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Tema [17]
2 years ago
9

Is a function f(x)= 1/x odd or even?​

Mathematics
2 answers:
AlekseyPX2 years ago
3 0

Answer:

the function is odd.

Step-by-step explanation:

f(x) is even if f(−x)=f(x) . f(x) is odd if f(−x)=−f(x) . Since −1x=−f(x).

lozanna [386]2 years ago
3 0

Answer:

Odd

Step-by-step explanation:

There are two ways a function can be determined even or odd.

1. Graph

If the line of symmetry is the y=axis, the function is even.

If it can be rotated 180˚ about the origin and lines up with the original equation, it is odd.

If none of the cases above are satisfied, the function is neither.

2. f(-x)

If you substitute -x for x and you get the equation to be the same as before, the function is even.

If you substitute -x for x and you get the previous equation * -1, the function is odd.

If none of the cases above are satisfied, the function is neither.

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A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e
katrin [286]

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

4

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

a+b>c\\ \\a+c>b\\ \\b+c>a

Use this rule in your case. So, if a=12 and b=8, then

12+8>c\\ \\12+c>8\\ \\8+c>12

Hence, you get

c-4\\ \\c>4

From these inequalities, you can state that

4

So, c must be smaller than 20 inches and greater than 4 inches.

5 0
3 years ago
Read 2 more answers
Which equation is represented by the graph below?
kirill115 [55]

Answer:

y = \frac{2}{3}x + 6

Step-by-step explanation:

8 0
3 years ago
INFO: The chairs are evenly spaced around
lana66690 [7]

Answer: About 72 feet

The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).

======================================================

Explanation:

Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.

  • M = center of the circle
  • N = location where the cable is anchored to the ground

We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.

The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.

-----------------

What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.

It turns out that the chord length c is connected to the radius r and central angle theta like so:

c = 2*r*sin(0.5*theta)

where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.

If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces

Those five spaces could be written as

  1. The jump from L to A
  2. The jump from A to B
  3. The jump from B to C
  4. The jump from C to D
  5. The jump from D to E

Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.

There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.

-----------------

Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.

c = 2*r*sin(0.5*theta)

80 = 2*r*sin(0.5*5pi/6)

80 = 2*r*sin(5pi/12)

80 = 2*r*0.9659258

80 = 2*0.9659258*r

80 = 1.9318516r

1.9318516r = 80

r = 80/1.931 8516

r = 41.4110483

The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.

-----------------

Now that we know the radius, we can determine how long chord JF is.

The central angle for chord JF is angle JMF

If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.

So,

c = 2*r*sin(0.5*theta)

c = 2*41.4110483*sin(0.5*2pi/3)

c = 71.7260397

Chord JF is roughly 71.7260397 feet long.

When rounding to the nearest foot, that's about 72 feet.

6 0
3 years ago
Maria has decided to invest to help with her retirement savings. How much would she have to invest to have $113,400 after 20 yea
Ipatiy [6.2K]

Answer:

$56,226

Step-by-step explanation:

x = investment

Earning interest of 3.57% is the equivalent of multiplying the initial balance (investment) by 1.0357;

Over 20 years, the new balance can be found by multiplying the initial balance by (1.0357)²⁰;

We can formulate an equation to solve to get the initial investment:

x(1.0357)²⁰ = 113400

(2.01687752)x = 113400

x = ¹¹³⁴⁰⁰/₍₂.₀₁₆...₎

x = 56225.5263 → 56226

5 0
2 years ago
The formula for the nth term of an arithmetic sequence can be found using the formula Which of the following is equivalent to th
djyliett [7]
The formula for the nth term is

a1 + (n-1)d     where a1 = first term and d = common difference
6 0
3 years ago
Read 2 more answers
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