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If the radius of a sphere is doubled, the surface area is
a. multiplied by 4.
b. multiplied by 2.
c. multiplied by 3.
d. multiplied by 8.
a. The formula for the surface area of a sphere is 4πr2. If the radius is doubled, this implies that the radius is also doubled. The formula then becomes 4π(2r)2. Solve this expression, 4π(4r2) equals 16πr2. Compare 4πr2 to 16πr2; 16πr2 is 4 times greater than 4πr2. Thus, the surface area is four times as great.
Sketch the phase portrait for the given system. Solution : From the last illustration we know that the eigenvectors and eigenvalues for this system are, This tu
Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 , y(2) = - 1, x > 0 Solution Thus, the first thing that we re
The Hurwiz method Hurwiz method was the concept of coefficient of optimism or pessimism introduced by L. Hurwicz. The decision maker takes into account both the minimum and max
Least Common Denominator Using Primes: A prime number is a whole number (integer) whose only factors are itself and one. So the first prime numbers are given as follows: 1,
3^2=8
10p=100
Calculate the value of the following limit. Solution: This first time through we will employ only the properties above to calculate the limit. Firstly we will employ prop
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Raul's bedroom is 4 yards long. How many inches long is the bedroom? There are 36 inches within a yard; 4 × 36 = 144 inches. There are 144 inches in 4 yards.
The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions
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