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2 years ago

Let f(x) = (x ^ 2 - 5x + 4)/(x - 1) and g(x) = 2 ^ (x - 3). For which value of x does f(g(x)) have a discontinuity ?

Mathematics

1 answer:

polet [3.4K]2 years ago

6 0

Answer:

There is a discontinuity at x=1

Step-by-step explanation:

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Can someone please help me... I am totally confusedd!!!

Bas_tet [7]

The length would be 6

3 0

3 years ago

The population of a town is 6500 and is increasing at a rate of 4% each year. Create a function for this scenario. At this rate,

Stella [2.4K]

Answer:

$P_4 = 7604.08$

Step-by-step explanation:

If the population increases at a rate of 4% per annum, then:

In year 1:

$P_1 = P_0 + 0.04P_0$

Where $P_0$ is the initial population and $P_n$ is the population in year n

In year 2

$P_2 = P_1 + 0.04P_1$

It can also be written as:

$P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)$

Taking out common factor $P_0$

$P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)$

Taking out common factor (1 + 0.04)

$P_2 = (1 + 0.04) (P_0 + 0.04P_0)$

Taking out again common factor $P_0$

$P_2 = (1 + 0.04) (1 + 0.04) P_0$

Simplifying

$P_2 = P_0 (1 + 0.04) ^ 2$

$P_n = P_0 (1 + 0.04) ^ n$

This is the equation that represents the population for year n

Then, in 4 years, the population will be:

$P_4 = P_0 (1 + 0.04) ^ 4\\P_4 = 6500(1 + 0.04) ^ 4\\P_4 = 7604.08$

3 0

3 years ago

LIEDUMICIS.ISLIULIULUI marks 4 1 point → An archer shoots an arrow into the air. The equation that describes the path of the arr

elena55 [62]

the arrow touches the ground when the heigth is 0

so we need to replace h=0 and solve for t

$\begin{gathered} h=17t-5t^2 \\ 0=17t-5t^2 \\ 0=t(17-5t) \\ 0=17-5t \\ 5t=17 \\ t=\frac{17}{5}=3.4 \end{gathered}$

the arrow tuches the ground at 3.4 seconds

$F=m\times a$

replacing

$185=m\times13.7$

solve for m

$\begin{gathered} m=\frac{185}{13.7} \\ \\ m=13.50 \end{gathered}$

the mass is 13.50Kg

4 0

1 year ago

Help pls 20 points due today

Alona [7]

Answer: A

Step-by-step explanation:

3 0

2 years ago

The first jumbo jet was the Boeing 747, which is 70.5 meters long. The wingspan of a 747 is 60 meters. A model 747 has a wingspa

nydimaria [60]

Answer:

94 cm

Step-by-step explanation:

Set up and solve an equation of ratios:

wingspan length

60 meters 70.5 m

----------------- = ----------------

80 cm x

Cross multiplying:

(60 m)x = (70.5 m)(80 cm)

Solve for x by dividing both sides of this equation by 60 m:

x = (70.5 m)(80 cm) / (60 m) = 94 cm

The length of the model should be 94 cm.

6 0

3 years ago