Mathematics College

In this problem, y = 1/(x2 +
c.is a one-parameter family of solutions of the first-order de y' + 2xy2 = 0. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(4) = 1/15

Answers

Answer 1
A family of solutions to the DE is given to be y = 1/(x^2 + c);
With given initial condition y(4) = 1/15.

Let's use this initial data to find a particular solution.
Plug 4 in for x, and 1/15 in for y,

1/15 = 1/(4^2 + c)
Solve for c.

Reciprocate each side,
15 = 4^2 + c
-1 = c

Plugging this c value back into our family of solutions will give us one particular solution to the DE,

y = 1/(x^2 - 1)

Related Questions

Determine all possible angles θ for equilibrium, 0∘<θ<90∘.

Answers

If the tension of a cable AB and BC is represented as Fab and Fac, using the equilibrium  equations equation 1:Fab cos 40 degrees - Fac cos x = 0where x is the angle we are looking for,0.766Fab - Fac cox x = 0equation 2:-200 + Fab sin 40 degress + Fac sin x = 00.643Fab + Fac sin x = 200solving the tension we getFab = 311.04lbFac = 238.26 lb
substitute 30 degrees to x on equation 1 and 2, we getFab = 184.31lb, Fac = 163lb
substitute 45 degrees to x on equations 1 and 2, we getFab = 141.9lb, Fac = 153.77lb
substitute 60 degrees to equation 1 and 2,we getFab = 101.5lb, Fac = 155.55lb
substitute 90 degrees to x on eqn 1 and 2 we getFab = 0lb, Fac = 200lb
There 90 is not a possible answer.
Possible angles are 30 degrees, 45 degrees and 60 degrees

Please need help as quick as you can . What is the slope of the line that passes through the points (16, –1) and (–4, 10)? A. -20/11 B. -11/20 C. 11/20 D. 20/11

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 16}}\quad ,&{{ -1}})\quad % (c,d) &({{ -4}}\quad ,&{{ 10}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-(-1)}{-4-16}\implies \cfrac{10+1}{-4-16} \\\\\\ -\cfrac{11}{20}[/tex]

For the x-values 1, 2, 3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?   A. Exponential growth   B. Decreasing linear   C. Increasing linear   D. Exponential decay

Answers

Answer:

Option A: Exponential growth

Step-by-step explanation:

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because  because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

Final answer:

The function described, where y-values form an increasing geometric sequence as x-values increase, is characterized as Exponential growth. This is consistent with an exponential curve where the rate of growth is proportional to the current value, which aligns with the behavior of a geometric sequence.

Explanation:

For the given scenario where the y-values of a function form a geometric sequence that increases for the x-values 1, 2, 3, and so on, the type of function is described as Exponential growth. This is because in a geometric sequence each term after the first is found by multiplying the previous term by a constant called the common ratio, which is analogous to the exponential function where the growth rate of the value is proportional to its current value. The more the x-value increases, the higher and faster the y-value grows, following the pattern of an exponential growth curve.

Answer A. Exponential growth fits the description as it involves an increasing geometric sequence. Answer B. Decreasing linear refers to a linear function that decreases with each increment in x, which does not describe the function in question. Similarly, Answer C. Increasing linear describes a function that increases at a constant rate, not geometrically. Answer D. Exponential decay would imply the y-values decrease as x increases, which is also not the case described.

five friends went to a local restaurant and all had the buffet at $6.75 each. the following is the restaurant bill. does it seem reasonable 5($6.75) =&67.50

Answers

No I think not really to sure
Yes because your food had cost $6.75 each for 5 people, so if you had a bill of $67.50 and your concern about is it reasonable just budget it out.

A car manufacturer claims that, when driven at a speed of 50 miles per hour on a highway, the mileage of a certain model follows a normal distribution with mean μ = 30 miles per gallon and standard deviation σ= 4 miles per gallon.

