If the limiting value of value of f(x). (f(x)-5) x-3 at x= 3 is 2 by using L' Hospital' rule, find the appropriate Write any one homogeneous differential equation in (x,y) and solve it. [3] The concept of anti-derivative is necessary for solving a differential equation. Justify this statement with example. [3]​

Answer:

1st option - \(\frac{1}{\sqrt[5]{7x } }\)

Step-by-step explanation:

A fractional power can be broken down.

The denominator will be the root number

The numerator will be the power

For example x^1/2 = √x^1 = √x

So :

\(\frac{1}{7x^{\frac{1}{5} } }\) = \(\frac{1}{\sqrt[5]{7x^{2} } }\)  = \(\frac{1}{\sqrt[5]{7x}}\)

So 1st option

Answer: the answer on the far left

Step-by-step explanation: i looked it up

Answer:

216 feet

Step-by-step explanation: Just do 27 x 96 to get 2592 inches and then convert that to feet and you get 216 feet

Answer:

about 221 or exactly 220.1 feet

Step-by-step explanation:

1 foot = 12 inches

27 5/8 inches = 2. 30 feet

2.30 feet * 96 steps = 220.1 feet

I'm pretty sure this is how its supposed to go if you meant 5/8 feet with it!

Answer:

38 because the 5 tells the 7 to round up to 8

hope this helps

have a good day :)

Step-by-step explanation:

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

The correct answer is D.

The function f(x) has some specific characteristics as shown in the graph.

The graph of f(x) has five intercepts, as can be seen from the graph.

The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.

The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.

At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.

The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.

Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).

This can be deduced from the symmetry of the graph about the origin.

Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.

At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

For such more questions on intercepts

https://brainly.com/question/24212383

#SPJ8

Answer:

9.48

Step-by-step explanation:

Answer:

Step-by-step explanation:

To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:

11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:

1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.

2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:

2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.

ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:

10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.

123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:

1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.

Now, let's perform the arithmetic operations:

234 + 1090 + 2748 - 83 = 3989.

Therefore, the result of the given expression in decimal form is 3989.

Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

For more such questions on future value

https://brainly.com/question/24703884

#SPJ8

The amount of money it would cost to recarpet the rectangular hotel room is equal to $1,752.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangular hotel room = 4 × 6

Area of rectangular hotel room = 24 yd²

Now, we can determine the cost as follows;

Cost of recarpet = $73.00 × 24 yd²

Cost of recarpet = $1,752.

Read more on area of a rectangle here: brainly.com/question/29604954

#SPJ1

Answer:

Vertex is (3, 1)

Axis of symmetry is x = 3

No zeroes of this function

y-intercept is (0, 7)

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

For similar question on population sample.

https://brainly.com/question/27859177  

#SPJ8

Answer:

They won 27 games

Step-by-step explanation:

10% of 30 is 3,

so 30-3= 27

Answer:

18000 m

Step-by-step explanation:

Hey there!

In order to solve this problem, we need to first know how many minutes are in an hour

As you know, there are 60 minutes in an hour so this means in 1 hour, he will climb 9000 meters two times

So 9000 two times is 18000,

Meaning, in 1 hour, Sam will climb 18000 m

Answer:

18,000m in an hour

Step-by-step explanation:

We know this because if its 9000 m in 30 minutes, we can do 9000 x 2 and get 18,000m for an hour.

Answer: 24

Step-by-step explanation:

3*4=12

12*2=24

If 3/4 of the remaining rocks are igneous, then you would only have three rocks left. You take the denominator of the 3/4, so 4, and multiply it by 4 to get what one half of the overall amount of rocks are. You then multiply it by 2, getting the answer 24. Hope this helped.

Answer: 17.46 oz

Step-by-step explanation:

Since we are looking for how much coffee we can buy, we can set up a proportion to solve. First, we have to convert the 2 pounds to ounces because that is the unit the question is asking for.

\(2lbs*\frac{16oz}{1lbs} =32 oz\)

Now that we have the ounces, we can set up the proportion.

\(\frac{32.98}{32oz} =\frac{17.99}{x}\)

We can cross multiply to find x.

\(32.98x=17.99*32\)

\(32.98x=575.68\)

\(x=17.46oz\)

Answer:

Function 1 has the greater rate of change.

Step-by-step explanation:

Function 1 has a rate of change of -5

Function 2 has a rate of change of -8

I really hope this helps!!

Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Answer:

Percent of the total food cost: 85%

Cost of the food: $17

Step-by-step explanation:

If the drink is 15% of the bill, then the other 85% is the cost of the food.

85% of 20 is 17

Stay safe! <3

To sketch the graph of

y<-3/2x + 3​

we need to draw the line:

y = -3/2x + 3​

Substituting x = 0:

y = -3/2(0) + 3​

y = 3

Substituting y = 0:

0 = -3/2x + 3​

-3 = -3/2x

-3*(-2/3) = x

2 = x

Then, the line (which is a dashed line because the points on the line are not a solution to the inequality) passes through (0, 3) and (2, 0)

Now, we have to find if a point is a solution or not. Replacing with (0,0) into the inequality:

0 < -3/2(0) + 3​

0 < 3​

which is correct, then we need to shade the side that includes (0,0)

The correct statement:

The slope is positive because as the age increases, the value increases.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The table:

x → y

5 →  0.75

10 → 5.75

15 →  10.75

20 → 15.75

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = 15.75 - 10.75 / 20 - 15

m = 1

Therefore, the slope is positive because as the age increases, the value increases.

