 50 mi/h. Use the mean value theorem to show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2. Please show line by line work and be as clear as possible.
If the tuition at a certain college is determined to cost $ 32000 in 10 years, how large must a trust fund that pays 7.5% compounded continuously be, in order for a child on her 8th birthday to ensure sufficient funds at age 18?
I have two problems (well, one problem with three parts and another one): 1. (a) Let f(x)=ax^2+bx+c, a does not equal zero, be a quadratic polynomial. How many points of inflection does the graph of f have? (b)Let f(x)=ax^3+bx^2+cx+d, a does not equal zero, be a cubic polynomial. How many points of inflection does the grap
A robot is guided towards an object by a software algorithm that controls its position such that the path of the robot is approximately sinusoidal, with a period 2, as shown in Figure B4 (attached). (a) Show that the length l of any single-variable function f(x), between the limits of x=a and b, can be expressed by th
Suppose m and k are positive numbers. Find u so that mu''(t) + ku(t)= 0 for all numbers t and u(0)=1 and u'(0)=2. (note: u'' = second derivative of u) Please clarify any shorthand that you are using. Thanks!
Show that the equation 3x - 2 + cos(pi x / 2) = 0 has exactly one root. (This problem may be clearer in the attached file.)
The curve 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a Lemniscates. Find the tangent line at (3,1). (The problem is also attached in MS Word with the appropriate fonts)
Given the ellipse x2/4 + y2/9 = 1 What are the points where the tangent line is vertical? (In narrative, the problem reads: given the ellipse x squared divided by 4, plus y squared divided by 9, equals 1, what are the points where the tangent line is vertical? The problem is also attached in MS Word, in case you need it
Solve for t. lim t-->0 (sin t)^2 / (4t)^2
A kite 100ft above the ground moves away horizontally at a speed of 8ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?