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Optimization Problems:
a)How close does the line y=1+2x come to the origin?
b) Find the dimensions of a right circular cylinder that is open on the top, isolated on the bottom, holds 1 liter, and uses the least amount of material.
c) A circular sector with radius r and angle (theta) has area A. Find r and theta so that the perimeter is smallest for a given area A. (Note: A=(1/2)*r*theta, and the length of the arc s=r*theta, when theta is measured in radians)
Which two variables have the strongest strength of relationship?
Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five. Set up a system of linear equations to represent the two angles.
Basic probability problems
so can you let me know if what i have is correct and answer the ones that i dont have a answer to.
The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?
Use Fermat's Little Theorem to compute 3^302 mod 5, 3^302 mod 7, and 3^302 mod 11. Use your results to find 3 ^ 302 mod 385
Let ubar and vbar be nonzero vectors in 2 or 3 space and let k=||u|| and m=||v||. Show that the vector Wbar=mubar +kvbar bisects the angle between ubar and vbar.
Among 250 latex gloves, 7 percent leaked viruses. Using 95 percent confidence interval tests a claim that Viny gloves have a larger virus leak rate than latex gloves. Basically you need to answer the following questions.
sketch the curve and find the area that it encloses
Create a system of equations that includes one linear equation and one quadratic equation and create a rational equation that has an extraneous solution.
Wing has different books to arrange on a shelf: 4 blue, 3 green, and 2 red. In how many ways can the books be arranged on a shelf? If books of the same color are to be grouped together, how many arrangements are possible?
In R2, let triangle ABC be a right triangle with right angle at angle C. Consider the altitude CH (it meets AB perpendicularly). Prove that |CH|^2 = |AH| * |BH|.
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