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Katyanochek1 [597]
3 years ago
6

Show that the sum of the reciprocals of three different positive integers is greater than 6 times the reciprocal of their produc

t.
Mathematics
1 answer:
Montano1993 [528]3 years ago
8 0
If a,b,c are the 3 positive integers
1/a +1/b +1/c > 6/abc
(bc+ac+ab)/abc >6/abc so
(bc+ac+ab)>6
The lowest positive integers that are different are 1,2,3 so the lowest value that (bc+ac+ab) could have is 1•2+2•3+1•3=2+6+3= 11 therefore
1/a +1/b +1/c > 6/abc is true
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Verify the identity. cot(x - pi/2) = -tan(x)
gizmo_the_mogwai [7]

Answer:

See below.

Step-by-step explanation:

\cot(x-\frac{\pi}{2})=-\tan(x)

Convert the cotangent to cosine over sine:

\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)

Use the cofunction identities. The cofunction identities are:

\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)

To convert this, factor out a negative one from the cosine and sine.

\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)

8 0
3 years ago
How many edgès does the figure have?
lbvjy [14]

Depending on the shape

4 0
2 years ago
Solve each equation for the given variable a-2b=-10 for b
Ymorist [56]
A-2b=-10
add 2b on both sides
a=2b-10
add 10 to both sides
a+10=2b
divide both sides by 2
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8 0
2 years ago
T. J. And Lindsey's lunch cost $30. They want to leave a 20% tip for their waiter. Use What is the amount of the tip that T.J. A
ahrayia [7]

Answer:

$6

Step-by-step explanation:

In order to find the amount of the tip that T.J. and Lindsey will leave for their waiter, you have to multiply the lunch cost for the percentage they want to leave as a tip for their waiter:

Lunch cost=$30

Percentage they want to leave as a tip= 20%

$30*20%=$6

According to this, the answer is that the amount of the tip is $6.

7 0
3 years ago
Solve for n. 24 = 3(n -5)​
Masteriza [31]

Answer:

n=13

Step-by-step explanation:

24=3(n-5)

24=3n-15

-3n=-24-15

-3n=-39

n=13

8 0
3 years ago
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