Answers

84 miles per gallon maybe 

Is the symbol (x¯¯) used for the population mean or sample mean?

choices are.....
population mean
sample mean

Answers

it use for population mean
x=poluation mean
Final answer:

The symbol x is the sample mean, and the Greek symbol μ is the population mean.

Explanation:

The symbol x is the sample mean, and the Greek symbol μ is the population mean. Calculating the Standard Deviation: If x is a number, then the difference x - mean is called its deviation. In a data set, there are as many deviations as there are items in the data set. The deviations are used to calculate the standard deviation. If the numbers belong to a population, in symbols, a deviation is x - μ. For sample data, in symbols, a deviation is x - x.

Find the area of the specified region shared by the circles r = 4 and r = 8sin

Answers

ind the area shared by the circles r=2cos(theta) and r=2sin(theta).

i know the general formula for finding the area, but i don't know which is the outside one, and which is the inside circle. but i've tried both ways and am still not getting the right answer. 

so let's just say i'll try it with integral .5(4cos(x)^2-.5(4sin(x)^2)
i can factor out a 2, giving me cos(x)^2-sin(x)^2. the integral of that, i believe, can be expressed as 4sin(2x). now i figured the limits of integration were from 0 to pi/4, because those are the two places the circles intersect. so evaluating there, i would get 4-0=4. but I've been told the answer is pi/2 -1. so where am i going wrong, because i'm way off.

Eric has 4 bags of 10 marbles and 6 single marbles . how many marbles does eric have

Answers

He has 46 marbles in total

First, you would multiply the number of bags by the quantity in each.
4 x 10 = 40

Next, you would add the single marbles. 
40 + 6 = 46

Your answer would be 46. 

I hope this helps!

Triangle ABC has two known angles. Angle A measures 55 degrees. Angle b measures 30 degrees.What is the measure of angle C?

Answers

95 Degrees, 180-55-30=95
The correct measure of angle C is 95 degrees. Hope this helps.

PLEASE HELP 15 POINTS WILL GIVE BRAINLIEST The following formula, F = ma, relates three quantities: Force (F), mass (m), and acceleration (a). A: Solve this equation, F = ma for a. B If F = -24 units and m = 10 units, what is the acceleration, a? Use the equation from Part (a) to answer the question. C: If F = 24 units and a = 12 units, what is the mass, m? Use the equation, F = ma, to plug in the known values and solve for m

Answers

Part A

The expression "ma" is the same as "m*a" (m times a). To isolate 'a', we divide both sides by m. Division is the inverse operation of multiplication. Think of it as undoing multiplication

F = ma
F = m*a
F/m = m*a/m
F/m = a
a = F/m

Answer: a = F/m
Note: the slash "/" without quotes means "divide"

===========================================
Part B

Use the result from part A. We will plug F = -24 and m = 10 into that equation

a = F/m
a = -24/10
a = -2.4

Answer: -2.4

===========================================
Part C

We will use the equation F = m*a

F = m*a
24 = m*12 ... plug in F = 24 and a = 12
24/12 = m*12/12
2 = m
m = 2

Answer: 2


Find the difference: 16.25 - 7.92

Answers

Your answer is going to be 8.33
the difference is 8.33.
give me the best plz

what is the least common denominator for 5/6 and 3/8

Answers

The least common denominator is 24.

A pizzeria baked 12 pizza pies in 3 hours. At this rate, how many pizza pies can they bake in 7 hours?

Answers

28; 12 divided by 3 is four. That is the rate. Then multiply 7x4=28
first find the hourly rate for how many pies they bake in 1 hour and multiply it by 7

12 pizzas / 3 hours is 4 pizzas per hour 

4 pizzas per hour * 7 hours = 28 pizzas

Suppose 8 out of every 20 students are absent from school less than 5 days a year.Predict how many students would be absent less than 5 days a year out of 40,000 students.

