Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is "normal", have many of each type of animal does he have

Answer:

12.25 ft

Step-by-step explanation:

(3/8)x + (5/8)x = √384

0.375x + 0.625x  = 19.6

x = 19.6

Since L = 5/8 * 19.6 = 12.25 ft

The length of the treehouse, we use the area (384 square feet) and the given ratio (width is 3/8 the length). After setting up the equation, we solve for the length to find that the length of the treehouse is 32 feet.

The length of the treehouse, we can set up an equation using the given area and the relationship between the width and length. Let L represent the length and W represent the width. According to the problem, W =  {3}/{8}L.

The area of the treehouse is given as 384 square feet. The formula for the area of a rectangle is Area = Length  imes Width, so we have:

L times W = 384 square feet

L times  {3}/{8}L = 384

{3}/{8}L² = 384

L² =  rac{384 times 8}{3}

L² = 128 times 8

L² = 1024

L =[tex]\sqrt{1024}[/tex]

L = 32 feet

Therefore, the length of the treehouse is 32 feet.

Answer:

We have: b = 823 foot

h = 534 Ft ,

Substitute their values,

A = 823 * 534

A = 439482 Ft² briefly, Your Answer would be: 439482 Ft²

~

For a fraction;

49 and 10/12

 multiply 8 and 2/3 by 5 and 3/4!

To figure this out, use the acronym SOHCAHTOA to determine which trigonometric function to use.

8 is opposite to <R and 3 is adjacent to <R so we use tangent.

Set up the following equation: tan(x)=8/3

Find the inverse (aka. tan^-1): x=69.44

So your answer is <R=69.4 degrees

Hope this helped!

It's 1.25 seconds, I just took the test and got 100% Good Luck!!! :)

The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).

To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).

Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.

Using the combination formula, C(27, 8) is calculated as:

27! / (8! * (27-8)!)

= 27! / (8! * 19!)

Factor out the common terms from the numerator and denominator

The remaining terms give us the total number of combinations

The probability is therefore: 1 / C(27, 8).

Answer:

X+y=237Litres

Step-by-step explanation:

Let a be mixture of milk and water.

Let x =milk

Let y= water

z = x+y

Final volume of mixture =63litres + z

5/12(3+z))+60=8/15(63-z)

z =x+y= 237litres

The value of [tex]x+y[/tex] is 237 liters.

Given information:

A 63 liter mixture contains milk and water in a ratio of 4:5.

Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].

The initial mixture can be written as,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]

The initial amount of water and milk will be,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]

x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.

The mixture, now, can be written as,

[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]

60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.

Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.

The final mixture can be written as,

[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]

Solve for x and y as,

[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]

So, the value of [tex]x+y[/tex] will be,

[tex]x+y=147+90\\=237[/tex]

Therefore, the value of [tex]x+y[/tex] is 237 liters.

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Quantitative in general involves number while qualitative does not involves number. For example, you can count the point scored in a football game which is considered as quantitative. While you cannot count racial composition because it involves different quality or type.  

Quantitative is further divided into two type; discrete and continuous. Discrete variable involves integers while in between two values of a continuous variable, there are an infinite number which is valid and this is not the case for discrete variables.

Qualitative is variable something that you cannot count.

Answer:

A. Points scored in a football game - Quantitative; discrete

B. Racial composition of a high school classroom - Qualitative

C. Heights of 15-year-olds - Quantitative; continuous

Points scored in a football game is a discrete quantitative variable, racial composition of a high school classroom is a qualitative variable, and heights of 15-year-olds is a continuous quantitative variable.

The variables given in this question can be classified as either qualitative or quantitative.