To learn more about the slope;

brainly.com/question/3605446

#SPJ2

It needs to do that route I guess. But I don't understand the last question well.

Answer:

six rational number are

3/5 × 4= 12/20

3/4 ×5 =15/20

we have to find six rational number between 12/20 and 15/20, so we have to multiply numerator and denominator by 7

12×7= 84

20×7=140

15/20×7=105/140

85 ,86 , 87 ,88 89 90

140, 140, 140, 140, 140 ,140

Answer:

\(\sf \dfrac{121}{200} \ ; \ \dfrac{122}{200} \ ; \ \dfrac{123}{200} \ ; \ \dfrac{124}{200} \ ; \ \dfrac{125}{200} \ ; \ \dfrac{126}{200}\)

Step-by-step explanation:

To find six rational numbers between the given numbers,

         LCM of 5 and 4 is 20.

            \(\sf \dfrac{3}{5}=\dfrac{3*4}{5*4}=\dfrac{12}{20}\\\\\\\dfrac{3}{4}=\dfrac{3*5}{4*5}=\dfrac{15}{20}\)

            \(\sf \dfrac{12*10}{20*10}=\dfrac{120}{200}\\\\\dfrac{15*10}{20*10}=\dfrac{150}{200}\)

\(\sf \text{six rational numbers between} \ \dfrac{3}{5} \ and \ \dfrac{3}{4}\ are :\)

       \(\sf \dfrac{121}{200} \ ; \ \dfrac{122}{200} \ ; \ \dfrac{123}{200} \ ; \ \dfrac{124}{200} \ ; \ \dfrac{125}{200} \ ; \ \dfrac{126}{200}\)

The value of X is 35 because the angle 35 measures the same as the angle X, hence their values are the same

Answer:

heag ar jn jt ej t

Step-by-step explanation:

Answer:

You got it wrong because you didn't distribute the 7 to the 3j.

Step-by-step explanation:

The answer should be 21j +70.

Answer:

In your original answer, you did not distribute the 7 to the 3j

Step-by-step explanation:

The distributive property basically states that the sum of any variables multiplied by a factor is equal to the sum of each product of every individual variable and the factor.

In short,

a(b+c) = ab + ac

or

x(y + w + z) = xy + xw + xz

or

9m + 9n = 9 (m+n)

Therefore, in order to solve 7(3j + 10)

you must multiply 7 by 3j and 7 by 10

(7 * 3j) + (7 * 10) = 21j + 70

Since 70 does not have the same terms as 21j (70 does not have j),

21j + 70 is in its most simplified form.

In your original answer, you didn't multiply the 3j by 7.

Using the Corresponding Angle Theorem, ∠m = 23 degree. So, the option A is correct.

In the given question, lines n and o are parallel and are cut by the transversal p.

We have to find the measure of ∠m and choose the correct option.

As we know that;

When two parallel lines are intersected by another line, corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal.

So using the Corresponding Angle Theorem

∠m = 23 degree

Hence, the option A is correct.

To learn more about Corresponding Angle Theorem link is here

brainly.com/question/16017873

#SPJ4

Yes , it is true that two pairs of adjacent sides of a kite are equal .

A quadrilateral with two pairs of adjacent sides equal in length is called a kite. Kites also have one pair of opposite angle equal as shown in the figure below.

Hence , the given statement is true .

​Learn more about kite here :

https://brainly.com/question/23279609

#SPJ9

If the 0.99 probability of completing the project on time, then the scheduled meeting date should he begin working on the project is 2.39 weeks

How to calculate the probability?

In math, the probability can be determined by first knowing the sample space of outcomes of an experiment and then by dividing the number of outcomes of an event by the total number of possible outcomes or sample space.

Here we have given that Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company.

And we need to find the If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project.

Here we know that the duration of the critical path determines the completion of the whole project.

Therefore, the mean completion time of the project =μ=15

And the the variance of the critical path = sum of the variances of the activities A, B, G, H, and I =0.03+0.44+0.44+0.11+0.03=1.06

Therefore, the standard deviation of the critical path or that of the whole project =σ=√1.06=1.03

Here we know that, if a 0.99 probability of completion is required, then the corresponding Z-score =2.3263

Then the actual completion time corresponding to a Z-score of

=> 2.3263 = μ+(Z×σ) = 15+(2.3263×1.03) = 15+2.39 = 17.39 weeks

Which states that the extra time needed over and above the mean completion time of the project of 15 weeks to have a 0.99 probability of completion =17.39−15=2.39 weeks

Therefore, in order to have a 0.99 probability of completing the project on time, the project should be started 2.39 weeks ahead of the scheduled meeting date.

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4