Find the slope: y=23x+10

Which of the following functions could be f(x) ?

notka56 [123]

Answer:

B. f(x) = -x^3 - x^2 + 7x - 4

Step-by-step explanation:

For this problem, we want to find the fastest-growing term in our given expressions and equate them when x is - infinite and when x is infinite to see the given trends.

For each of these equations, we will simply take the terms with the highest power and consider those. The two cases we need to consider is + infinite for x and - infinite for x. Let's check each of these equations.

Note, any value raised to an even power will be positive. Any negative value raised to an odd power will be negative.

[A] - x^4

When x is +∞ --> - (∞)^4 --> f(x) is -∞

When x is -∞ --> - (-∞)^4 --> f(x) is -∞

[B] - x^3

When x is +∞ --> - (∞)^3 --> f(x) is -∞

When x is -∞ --> - (-∞)^3 --> f(x) is ∞

[C] 2x^5

When x is +∞ --> 2(∞)^5 --> f(x) is ∞

When x is -∞ --> 2(-∞)^5 --> f(x) is -∞

[D] x^4

When x is +∞ --> (∞)^4 --> f(x) is ∞

When x is -∞ --> (-∞)^4 --> f(x) is ∞

Notice how only option B, when looking at asymptotic (fastest-growing) values, satisfies the originally given conditions for the relation of x to f(x).

Cheers.

8 0

3 years ago

Your task is to build a road joining a ranch to a highway that enables drivers to reach the city in the shortest time. The perpe

lubasha [3.4K]

Answer:

(a)In the attachment

(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.

Step-by-step explanation:

(a)In the attachment

(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)

First, let us determine length of line RM.

Using Pythagoras theorem

$|RM|^{2}=30^2+x^2\\|RM|=\sqrt{30^2+x^2}$

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.

Time Taken = Distance/Time

Time taken on the road $=\frac{\sqrt{30^2+x^2}}{60}$

Time taken on the highway $=\frac{50-x}{110}$

Total time taken to travel, T $=\frac{\sqrt{30^2+x^2}}{60}+\frac{50-x}{110}$

Minimum time taken occurs when the derivative of T equals 0.

$T^{'}=\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}\\\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}=0\\\frac{x}{60\sqrt{30^2+x^2}}=\frac{1}{110}\\110x=60\sqrt{30^2+x^2}\\$

Square both sides

$12100x^2=3600(30^2+x^2)\\12100x^2=3240000+3600x^2\\12100x^2-3600x^2=3240000\\8500x^2=3240000\\x^2=\frac{3240000}{8500} =381.18\\x=\sqrt{381.18} =19.52$

The road should be built such that it joins the highway at 19.52km from the point P.

In fact,

$|RM|=\sqrt{30^2+19.52^2}=35.79km$

4 0

3 years ago

Which description matches the graph of the inequality y ≥ |x + 2| – 3? a shaded region above a solid boundary line a shaded regi

Alex777 [14]

The given inequality is y ≥ |x + 2| -3.

This inequality may be written two ways:
(a) y ≥ x + 2 - 3
or
y ≥ x - 1

(b) y ≥ -x -2 - 3
or
y ≥ -x - 5

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Answer: A shaded region above a solid boundary line.

6 0

3 years ago

In the game fortrix, a player can earn 3, 7, or 11 points on a turn. how many different scores are possible for a single player

BARSIC [14]

18 or 3 * 6 because to find out how many possible contengencys you muktiplyy the factors.

3 0

3 years ago

What’s the new value of x ??! Will mark Brianliest !!!!!!!! PLEASE help !!!!!!!!!!!!!

gayaneshka [121]

Answer:

49

Step-by-step explanation:

add 67 plus 64 and subtract that sum from 180

3 0

2 years ago