Answers

Answer:
8/20 * 40,000 = 16,000

How much do parents pay per day? If a childcare center charges $150 per week during the school year. In the summer, parents can pay a prorated amount based on the number of days of attendance.

Answers

During the school year, children usually go to the childcare 5 days per week.
Knowing that parents pay $150 per week, we can divide this amount by the number of days children go to the childcare in order to find the daily payment.

This is done as follows:
daily payment = $150 / 5 = 30$ per day

a construction crew Must build 4 miles of road in one week on Monday they build 1/2 mile of road in one week on Tuesday they build 1/3 mile of road how many more miles of road are left to build

Answers

To solve this, you need to make the amount they built on Monday and the amount they built on Tuesday compatible with each other so you can add them together to subtract that amount from 4.

Start by multiplying 1/2 by 3, and 1/3 by 2.

This gives you 3/6 and 2/6. Now add them together:

3/6 + 2/6 = 5/6

Finally, subtract this amount from 4:

4 - 5/6 = 3 1/6 (19/6 works too)

Hope this helps! :)
4        -        1/2     -    1/3
24/6   -        3/6     -    2/6    =   19/6  =  3 1/6


Lilly has a bag of 140 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Lilly arranged all of the green marbles in groups of 8 and all of the blue marbles in groups of 7, how many red marbles are in the bag?

Answers

Okay. I think to find the number of green and blue marbles each, we have to find the LCM of 8 and 7. The LCM of 8 and 7 is 56. There are 56 green marbles and 56 blue marbles. That a total of 112 marbles combined. 140 - 112 = 28. There are 28 red and yellow marbles. There are an equal number of both. 28/2= 14. There are 14 red marbles in the bag.

A polygon has vertices at (4, 1), (4, 7), (10, 7) and (10, 1). How does the perimeter of the polygon change if each coordinate is multiplied by 3?

Answers

check the picture below.

multiplying each point by 3, will give us the larger square of (12,3), (13, 21), 30,21) and (30,3).

notice what happened to the perimeter.

F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.

Answers

Take partial derivatives and set them equal to 0:

[tex]\nabla F(x,y)=\langle2x+4,2y-4\rangle=\mathbf 0[/tex]

We find one critical point within the boundary of the disk at [tex](x,y)=(-2,2)[/tex]. The Hessian matrix for this function is

[tex]\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&0\\0&2\end{bmatrix}[/tex]

which is positive definite, and incidentally independent of [tex]x[/tex] and [tex]y[/tex], so [tex]F(x,y)[/tex] attains a minimum [tex]F(-2,2)=-8[/tex].

Meanwhile, we can parameterize the boundary by [tex]\mathbf r(t)=\langle9\cos t,9\sin t\rangle[/tex] with [tex]0\le t\le2\pi[/tex], which gives

[tex]F(x,y)=F(x(t),y(t))=f(t)=81\cos^2t+81\sin^2t+36\cos t-36\sin t=81+36(\cos t-\sin t)[/tex]

with critical points at

[tex]f'(t)=0\implies 36(-\sin t-\cos t)=0\implies\sin t+\cos t=0\implies t=\dfrac{3\pi}4,\dfrac{7\pi}4[/tex]

At these points, we get

[tex]f\left(\dfrac{3\pi}4\right)=81-36\sqrt2\approx30.0883[/tex]
[tex]f\left(\dfrac{7\pi}4\right)=81+36\sqrt2\approx131.9117[/tex]

so we attain a maximum only when [tex]t=\dfrac{7\pi}4[/tex], which translates to [tex](x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right)[/tex].

The extreme values of a function are the minimum and the maximum values of the function.

