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3 years ago

For the function f(x)=1/x-2 +5 notice that a=1, h=2, k=5

Mathematics

1 answer:

saul85 [17]3 years ago

7 0

Answer:

x = 2 is the vertical asymptote

y = 5 is the horizontal asymptote

Step-by-step explanation:

The vertical asymptote is when it is undefined, or when the denominator is 0. This is when x = 2.

To find the horizontal asymptote, we need to find the value y can never be. Notice 1/(x-2) is never 0, so when y = 5, that value has to be 0, but this is not possible, so y = 5 is the vertical asymptote.

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if a duck is quacking upside down and I drive my car into the refrigerator then why is there an octopus on my ceiling?

Amanda [17]

Since the ducks quack in the reverse position of upright is louder than normal, it obstructs your driving causing you to drive into a refrigerator. the octopus had always been there

7 0

3 years ago

6. There are six professors teaching the introductory dis- crete mathematics class at a university. The same final exam is given

podryga [215]

Complete question is;

There are six professors teaching the introductory discrete mathematics class at a university. The same final exam is given by all six professors. If the lowest possible score on the final is 0 and the highest possible score is 100.

How many students must there be to guarantee that there are two students with the same professor who earned the same final examination score?

Answer:

607 students

Step-by-step explanation:

To solve this question means we have to use Pigenhole principle which states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.

Now, let's find the number of boxes and objects:

If possible scores are from 0 to 100 with both inclusive it means number of possible scores = 101.

Now, If there was only one professor grading the students, in order to ensure that that there are two students with the same professor who earned the same final examination score,

The number of students would have to be = 101 + 1 = 102 students

Meanwhile, for each student, since there are 6 professors, the possible combination for a score will be = 6 possible combinations.

Therefore, number of students that will guarantee that there are two students with the same professor who earned the same final examination score must be a minimum of: (6 × 101) + 1 = 607

3 0

3 years ago

Problem 2. A random variable has the following density function:

kolbaska11 [484]

If <em>f(x)</em> is a density function, then its integral over the entire real line should be 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_0^2(1-0.5x)\,\mathrm dx=(x-0.25x^2)\bigg|_0^2=2-1=1$

so yes, <em>f(x)</em> is indeed a density function.

6 0

3 years ago

A rational function is a function whose equation contains a rational

mariarad [96]

Answer:

True

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

George is considering two different investment options. The first offers 7.4% per year simple interest on the initial deposit. T

pentagon [3]

Answer:

Part A) $\$12,220.00$

Part B) $\$12,134.08$

Part C) The simple interest investment is better than the compounded interest investment at the end of three years.

Part D) see the explanation

Step-by-step explanation:

Part A) Determine the value of the simple-interest investment at the end of three years

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=3\ years\\ P=\$10,000\\r=7.4\%=7.4/100=0.074$

substitute in the formula above

$A=10,000(1+0.074*3)$

$A=10,000(1.222)$

$A=\$12,220.00$

Part B) Determine the value of the compound-interest investment at the end of three years

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=3\ years\\ P=\$10,000\\r=6.5\%=6.5/100=0.065\\n=4$

substitute in the formula above

$A=10,000(1+\frac{0.065}{4})^{4*3}$

$A=10,000(1.01625)^{12}$

$A=\$12,134.08$

Part C) Which investment is better over the first three years?

Compare the two investment

$\$12,134.08 < \$12,220.00$

The compounded interest investment is less than the simple interest investment

therefore

The simple interest investment is better than the compounded interest investment at the end of three years

Part D) How would you advise George to invest his money if he is unsure how long he’ll keep the money in the account?

we have

$A=10,000(1+0.074t)$ ----> simple interest formula as a function of the time t

$A=10,000(1.01625)^{4t}$ ----> compound interest formula as function of the time t

Look to the attached graph below

The red line represents the simple interest investment

The blue curve represents the compounded interest investment

After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest

After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest

therefore

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

4 0

3 years ago