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3 years ago

Limit of y--> infinity Y = x^2 + 1/x^2

1 answer:

8 0

As x approaches infinity the value of the function Y approaches infinity. There is a vertical asymptote at x = 0 (Solve denominator for x) and since the degree of the numerator is greater than the denominator there are no horizontal asymptotes. You can simplify the limit by merging the expression into (x^4 + 1)/x^2 and dropping the one and simplifying to x^2 which in x^2 as x approaches infinity Y approaches infinity. Hope that helps!

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Simplify 3(x - 2) + 5x

Gre4nikov [31]

First, you distribute the 3 into the brackets,

3(x - 2) + 5x
=3(x) + 3(-2) + 5x
=3x - 6 + 5x

Adding the like terms, 3x and 5x, gives you

=8x - 6

6 0

3 years ago

Sketch the quadratic function ƒ(x) with a vertex at (–1, 2) and the points (0, 0) and (–2, 0). Which statement describes the par

KATRIN_1 [288]

Answer:

I believe it is C) decreasing when x > -1

Step-by-step explanation:

If you plot all 3 points on a graph, you will notice that the parabola is facing downwards. This means that on the left side of the vertex, it is increasing (the y-value increases). On the right side of the vertex, it decreases (y-value decreases). Note that "decreasing" refers to the y values.

So, since the vertex's x-value is -1 (we know this from the point (-1, 2)), any x-value greater than -1 will be to the right of the vertex. For example, 0, 1, 2, 3, etc. are all greater x-values than -1, so they are all to the right of -1. Since they are on the right, that means the corresponding-values will be decreasing.

Therefore, when x > -1, the parabola is decreasing.

4 0

4 years ago

Read 2 more answers

Write a quadratic relation in the form y = ax2 + bx + c with roots 4 and - 3 and

earnstyle [38]

Answer:

2x²-2x-24

Step-by-step explanation:

Something has roots of 4 and -3 we can write

(x-4)(x+3)

We then attach a constant, a that will ensure that it passes through the correct point

a(x-4)(x+3)

now plug in the numbers and solve for a

a(3-4)(3+3)= -12

a(-1)(6)= -12

-6a= -12

a=2

So we have

2(x-4)(x+3)

and now it's just a matter of mulitplying/simplifying things

(x-4)(x+3)= x²-x-12

2(x²-x-12)= 2x²-2x-24

6 0

4 years ago

Read 2 more answers

Pete is ahead of nick by 11 meters. Oliver is ahead of manny by 10 meters. Oliver is ahead of pete by 5 meters. How far is the r

Leokris [45]

Answer:

The runner in first place is 16 meters ahead of the runner in last place

Step-by-step explanation:

There are 4 boys racing - Pete, Nick, Manny, and Oliver.

Pete is 11 meters ahead of Nick, Oliver is 10 meters ahead of Manny, and Oliver is ahead of Pete by 5 meters.

This means Oliver is ahead of the other three racers, putting him in first place, and Manny is between Nick and Pete.

So in order to find out the distance between the racer in first place (Oliver) and the racer in last place (Nick), add the distance between Oliver and Pete and the distance between Pete and Nick.

Add the distances: 5 + 11

Therefore, the runner in first place (Oliver) is 16 meters ahead of the runner in last place (Nick).

7 0

2 years ago

The length of a rectangle is 5 yd longer than its width.

romanna [79]

Answer:

w = 13yd, l = 18yd

Step-by-step explanation:

let x be width, so x+5 = length

Perimeter is sum of all 4 sides, and since opposite sides equal in rectangle,

P = 2(l+w)

= 2(x+5 +x)

= 4x + 10

Since perimeter is give as 62yd, equation is

4x + 10 = 62

4x = 52

x = 13

8 0

3 years ago