Please help1 through 5

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

5 0

Answer:

Step-by-step explanation:

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Identify a counterexample to disprove 6n>n^2/6,where n is a real number.

scZoUnD [109]

Any number larger than 36 would be a counter examples.

When n is equal to 36, both sides of the inequality are equal to 216. As you get larger than 36 the right side is larger than the left side. Therefore, the inequality is not true.

3 0

3 years ago

The naturalist views an elephant in the distance, but he doesn’t know how far away the elephant is from him. He takes a view to

andrezito [222]

Answer:

10.11 feet

Step-by-step explanation:

Let H ft be the elephant's height and x ft be the initial distance from naturalist to the elephant.

1. Naturalist takes a view to find the a 22 degree angle of elevation, then

$\tan 22^{\circ}=\dfrac{H}{x}.$

2. Naturalist moves backwards from the elephant pacing off a distance of 27 feet, the distance from naturalist to the elephant becomes (x+27) ft. He takes a second view and determines a new angle of elevation of 11 degrees. Then

$\tan 11^{\circ}=\dfrac{H}{x+27}.$

3. Solve the system of two equations:

$\left\{\begin{array}{l}\tan 22^{\circ}=\dfrac{H}{x}\\\tan 11^{\circ}=\dfrac{H}{x+27}\end{array}\right.\Rightarrow \dfrac{x+27}{x}=\dfrac{\tan 22^{\circ}}{\tan 11^{\circ}}\approx 2.0785,\\ \\ \\x+27=2.0785x,\\ \\1.0785x=27,\\ \\x\approx 25.0347\ ft.$