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Calculus
1)Give two different parameterizations for the linear path from (-3,-4,-1) to (4,3,8) for the t-values:
a) 0<=t<=1
b)2<=t<=11
2)Determine where the line of problem 1 intersects the sphere of radius 8 centered at the origin.
a) 0<=t<=1
b)2<=t<=11
2)Determine where the line of problem 1 intersects the sphere of radius 8 centered at the origin.
Calculus
∫[0,2/π,(√(cos(x)))/(√sin(x)+√(cos(x))),x]
Calculus
Angela works at the local beach as a part of a surf patrol unit. During her patrol, she notices that an old lady is having difficulty in the surf. She estimates that the distance is approxiamtely 220 m along the beach and then 75 m out (in water) to the woman. Angela can run along the beach at a speed of 180 metres per minute and can swim at a speed of 80 metres per minute.
1. How long will it take her to reach the woman if she run the full 220 m on the beach and swim 75 m?
2. In hindsight, Angela thinks that it may be quicker to swim directly out to the woman in trouble. How long would it have taken her if she had swum the entire distance?
3. Find the quickest time (down to the nearest metre) for Angela to reach the woman.
Could you please show all working out and explain it? & Thank you.
1. How long will it take her to reach the woman if she run the full 220 m on the beach and swim 75 m?
2. In hindsight, Angela thinks that it may be quicker to swim directly out to the woman in trouble. How long would it have taken her if she had swum the entire distance?
3. Find the quickest time (down to the nearest metre) for Angela to reach the woman.
Could you please show all working out and explain it? & Thank you.
Calculus
A firm’s Marginal Cost function is MC=4q+4, where q is output. If output is increased
from 25 to 50, find the increase in the firm’s total cost of production
from 25 to 50, find the increase in the firm’s total cost of production
Calculus
Find the formula and limit as requested. For the function f(x)=2x+6, find a formula for the upper sum obtained by dividing the interval [0,3] into n equal sub intervals. Then take the limit as n approaches infinity to calculate the area under the curve over [0,3]
Calculus
Find the curve y=f(x) in the xy-plane that has the given properties. f(x) has a slope at each point given by -(1/x^2) and passes through the point (1/4,6)
Calculus
V=(4/3)Pi r^3, where r is the radius, in centimeters. By approximately how much does the volume of a sphere increase when the radius is increased from 1.0 cm to 1.2 cm? (use 3.14 for pi)
Calculus
For a motorcycle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorcycle may be approximated by the formula d=.05v^2+v. Find the instantaneous rate of change of distance with respect to velocity when the speed is 47mph,
Calculus
The posistion of a particle moving along a coordinate line is s=sqrt(4=12t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec
Calculus
Given Marginal Revenue function, MR=100-2q, find
a. The total revenue function
b. The demand function
a. The total revenue function
b. The demand function