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Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 3x

Comparing with the slope intercept form, slope = 3

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (4,-2) is - 1/3

To determine the intercept, we would substitute m = - 1/3, x = 4 and

y = -2 into y = mx + c. It becomes

- 2 = - 1/3 × 4 + c = 4/3 + c

c = - 2 + 4/3 = - 2/3

The equation becomes

y = - x/3 - 2/3

Answer:

  sin(13π/40)

Step-by-step explanation:

The given expression matches the pattern ...

  sin(a)cos(b) +cos(a)sin(b) = sin(a+b)

Then ...

  sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)

  = sin(13π/40)

_____

  π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)

The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.

The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).

Answer:

There are 1240 students who attended Washington Middle School.

Step-by-step explanation:

Given:

Students who attend Washington Middle School are either in seventh or eighth grade.

At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.

Seventh graders represented 60% of the students on the honor roll.

If 124 students on the honor roll were in eighth grade.

Now, to find the students attend Washington Middle School.

Let the total number of students be [tex]x.[/tex]

So, the students at Washington Middle School were on the honor roll:

25% of [tex]x[/tex]

[tex]=\frac{25}{100} \times x[/tex]

[tex]=\frac{25x}{100}[/tex]

[tex]=\frac{x}{4}[/tex]

As, given seventh graders represented 60% of the students.

So, the students on the honor roll represented as seventh graders:

[tex]60\%\ of\ \frac{x}{4}[/tex]

[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]

[tex]=0.6\times \frac{x}{4}[/tex]

[tex]=\frac{0.6x}{4}[/tex]

As, 124 students on the honor roll were in eighth graders.

Thus,

According to question:

[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]

[tex]\frac{x-0.6x}{4} =124[/tex]

[tex]\frac{0.4x}{4} =124[/tex]

Multiplying both sides by 4 we get:

[tex]0.4x=496[/tex]

Dividing both sides by 0.4 we get:

[tex]x=1240.[/tex]

Therefore, there are 1240 students who attended Washington Middle School.

Answer:

x = 28.5 minutes

Step-by-step explanation:

Let x be the time taken for finishing the bike race.

Given:

Ella finished a bike race = 37.6 minutes

Miranda finished the race sooner than Ella = [tex]9\frac{1}{10} = \frac{91}{10} = 9.1\ minutes[/tex]

We need to find the minutes did it take Miranda to finish the race.

Solution:

From the statement, Miranda finished the race 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.

So, time taken by Miranda to finish the race:

[tex]Mirianda\ finshed\ a\ bike\ race = (Ella\ finshed\ a\ bike\ race) - 9.1[/tex]

[tex]x=37.6-9.1[/tex]

x = 28.5 minutes

Therefore, Miranda finished the bike race in 28.5 minutes.

Answer:

Influencer

Step-by-step explanation:

An influencer is a person who has the power affect purchase decisions of others because of his ability such as knowledge, position with audience.

Final answer:

A person acting as a specifier in the buying center provides product specifications and may influence the purchase decision by setting requirements, interacting with both customer and seller but not making final purchasing decisions.

Explanation:

Depending on the product, there may be a person who acts as specifier in the buying center, often by providing specifications for the product being purchased or the vendor being considered.

A specifier plays a crucial role in the procurement process, ensuring that the product or service meets the organization's needs and standards. In a buying center, this individual might not have the authority to make final purchase decisions but is influential by setting the requirements that the potential products or suppliers must meet.

A specifier may interact closely with both the customer and seller to ensure that the right features, quality, and functionalities are captured in the procurement specifications.

This person may also assess the long-term reliability of supplier relationships, such as through exclusive dealer agreements, to safeguard the company's interests. The role of the specifier is analogous to that of a product consultant, providing insights without directly engaging in sales or price negotiations.

Answer:

Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]

Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]

Also Given:

Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]

[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]

Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]

Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Final answer:

Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.

Explanation:

Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:

Next, we add these two amounts together:

(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.

Now we convert 251/20 hours to a mixed number:

251/20 = 12 11/20 hours

They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:

20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.

Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:

149/20 hours = 7 9/20 hours.

So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.

