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3 years ago

Find the Least Common Multiple of of these two monomials:

Mathematics

1 answer:

ZanzabumX [31]3 years ago

7 0

LCM of 15 & 6 = 30

then take the highest exponent for each variable

answer is:

30x^4y^8z^9

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

What is the answer?

rosijanka [135]

Answer: 60

Step-by-step explanation:

It’s an equilateral triangle based on the congruent sides.

4 0

3 years ago

Of the Students that attended Roosevelt Elementary 6/8 of the school play a sport. Of the students are playing a sport 3/5 of th

soldier1979 [14.2K]

Answer:

$\frac{9}{20}$ students.

Step-by-step explanation:

We have been given that of the students that attended Roosevelt Elementary 6/8 of the school play a sport. Of the students are playing a sport 3/5 of the students are also involved in the drama club.

To find the students are both play a sport and a part of the drama club, we need to find 3/5 part of 6/8 as:

$\text{Students who play a sport and a part of the drama club}=\frac{6}{8}\times \frac{3}{5}$

$\text{Students who play a sport and a part of the drama club}=\frac{3}{4}\times \frac{3}{5}$

$\text{Students who play a sport and a part of the drama club}=\frac{3\times 3}{4\times 5}$

$\text{Students who play a sport and a part of the drama club}=\frac{9}{20}$

Therefore, $\frac{9}{20}$ students play sport and part of the drama club.

5 0

3 years ago

The value of a semi-trailer when new is $625 000. The value of the semi-trailer depreciates by

Nina [5.8K]

Answer:

$546,875

Step-by-step explanation:

if the trailer brand new costs $625,000 and decreases by 12.5% you want to find 10% which is $62,500. then you want to find 5% which would be $31,250. but you want 2.5% so you need to divide $31,250 by 2 which is $15,625. add $62,500 and $15,625 together which is $78,125. then do $625,000-$78,625 which gets you $546,875.

4 0

3 years ago

Solve(100 points to right answer)If you get it wrong or type random stuff you will be reported

anygoal [31]

Answer:

24 ft

Step-by-step explanation:

Hypotenuse = √9²+16²=√81+256=√400=20ft

the upper side of the stuff = 4 ft

total = 20+4=24

5 0

2 years ago