It looks like the differential equation is
[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]
Factorize the right side by grouping.
[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]
[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]
Now we can separate variables as
[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]
Integrate both sides.
[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]
[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]
[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]
You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
the perimeter of a rectangle is 30cm while it breadth is 5cm find the length of the rectangle
Answer:
10 cm
Step-by-step explanation:
See attached image
Answer:
length = 10 cm
Step-by-step explanation:
Fyi, breadth is a synonym to width.
Since P=30, we must find the length.
l = length
w = width
P=w+w+l+l
30 = 5+5+l+l
30 = 10+2l
-2l = -20
l = 10
Hence, the length is 10 cm.
I need help with question 20
Photo is attached!!!!!! Pleaseeee help!!!
Answer:
1.) ∞
2.) -∞
3.) 0
4.) 0
Step-by-step explanation:
As you approach x = -2 from the left, the "y" values are going to infinity. You never actually get a "y" value that equals x = -2 because of the vertical asymptote.
As you approach x = -2 from the right, the "y" values are going to -infinity. You never actually get a "y" value because there is a vertical asymptote.
As you approach x = 2, both sides converge to y = 0. At this point, there is a smooth, uninterrupted line.
The actual "y" value at x = 2 is 0 because the function goes straight through this point. So, you can just read this point as usual.
2 over 5 of a bag of chips is in the cupboard. you eat 3 over 4 of what is left. how ,uch of the whole bag did you eat?
Answer:
3/10
Step-by-step explanation:
So you have 2/5 left in your cupboard. Say the amount of chips originally in your cupboard would be 30. 2/5 of 30 would be 12.
Then multiply 12 by 3/4 so it would be 3/4 of 12.
The result would be 9
9/30 = 3/10
this is complicated explanation
there are much easier explanations tho
make w the subject of the formula p = 2w+7 divided by 12
Answer:
w = (12p - 7) / 2
Step-by-step explanation:
p = (2w + 7) / 12
12p = 2w + 7
2w = 12p - 7
w = (12p - 7) / 2
Find the surface area of the square pyramid. Enter your answer in the box.
A square pyramid. The side length of the base is 11 centimeters. The height of each of the 4 triangular faces is 10 centimeters.
(answer)_cm²
pls answer A.S.A.P
help I will gave u brilliant answer please help
Answer:
a) 15/8 b) 25/18
Step-by-step explanation:
a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator: [tex]\frac{5+4+6}{8} =\frac{15}{8}[/tex]
Since this can not be simplified any further, your final answer is 15/8.
b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: [tex]\frac{12+3+10}{18} = \frac{25}{18}[/tex]
Since this cannot be simplified further either, your final answer is 25/18.
Hope this helps! :)
Answer:
so to add we need to find lcm
Step-by-step explanation:
a) 5/8 + 1/2+3/4 lcm of 2,4 and 8 = 8
5/8 = 5/8
1x4
2x4 = = 4/8
3x2
4x2 = 6/8
5/8 + 4/8 + 6/8 = 15/8
b) 2/3 + 1/6 + 5/9 lcm of 3 , 6 and 9 = 18
2x6
3x6 = 12/18
1x3
6x3 = 3/18
5x2
9x2 = 10/18
12/18 + 3/18 + 10/18 = 25/18
What is the range of this data set?
{5, 12, 15, 11, 15, 7, 15, 10, 13}
options:
8
10
12
15
Answer: 10 is the range, option B/ option G
Step-by-step explanation: range is the most subtracted by the least, so organize the data set which makes it (5, 7, 10, 11, 12, 13, 15, 15, 15)
15 - 5 is 10.
On a coordinate plane, a curved line crosses the x-axis at (negative 1.5, 0), the y-axis at (0, negative 2), and the x-axis at (1.5, 0).
Determine the domain and range of the given function.
The domain is
all real numbers
.
The range is
.
Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
What is the domain and range of a function?A domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
The curve points are
P₁ ( -1,5 , 0 ) Q ( 0. -2 ) and P₂ ( 1,5 , 0 )
We can see that P₁ and P₂ are symmetric around the y-axis, and point Q looks like a vertex so we can conclude the curve as
ax² + bx + c = y
The curve is a parabola
when x = 0
y = -2
then c = - 2
The equations we get,
a (-1.5)² + b (-1.5) + c = 0
2.25a - 1.5b - 2 = 0
a (1.5)² + b ( 1.5) + c = 0
2.25a + 1.5b -2 = 0
Adding these two equations
4.5a - 4 = 0
a = 4/4.5
The vertex is Q ( 0 , -2 )
x = - b/2a
0 = - b/ 9
b = 0
Therefore the equation of the function :
ax² + c = 0
(4/4.5) x² - 2 = 0
Therefore, Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]
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Answer:
In a shorter explanation of what the guy above me is saying
The domain is all real numbers or A
The range is "all real numbers greater than or equal to –2" or B
Step-by-step explanation:
Which of the following could be the value of x in the equation x^2 - 21 = 100 Choose all the correct answers
How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11
There are a rack of 14 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 14 contain stripes. If one ball is selected at random, determine the odds against it being striped.
Answer:
3/7 / 42.8% chance
Step-by-step explanation:
There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.
(6 / 14 = 3 / 7)
this means that the probability of a ball being striped has the odds of 3/7
(3/7 = about 42.8% chance)
Will Give 50 POINTS If CORRECT
Arrange the steps in order that would be used to algebraically solve a system of linear and quadratic equations.
1) Solve each equation for y.
2) Solve for x.
3) Set the 2 equations equal.
4) Insert x back into an equation to find the y value.
Answer:
3, 2, 4, 1
Step-by-step explanation:
Is this right if not please tell me explanation
Answer:
No, right answer is = 1017.36
Answer:
1017.36
Step-by-step explanation:
All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:
[tex]\pi * 6^{2}*9 = 1017.88[/tex]
instead of
[tex]3.14*6^{2}*9 = 1017.36[/tex]
like you had written above. So the final is actually supposed to be 1017.36
5. Sabrina put $3,000 into a Money Market (high-yield savings)
account with an interest rate of 2.6% compounded quarterly.
a. Write an equation to model the amount in the account over
time.
b. Assuming no deposits or withdrawals are made, how much
money would be in the account after 15 years? Show your
calculation.
c. How would this problem be different if it was compounded
"continuously" instead? Calculate the amount after 15 years.
d. Name 2 or more other situations (other than a savings
account) where you might encounter compound interest later in
your life.
let me answer the last one first
compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.
hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.
hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.
now let's do the others
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]
Which expression would be easier to simplify if you used the associative
property to change the grouping?
Answer:
B
Step-by-step explanation:
Find the value of x. Round to the nearest tenth. X A B 68° 13 x = [?] X Law of Sines; sin A 83° C
Step-by-step explanation:
hope you have a great day
The value of x will be;
⇒ x = 13.9
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now,
Since, We know that;
The sine rule is;
⇒ sin A / a = sin B / b = sin C / c
By given figure, we get;
⇒ sin 83° / x = sin 68° / 13
⇒ sin 83° × 13 / sin 68° = x
⇒ x = 0.99 × 13 / 0.92
⇒ x = 13.9
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what function is increasing at the highest rate
What is the area of the figure below
Answer:
Total Area = 68
Step-by-step explanation:
Comment
There is 1 square at each end.
There are 2 congruent trapezoids in the middle
Draw a 7 inch line across the widest part of the middle
Area of the squares
Area = s^2
s = 3
Area = 3^2
Area = 9
But there are 2 of them 18
Area of the 2 trapezoids
Area = (b1 + b2)*h / 2
b1 = 3
b2 = 7 Notice that 7 was the line you drew
h = 5
Area = (3 + 7)*5/2
Area = 50 / 2
Area = 25
But there are 2 of them 50
Total Area 68
The area of a circle with a diameter of 240
Answer:
in terms of pi: A = 14,400pi
A = 14,400(3.14) is 45,216
Step-by-step explanation:
Area of a circle is pir^2
Radius = diameter / 2
Radius = 240 / 2 which is 120
A = pi(120)^2
A = 14,400pi
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the area of a circle with a diameter of 240.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First of all, we need to find the radius.We can find the radius by dividing the diameter by 2:
[tex]\star~\large\pmb{240\div2=120}[/tex]
The radius is 120. Now it's time to compute the area!
