All categories

3 years ago

Locate the points of discontinuity in the piecewise function shown below.

Mathematics

1 answer:

algol133 years ago

8 0

Answer:

Step-by-step explanation:

The given piecewise function i

From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.

For x=-1,

LHL:

Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.

For x=2,

LHL:

Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.

Therefore, the correct option is A.

You might be interested in

Please help me I don’t understand

Brilliant_brown [7]

Ajaksajakakakkaakajakkaak

5 0

3 years ago

Read 2 more answers

Duane is making cookies. The recipe calls for two times as many cups of sugar as butter, two times as many cups of oats as sugar

Tamiku [17]

Answer:

6.0

Step-by-step explanation:

: (2.0+(2.0+2.0)) = 6.0

6 0

3 years ago

A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i

Over [174]

Answer:

a) $\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

b) $C(5) = 100 e^{-0.16*5}= 44.9329$

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

$\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

$C(5) = 100 e^{-0.16*5}= 44.9329$

7 0

3 years ago

If you want to be 95% confident of estimating the population mean to within a sampling error of plus or minus3 and the standard

Aleksandr [31]

Answer:

The sample size required is at least 171

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

What sample size is required?

A samle size of at least n is required, in which n is found when $M = 3, \sigma = 20$

$M = z*\frac{\sigma}{\sqrt{n}}$

$3 = 1.96*\frac{20}{\sqrt{n}}$

$3\sqrt{n} = 20*1.96$

$\sqrt{n} = \frac{20*1.96}{3}$

$(\sqrt{n})^{2} = (\frac{20*1.96}{3})^{2}$

$n = 170.7$

Rouding up

The sample size required is at least 171

5 0

3 years ago

In APRT, PS = 12 cm, UV = 2 cm, and ST = 7 cm. What is the measure of RV?

Bezzdna [24]

Answer:

Which real-world situation involves division with a negative number?

splitting a $22.5 million company debt evenly among 2.4 million shareholders

converting 29.21 centimeters to inches by dividing by 2.54

calculating how much a 6.3 inch plant grew each day, on average

calculating the price of one pound of bananas if 3.9 pounds costs $2.34

Step-by-step explanation:

5 0

2 years ago