The extreme values are: -8 and 131.91

The given parameters are:

[tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]

[tex]\mathbf{x^2 + y^2 \le 81}[/tex]

Find the gradient of F(x,y)

[tex]\mathbf{f_x(x) = 2x + 4}[/tex]

[tex]\mathbf{f_y(y) = 2y - 4}[/tex]

Set to 0, to solve for x and y

[tex]\mathbf{2x + 4 = 0}[/tex]

[tex]\mathbf{2x = -4}[/tex]

[tex]\mathbf{x = -2}[/tex]

[tex]\mathbf{2y - 4 = 0}[/tex]

[tex]\mathbf{2y = 4}[/tex]

[tex]\mathbf{y = 2}[/tex]

So, the critical point is:

[tex]\mathbf{(x,y) = (-2,2)}[/tex]

Also, we have: [tex]\mathbf{x^2 + y^2 \le 81}[/tex]

Calculate the gradients

[tex]\mathbf{g_x = 2x}[/tex]

[tex]\mathbf{g_y = 2y}[/tex]

Equate the gradients as follows:

[tex]\mathbf{f_x = \lambda \cdot g_x}[/tex]

[tex]\mathbf{f_y = \lambda \cdot g_y}[/tex]

So, we have:

[tex]\mathbf{2x + 4 = \lambda \cdot 2x}[/tex]

[tex]\mathbf{2y - 4 = \lambda \cdot 2y}[/tex]

Make [tex]\mathbf{\lambda}[/tex] the subject, in the above equations

[tex]\mathbf{\lambda = \frac{x + 2}{x}}[/tex]

[tex]\mathbf{\lambda = \frac{y - 2}{y}}[/tex]

Equate the above equations, so we have:

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

Cross multiply

[tex]\mathbf{xy + 2y = xy - 2x}[/tex]

Subtract xy from both sides

[tex]\mathbf{2y =- 2x}[/tex]

Divide both sides by 2

[tex]\mathbf{y =- x}[/tex]

Substitute [tex]\mathbf{y =- x}[/tex] in [tex]\mathbf{x^2 + y^2 = 81}[/tex]

[tex]\mathbf{x^2 + (-x)^2 = 81}[/tex]

[tex]\mathbf{x^2 + x^2 = 81}[/tex]

[tex]\mathbf{2x^2 = 81}[/tex]

Divide both sides by 2

[tex]\mathbf{x^2 = \frac{81}{2}}[/tex]

Take square roots

[tex]\mathbf{x = \±\frac{9}{\sqrt2}}[/tex]

Rationalize

[tex]\mathbf{x = \±\frac{9\sqrt2}{2}}[/tex]

Recall that: [tex]\mathbf{y =- x}[/tex]

So, we have:

[tex]\mathbf{y = \±\frac{9\sqrt2}{2}}[/tex]

The ordered pairs are:

[tex]\mathbf{(x,y) = \{(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]

Hence, the points are:

[tex]\mathbf{(x,y) = \{(-2,2),(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]

Substitute these values in [tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]

[tex]\mathbf{F(2,2) = (-2)^2 + 2^2 + 4(-2) - 4(2) =-8}[/tex]

[tex]\mathbf{F(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}) = (\frac{9\sqrt2}{2})^2 + (-\frac{9\sqrt2}{2})^2 + 4(\frac{9\sqrt2}{2}) - 4(-\frac{9\sqrt2}{2}) =131.91}[/tex]

[tex]\mathbf{F(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2}) = (-\frac{9\sqrt2}{2})^2 + (\frac{9\sqrt2}{2})^2 + 4(-\frac{9\sqrt2}{2}) - 4(\frac{9\sqrt2}{2}) =30.09}[/tex]

Hence, the extreme values of the function are: -8 and 131.91

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If a radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there?

Answers

There are a total of 26 letters that can be made to follow. There are 4 independent events here, namely:

First: Starts with K and followed by two additional letters = 1 * 26 * 26 = 676

Second: Starts with K and followed by three additional letters = 1 * 26 * 26 * 26 = 17,576

Third: Starts with W and followed by two additional letters = 1 * 26 * 26 = 676

Fourth: Starts with W and followed by three additional letters = 1 * 26 * 26 * 26 = 17,576

 

The total possibilities that can be made from here is:

Total possibilities = 676 + 17,576 + 676 + 17,576

Total possibilities = 36,504

the weight of an object on the moon is about .167 of its weight on Earth. How much does a 180 lb astronaut weigh on the moon?

