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Let u be a harmonic function on the unit ball B1 with ||u||∞ = supz∈B1|u (z)|< ∞, show that |∇u (0)|<=||u||∞. Here c is an absolute constant.
the width of a rectangle is 19 centimeters. Find all possible values for the length of the rectangle is the permitter is at least 404 centimeters.
A ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 16 m above ground level?
An artifact was found and tested for its carbon-14 content. If 88% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)
Assume that the drawer contains 11 coins: 5 quarters, 3 dimes, and 3 nickels. One coin is randomly selected. What is the expected value of the coin selected (in cents)?
Write a 90% confidence interval for the mean daily income this parking garage will generate.
A central angle of a circle of radius 30cm intercepts an arc of 6cm the central angle in terms of degrees is? The reference angle of 3.22 rev?
Write and simplify an expression that represents this scenario.
The half-life of radium is 1690 years. If 10 grams are present now, how much will be present in 50 years?
a slice of pie with a scoop of ice cream has 850 calories. The calories in the pie alone are 100 more than twice the calories in the ice cream alone. How many calories are in each food?
An arrow is accidentally shot into the air. The formula y = - 14x2 + 56x + 18 models the arrow's height above the ground, y, in feet, x seconds after it was released.
A machinist can produce 114 parts in 6 minutes .At this rate , how many parts can the machinist produce in 15 minutes.
in 1991 author tom heymann took an unofficial u.s. census. the table shows how many people believed various common
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