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Ksivusya [100]
3 years ago
9

Prove that 3n< n! if n is an integer greater than 6.

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
4 0
Let n=7. Then

3(7)=21

Assume the inequality holds for n=k, so that 3k. Then for n=k+1, you have, for k>7,

3(k+1)

so the statement is true.
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Ineed help help me please
melamori03 [73]
The symbol ₁₂P₉ represents the permutations of 9  quantities out of 12.
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12! = 479,001,600
3! = 6

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How can you use a number line to order rational numbers? Give an example.
Margaret [11]

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4 0
3 years ago
Trigonometry questions
trasher [3.6K]

We'll use standard labeling of right triangle ABC, C=90 degrees, legs a, b, hypotenuse c.

11.

Right triangle, cliff peak A, boat B, angle opposite cliff is B=28.9 deg. adjacent leg a=65.7 m, cliff height is leg b.

tan B = b/a

b = a tan B = 65.7 tan 28.9° = 36.3 m

12.

Similar story, boat at B, opposite b=3.5 m, rope c=12 m

sin B = b/c

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13.

c=124 m, A=58°

sin A = a/c

a = c sin A = 124 sin 58 = 105.2 m

14.

That's a hypotenuse c=4-1.2 = 2.8 m to a height b=1.8m so

cos A = b/c

A = arccos b/c = arccos (1.8/2.8) = 50.0°

15.

Not a right triangle, an isosceles triangle.  Half of it is a right triangle with hypotenuse one arm, c=9.8 cm and angle opposite half the base of B=62/2=31°.  We're after d=2b:

sin B = b/c

b = c sin B

d = 2b = 2 c sin B = 2(9.8) sin 31 = 10.1 cm

Almost equilateral


4 0
3 years ago
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