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Simplify the logarithmic expressions by using logarithmic properties.
Simplify the given logarithmic expressions :
1) log 1
2) log 10
3) log 1000
4) log 1
5) log e
1) log 2 + log 5
2) log 50 - log 5
3) log 105
The base of an aquarium with volume V = 250 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
use double integrals to find the volume of the tetrahedron bounded by the planes x+2y+3z=6, x=y, z=0, y=0
Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.
Binomial Probability Distribution : explained. Thirty percent of women are basketball fans . Four women are randomly selected . Find the probability distribution of the random variable X,
The edge of a cube was found to be 40 cm with a possible error of 0.3 cm. Use differentials to estimate the maximum possible error in the calculated volume of the cube.
A ball drops from a height of 21 feet. Each time it hits the ground, it bounces up 80 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
About 35.9% of all charitable contributions are made to religious organizations. In 2003, about $86.4 billion was given to religious organizaions. How much was given to charities in general, given the aforementioned data?
A 6 foot tall man is standing near a tree on level ground. If the man's shadow is 4 feet long, how many feet tall is the tree?
A manufacturer of lightning fixtures has a daily production costs of C(x)=800-10x+0.25x^2 where C is the total cost (in dollars) and x is the number of units produced.How many fixtures should be produced each day to yield a minimum cost?
Destiny shows her friend Kaitlyn a deck of cards. Assuming the cards are randomly distributed, what is the probability that Destiny draws an ace and does not replace it, and then draws another ace?
Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
person jogs 430 kj of work and gives off 380kj heat what is the interal energy?
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