3x2+3y2+2x-8=0<br><br> Find the center and radius

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 1

balandron [24]

Question:

Which statement is true about the discontinuities of the function $f(x) = \frac{x-5}{3x^2-17x-28}$

A)There are holes at x = 7 and .

B)There are asymptotes at x = 7 and .

C)There are asymptotes at x = –7 and .

D)There are holes at (–7, 0) and .

Answer:

B)There are asymptotes at x = 7 and $(x = \frac{-4}{3})$

Step-by-step explanation:

Given:

$f(x) = \frac{x-5}{3x^2-17x-28}$

Required:

Find the true statement

$f(x) = \frac{x-5}{3x^2-17x-28}$

We'll first factorize the denominator.

$f(x) = \frac{x-5}{(3x+4)(x-7)}$

Make x subject of the formula in (3x+4) and (x-7):

3x + 4 =

3x = -4

Divide both sides by 3:

$x = \frac{-4}{3}$

x - 7

x = 7

Now check for the limit when $(x = \frac{-4}{3})$ and (x = 7)

lim f(x) when $(x = \frac{-4}{3})$ = ±∞

lim f(x) when (x=7) = ±∞

Sinve they both make the denominator tend to zero, they are asymptotes

Therefore, there are asymptotes at $(x = \frac{-4}{3})$ and x=7

Option B is correct

6 0

2 years ago

In 1900, there was an Olympic underwater swimming event. The score was calculated by giving one point for each second the swimme

mash [69]

68.4*1= 68.4 60.2*2= 120.4 68.4+120.4= 188.8

4 0

2 years ago

Read 2 more answers

A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is th

vazorg [7]

Because there isnt 90 degrees angle in this triangle (triangle - starting point - point where he starts climbing- ending point) we will use cosine law to find magnitude of displacement. For cosine law we need 2 sides of triangle and angle between them which is exactly what is given.

a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters

to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.

cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees