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3 years ago

Find the smallest value of m such that the LCM of m and 34 is 374.

Mathematics

1 answer:

wlad13 [49]3 years ago

8 0

Answer:

<em>11</em>

first you use a number tree

34 374

/\ /\

2 17 2 187

11 17

express the numbers in prime factors

374=2×11×17

34 =2×17

in finding LCM you use the highest prime factors in this case the highest prime factors are 2, 11 and 17

So m factors are 2 and 11

which means m is 2×11=22

22 in its smallest form is 11

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Answer:

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Step-by-step explanation:

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3 years ago

A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready func

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Answer:

$y=120 * 1.1^x$ --- function

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Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y=ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 = a * b^0$

$120 = a * 1$

$120 = a$

$a=120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute: $a=120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

So, the function is:

$y=ab^x$

$y=120 * 1.1^x$

To calculate the monthly rate (r), we have:

$y =a(1 + r)^x$

Compare to: $y =ab^x$

$1 + r = b$

Make r the subject

$r = b-1$

Substitute $b = 1.1$

$r = 1.1-1$

$r = 0.1$

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$r = 0.1*100\%$

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