Answer:

the answer is c

Step-by-step explanation:

i took the test and got a 100

The range of the function is all real numbers less than or equal to 0.

A function is an expression that shows the relationship between two or more variables or numbers.

The domain of a function is the set of input values while the range is the set of output values.

From the graph, The range of the function is all real numbers less than or equal to 0.

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Answer:

Step-by-step explanation:

It would take them 8 hours to complete the painting task if they worked together.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

If painter A can paint the area in 3 hours, and painter B can paint the same area in 5 hours, then it would take them a total of 3+5=8 hours to paint the area together.

It's worth noting that this assumes that both painters are able to work at their full capacity while working together and that they are able to divide the work between them in an efficient manner. If either of these conditions is not met, it could take them longer than 8 hours to complete the job.

Hence, working together, it would take them 8 hours to complete the painting job.

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Answer:

79 years old

Step-by-step explanation:

Let his age be x

400-3x=163

400-163=3x

237=3x

Divide both side by 3

237/3 =3x/3

79=x

The man's age (x) =79 years old

Answer:

x=-5 and x=-1.5

Step-by-step explanation:

The given function is

[tex]v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15} [/tex]

The points of discontinuity occurs at where the denominator is zero.

[tex]2 {x}^{2} + 13x + 15= 0[/tex]

We solve by factoring.

We first split the middle term:

[tex]2 {x}^{2} + 3x + 10x + 15= 0[/tex]

We factor by grouping:

[tex]x(2x + 3) + 5(2x + 3)= 0[/tex]

[tex](x + 5)(2x + 3) = 0[/tex]

The points of discontinuity occur at x=-5, and x=-1.5

Final answer:

The function v(x) has discontinuities at x = -3 and x = -5/2.

Explanation:

A point of discontinuity in a mathematical function refers to a location where the function fails to be continuous. In other words, it's a point at which the function exhibits a break or abrupt change in its behavior.

The point of discontinuity for the function [tex]v(x) = (x^2-25)/(2x^2+13x+15)[/tex] can be found by setting the denominator equal to zero and solving for x. In this case, the denominator factors to (x+3)(2x+5), indicating discontinuities at x = -3 and x = -5/2. These are the points where the function is not defined.

Points of discontinuity are essential to understanding the behavior and properties of functions, particularly in areas like calculus and real analysis. They are critical in identifying where a function fails to meet the criteria for continuity and in analyzing the behavior of functions in various contexts.

Answer: 25/36

Step-by-step explanation:

A die has six faces, therefore its sample space S is 6

Since we are rolling a die twice(at different times), the probability of one turning up the first time is 1/6(i.e expected outcome/total outcome)

Similarly, if we throw the die the second time, the probability of one turning up the second time is also 1/6

The probability of having number greater than 1 land at each time will be (1- 1/6) which is 5/6.

Therefore the probability of having number greater than 1 land at "both times" will be 5/6×5/6 = 25/36

Answer:

Line ED

Explanation:

Opposite side is EF (because its opposite to the angle)

Hypotenuse side id FD (opposite of right angle)

Adjacent is the line leftover

Answer:

B

Step-by-step explanation:

Adjacent is the one with 90° and the angle, theta

ED in this case

Answer:

c

Step-by-step explanation:

Answer:

The enlargement will be 2,250 which is 25 the times

Step-by-step explanation:

In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.

It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.

The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.

The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.

To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.

To calculate the area of a square, use the formula below, where s is the length of the side of the square.

Now, calculate the areas of of the two logos.

Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.

Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.

Answer:

The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].

Step-by-step explanation:

The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.

[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]

The sample space of flipping two coins is:

S = {HH, HT, TH and TH}

Total number of outcomes = 4

Compute the probability of flipping Heads at least once as follows:

Let X = heads.

P (X ≥ 1) = P (X = 1) + P (X = 2)

             [tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]

Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].

The experiment of flipping a coin is a binomial experiment.

