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3 years ago

How to write all real numbers in set notation?

1 answer:

7 0

Hi, this is the notation for inclusion of all real numbers.

$x \in \mathbb{R}$

We can also state numbers which are positive or negative with a sign on top of the R notation like so:

$x \in \mathbb{R}^{+} \text{ or } x \in \mathbb{R}^{-}$

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f(x) = square root ( x^4 -16x^2) let f be the function given by: . . a) Find the domain of f.. b) Find f '(x). c) Find the slope

Bond [772]

A ) The domain:
$x^{4} -16 x^{2} \geq 0 \\ x^{2} ( x^{2} -16) \geq 0 \\ x^{2} -16 \geq 0 \\ x^{2} \geq 16$
x ≤ -4 and x≥ 4 or: x ∈ ( - ∞ , - 4 ) ∪ ( 4 , + ∞ )
b ) f ` ( x ) = $\frac{1}{2 \sqrt{ x^{4} -16 x^{2} } } *( 4 x^{3} - 32 x ) = \\ = \frac{2x( x^{2} -8)}{ \sqrt{ x^{4}-16 x^{2} } }$
c ) The slope of the line normal to the graph at x = 5
m = -1 / f `(x)
f ` ( x ) = $\frac{10(25-8)}{ \sqrt{625-400} }= \frac{10*17}{15} = \frac{34}{3}$
m = - 3/34

8 0

3 years ago

What is the measure of angle 1?<br> 20°<br> 42°<br> 138°<br> 160°

nikdorinn [45]

Step-by-step explanation:

line s || line t

r is the transversal,

Therefore,

(7x-2)°= (6x+18)° {exterior alternate angles}

7x-6x=18+2

x=20°

r is also a straight line,

therefore,

7x-2+angle1=180° (straight angle)

7x-2+ angle1=180°

7(20)-2+ angle 1= 180°

140°-2+ angle 1= 180°

angle 1= (180-140+2 )°= 42°

angle 1= 42°

8 0

3 years ago

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On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(3, 4), a

Mumz [18]

Answer:

9.7 miles

Step-by-step explanation:

The shortest distance between 2 points is a straight line

The distance from point A to point B is

d = sqrt( ( x2-x1)^2 + ( y2-y1) ^2)

d = sqrt( ( 3 - -3)^2 + ( 4-1) ^2)

d = sqrt( ( 6)^2 + ( 3) ^2)

d = sqrt(36+9)

d = sqrt(45)

d =6.7 to the nearest tenth

The distance from point B to point C is

d = sqrt( ( x2-x1)^2 + ( y2-y1) ^2)

d = sqrt( ( 3 - 3)^2 + ( -2-4) ^2)

d = sqrt( ( 0)^2 + ( -6) ^2)

d = sqrt(36)

d = 6

But They only made it half way so 1/2 (6) =3

Add the distances together

6.7+3 = 9.7 is the minimum distance

7 0

3 years ago

What is the equation of the line that passes through the point -8, 0 and has the slope of -1 / 4

svetlana [45]

Answer:

y=-1/4x-8

Step-by-step explanation:

4 0

3 years ago

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Geometry help !! Please

attashe74 [19]

A = 1/2bh = 1/2(23)(7) = 80.5

answer
D. 80.5

8 0

3 years ago

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