Answers

[tex]\bf \begin{array}{ccll} \stackrel{lbs}{earth}&\stackrel{lbs}{moon}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&0.167\\ 180&x \end{array}\implies \cfrac{1}{180}=\cfrac{0.167}{x}\implies x=\cfrac{180\cdot 0.167}{1}[/tex]
The astronaut will weigh less on the moon.  Determine how much the scale will indicate by multi. 180 lb by 0.167:  (180 lb)(0.167) = 30.06 lb.

There are 365,493 blue pens and 549,384 black pens how many more black pens are there then blue pens

Answers

Take the larger number and subtract the smaller number and you get 183,891

By subtracting the number of blue pens from the number of black pens, we find that there are 183,891 more black pens than blue pens.

To find out how many more black pens there are than blue pens, we need to subtract the number of blue pens from the number of black pens. The student provided the numbers as 365,493 blue pens and 549,384 black pens.

Here is the calculation:

Number of black pens: 549,384Number of blue pens: 365,493Difference (black pens - blue pens): 549,384 - 365,493 = 183,891

There are 183,891 more black pens than blue pens.

What percent of 9.2 is 43.7

Answers

if we take 9.2 to be the 100%, what is 43.7 off of it in percentage then?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 9.2&100\\ 43.7&p \end{array}\implies \cfrac{9.2}{43.7}=\cfrac{100}{p}\implies p=\cfrac{43.7\cdot 100}{9.2}[/tex]

The requried 475% of 9.2 is 43.7, as of the given percentage situation.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
In the question, we are asked to determine the 43.7 is what percent of 9.2.

So, let the percent be x,
x % of  9.2 = 43.7
x/100 × 9.2 = 43.7
x = 43.7/9.2 × 100%
x = 475%

Thus, the requried 475% of 9.2 is 43.7, as of the given percentage situation.

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What is the meaning of the term theorem

Answers

There are 4 terms in the world of *Mathematical proof*
Lemma, Proposition, Corollary and Theorem.
There is no difference between a lemma,
proposition, theorem, or corollary - they are all claims waiting to be proved. However, we use these terms to suggest different levels of importance and difficulty. A lemma is an easily proved claim which is helpful for proving other propositions and theorems, but is usually not particularly interesting in
its own right. A proposition is a statement which is interesting in its own right, while a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma. A corollary is a quick consequence of a proposition or theorem that was proven recently





Write the equation of a line, in general form , that has an slope of zero and a y-intercept of (0, -6).

Answers

Use the slope-intercept form.
y = mx + b,

where m = slope and b = y-intercept.
Your y-intercept is -6, so b = -6.
The slope is zero, so m = 0

y = mx + b

y = 0x + (-6)

y = -6

Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters

Answers

P = 128 meters = 2W + 2L.  We want to maximize the area:  A = L*W

Solve 128 meters = 2W + 2L for either W or L:

64 meters = W + L, so W = 64-L
and subst. your result into 

A = L*W:    A = L*(64-L).  Then A(L) = 64L - L^2.  You could graph this and find the approx value of L at which A(L) is at its max.  

Or, if you know calculus, differentiate A(L) and set the result = to 0.  Solve for L.

L + W = 64, so you can subst. your value for L into this eqn to find W.

How many dozens are there in 22 gross of nails

Answers

One gross is 144 nails. You have to multiply 22 by 144 to see how many nails in total there are: 
22 * 144 = 3168
One dozen has 12 items. So in order to see how many dozens there are, you have to divide 3168 by 12:
3186 / 12 = 264

The correct answer is 264 dozens.