Since there are only two outcomes of the experiment, either a Heads or a Tails.

So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.

Answer:

k  = 0.0916

Step-by-step explanation:

T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]

from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C

60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]

60-50 = 30 [tex]e^{-12k}[/tex]

10/30 =  [tex]e^{-12k}[/tex] (Taking natural Log of both sides)

In(0.3333) = In [tex]e^{-12k}[/tex]

-1.0986 = -12k

k = 0.0916

Answer:

The answer is x = -6.6

Step-by-step explanation:

Answer:

X= -6.6

Step-by-step explanation:

Just do 13.8 - 20.4. It will equal -6.6.

Answer:

20,158 cases

Step-by-step explanation:

Let [tex]t=0[/tex] represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

[tex]F(t)=102,390(1-0.15)^t[/tex]

[tex]F(t)=102,390(0.85)^t[/tex]

To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:

[tex]F(10)=102,390(0.85)^{10}[/tex]

[tex]F(10)=102,390(0.1968744043407227)[/tex]

[tex]F(10)=20,157.970260446597\approx 20,158[/tex]

Therefore, 20,158 cases  will be reported in 2020.

Answer: B. 33%

Step-by-step explanation:

Given : Response  - Frequency

          Not satisfied - 20

              Satisfied - 40

         Highly satisfied - 60

Total customers = (Number of customers  Not satisfied) +  (Number of customers satisfied) + ( (Number of customers  Highly satisfied) )

= 20+40+60=120

Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]

[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]

Hence, the percentage of the responses indicated that customers were satisfied = 33%

Thus , the correct answer is B. 33%

To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.

To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.

Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.

To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.

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Answer:

1. Yes, the lines are perpendicular.

2. [tex]y=\frac{5}{4}x+6[/tex]

Step-by-step explanation:

The first equation of Exercise 1 is incomplete. Let's assume that it is:

[tex]2x + 3y =n[/tex]

Where "n" is a number.

First, it is important to remember that the equation of a line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

By definition, the slopes of perpendicular lines are negative reciprocals.

1 . If you solve for "y" from the first equation, you get:

[tex]2x + 3y =n\\\\3y=-2x+n\\\\y=-\frac{2}{3}x+\frac{n}{3}[/tex]

You can identify that the slope is:

[tex]m=-\frac{2}{3}[/tex]

The second equation of the line is:

[tex]y=\frac{3}{2}x+4[/tex]

And its slope is:

[tex]m=\frac{3}{2}[/tex]

Since the slopes are negative reciprocals, the lines are perpendicular.

2. Given the first equation of the line:

[tex]y= -\frac{4}{5}x+6[/tex]

You can identify that:

[tex]m=-\frac{4}{5}\\\\b=6[/tex]

Since the first line and the second one are perpendicular, you know that the slope of the other line is:

[tex]m=\frac{5}{4}[/tex]

According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:

[tex]y=\frac{5}{4}x+6[/tex]

6.60 would be the total cost for both 3 pounds and two pounds :D

Answer:

$6.60

Step-by-step explanation:

multiply 1.20 (red apples) by 3 (lbs) = 3.6

and 1.50 (green apples) times 2 (lbs) = 3

then add the two totals = $6.60

Answer:

The solution to the differential equation

y' = 1 + y²

is

y = tan x

Step-by-step explanation:

Given the differential equation

y' = 1 + y²

This can be written as

dy/dx = 1 + y²

Separate the variables

dy/(1 + y²) = dx

Integrate both sides

tan^(-1)y = x + c

y = tan(x+c)

Using the initial condition

y(0) = 0

0 = tan(0 + c)

tan c = 0

c = tan^(-1) 0 = 0

y = tan x

In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:

[tex]y = tan x[/tex]

Then say the differential equation as:

[tex]y' = 1 + y^2[/tex]

then rewriting as:

[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]

Integrate both sides, we have that:

[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]

So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:

[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]

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