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3 years ago

On a number line, show all values of x for which… |x |< 1

Mathematics

1 answer:

aleksley [76]3 years ago

4 0

Answer:

See attachment

Step-by-step explanation:

We want to show all values of x, for

$|x| \: < \: 1$

on the number line.

By the definition of absolute value function:

$- x \: < \: 1 \: or \: x \: < \: 1$

Divide through the first inequality by -1 and reverse the sign.

$x \: > \: - 1 \: or \: x \: < \: 1$

On the number line, we can represent this as shown in attachment.

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4 years ago

Read 2 more answers

A manufacturer produces bolts of a fabric with a fixed width. A quantity q of this fabric (measured in yards) that is sold is a

BigorU [14]

Answer:

$R'(20) = 2000$

Step-by-step explanation:

We are given the following in the question:

Quantity, q

Selling price in dollars per yard, p

$q=f(p)$

Total revenue earned =

$R(p)=pf(p)$

f(20)=13000

This means that 13000 yards of fabric is sold when the selling price is 20 dollars per yard.

f′(20)=−550

This means that increasing the selling price by 1 dollar per yards there is a decrease in fabric sales by 550.

We have to find R'(20)

Differentiating the above expression, we have,

$R'(p) = \displaystyle\frac{d(R(p))}{dp} = \frac{d(pf(p))}{dp} = f(p) + pf'(p)$

Putting the values, we get,

$R'(p) = f(p) + pf'(p)\\\\R'(20) = f(20) + 20(f'(20))\\\\R'(20) = 13000 + 20(-550) = 2000$

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4 years ago

If the basic measuring unit in base-7 is 49 circles, what does the measuring unit of size .001seven look like

Serjik [45]

The measuring unit is the standard unit of a quantity

The measuring unit of size 0.001 is represented by one millionth circle

<h3>How to determine the unit of base 0.001</h3>

The basic measuring unit in base 7 is given as:

49 circles

The above can be represented as:

Base 7 = 49 circles

Represent the base with n.

So, we have the following rule

$Circle = n^2$

For measuring unit 0.001, we have:

$Circle = 0.001^2$

Evaluate the square

$Circle = 0.000001$

This means that,

The measuring unit of size 0.001 is represented by one millionth circle