In 22 gross of nails, there are 264 dozens as one gross is equal to 12 dozen.

To find out how many dozens are there in 22 gross of nails, we need to determine the number of dozens in one gross and then multiply it by 22.

One gross is equal to 12 dozen.

So, to find the number of dozens in 22 gross of nails.

we can multiply 12 (number of dozens in one gross) by 22:

12 x 22

= 264

Therefore, there are 264 dozens in 22 gross of nails.

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I keep getting 13. It's supposed to be 3. Can you show me how it's done? 3(a-5) = -6

Answers

First, divide both sides by 3. I think your mistake was that you were multiplying -3. Please note that in order to cancel something out you need to do the reverse operation. The reverse operation of subtraction is addition and the reverse of multiplication is division.

3(a - 5) = -6
a - 5 = -2

Now add 5 to both sides

a - 5 = -2
   +5    +5
a = 3

Hope this helps!
3(a-5) = -6

Start by distributing...

3a - 15 = - 6 

Add 15 to both sides...

3a = 9

Divide both sides by 3 to get a by its self

a = 3

The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop

Answers

  s = 60t - 3t^2 
v = ds/dt = 60 - 6t 

when it comes to rest, v = 0, 
so t = 10 sec 

now distance travelled = time taken x average velocity 
= 10 x (60 + 0)/2 
= 300 ft 

After time  [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

What is time?

" Time is defined as the measurable slot of period in which required action is done."

Formula used

[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]

According to the question,

Position of the car [tex]'s' = 54t - 3t^{2}[/tex]

[tex]'s'[/tex] represents the distance

[tex]'t'[/tex] is the time in seconds

When driver applies break [tex]v= 0[/tex],

[tex]v = \frac{ds}{dt}[/tex]

Calculate the first derivative with respect to time we get,

[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]

As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,

[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]

Hence, after time  [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

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help me solve this, Pre-Calculus Question
I only need the last part

Answers

first do f(a+h)-f(a)
[tex] \frac{5a+5h}{a+h-1} - \frac{5a}{a-1} [/tex]

make the denominators the same and simplify:
[tex] \frac{(5a+5h)(a-1)}{(a+h-1)(a-1)} - \frac{5a(a+h-1)}{(a+h-1)(a-1)} [/tex]

expand: [tex] \frac{5a^2-5a+5ah-5h-(5a^2+5ah-5a)}{(a+h-1)(a-1)} [/tex]
simplify: [tex] \frac{-5h}{(a+h-1)(a-1)} [/tex]

now divide it by h, you have: [tex] \frac{-5}{(a+h-1)(a-1)} [/tex]

[tex]\bf \cfrac{f(a+h)-f(a)}{h}\implies \cfrac{\frac{5a+5h}{a+h-1}~~-~~\frac{5a}{a-1}}{h}\impliedby \stackrel{LCD}{(a+h-1)(a-1)} \\\\\\ \cfrac{\frac{(a-1)(5a+5h)~~-~~(a+h-1)(5a)}{(a+h-1)(a-1)}}{h} \\\\\\ \cfrac{\frac{5a^2+5ah-5a-5h~~-~~(5a^2+5ah-5a)}{(a+h-1)(a-1)}}{h}[/tex]

[tex]\bf \cfrac{\frac{\underline{5a^2+5ah-5a}-5h~~\underline{-5a^2-5ah+5a}}{(a+h-1)(a-1)}}{h}\implies \cfrac{\frac{-5h}{(a+h-1)(a-1)}}{h} \\\\\\ \cfrac{\frac{-5h}{(a+h-1)(a-1)}}{\frac{h}{1}}\implies \cfrac{-5h}{(a+h-1)(a-1)}\cdot \cfrac{1}{h} \\\\\\ \cfrac{-5\underline{h}}{\underline{h}(a+h-1)(a-1)}\implies \cfrac{-5}{(a+h-1)(a-1)}[/tex]
Other Questions
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