///\\\///\\\///\\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\
Computing The Area
The formula for the area is:
[tex]\star~\large\pmb{Area_{(circle)}=\pi r^2}}[/tex]
See, there's the radius, r; we found a minute ago, and it equals 120 cm.
Now, substitute the value of r into the formula:
[tex]\begin{gathered} \sf{\longmapsto{A=\pi (120)^2} \\ \sf{\longmapsto{A=\pi\times14,400} \\ \sf{\longmapsto{A=45,238.9\;cm^2 \end[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Question 5 of 5
Drag each tile to the correct box. Not all tiles will be used. Consider the recursively defined function below. f(1) = 0.75 f(n) = f(n-1) + 0.35, for n = 2, 3, 4, ...
Create the first five terms of the sequence defined by the given function.
1.8
0.75
2.15
1.0
1.35
1.7
1.1
1.45
Based on the calculations, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
How to create the terms of the sequence?In this exercise, you're required to create the first five (5) terms of the sequence defined by the given function as follows:
For the first term, we have:
f(1) = 0.75
For the second term, we have:
f(2) = f(2-1) + 0.35
f(2) = 0.75 + 0.35
f(2) = 1.1.
For the third term, we have:
f(3) = f(3-1) + 0.35
f(3) = 1.1 + 0.35
f(3) = 1.45.
For the fourth term, we have:
f(4) = f(3-1) + 0.35
f(4) = 1.45 + 0.35
f(4) = 1.80.
For the fifth term, we have:
f(5) = f(3-1) + 0.35
f(5) = 1.80 + 0.35
f(5) = 2.15.
Therefore, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
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Please help on this two questions!!
Two points A and B whose heights differ by 10 metres are shown 1.2 cm apart horizontally on a map whose scale is 1: 10 000. a) Work out the actual horizontal distance between A and B.
Answer:
120 meters
Step-by-step explanation:
1.2 x 10 000 = 12000 cm = 120 meters
Brenda earns $18,200 per year. What’s her semi monthly salary.
Bobby is having a summer barbecue. He is inviting 7 of his friends. He wants to have enough food for everyone to have two hot dogs. How many hot dogs will bobby need to cook for himself and his friends?
Answer:
16
Step-by-step explanation:
7 friends = 14 hotdogs + bobby (2 hotdogs) = 16 hotdogs
Answer:
16 hot dogs
Step-by-step explanation:
since he has 7 friends + himself, we're going to have a total of 8 persons
and since it's expected for each person to have two hot dogs,
total hotdogs Bobby need to cook= 8×2= 16 hot dogs
5. In how many ways can four boys and three girls be seated in a row con taining seven seats ( a ) if they may sit anywhere , ( b ) if the boys and girls must alternate ?
I need two question please
i needs help with it please
Answer:
d. ΔMNO
Step-by-step explanation:
In geometry, two figures are congruent if they are the same shape and size (they can also be a mirror image of each other). If they are the same shape but a different size (e,g, one is an enlargement or reduction of the other), then they are similar.
All the given triangles have the same interior angles, so we need to find a triangle with the same side lengths as ΔABC.
The only triangle that has the same side length as ΔABC is ΔMNO:
they both have bases of 8cm.
Therefore, ΔMNO is congruent to ΔABC.
N(t) = 100,000e−(t − 10)2/8
The secant line can be used to approximate the derivative at a particular point on the graph by placing either the right or the left side of the secant line on that point. (Round your answer to the nearest integer.)
(a) Consider the point on the graph at t = 10 days and set one end of the secant line at this point. Set the other end of the secant line at the point that is 1 day earlier. What is the approximation of the slope of the graph at t = 10 days using this secant line?
(b) Consider again the point on the graph at t = 10 days. Set one end of the secant line at t = 10 days and the other end at the point that is 1 day later. What is the approximation of the slope of the graph at t = 10 days using this secant line?
The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
How to determine the slope of the secant lines?(a) t = 10 days and a day earlier
This means that:
t = 10 and t = 9
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
Calculate N(10)
[tex]N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}[/tex]
Evaluate
N(10) = 100000
Next, calculate N(9)
[tex]N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}[/tex]
Evaluate
N(9) = 88249.6902585
The slope is then calculated using"
[tex]m = \frac{N(10) - N(9)}{10 - 9}[/tex]
This gives
[tex]m = \frac{100000 - 88249.6902585}{10 - 9}[/tex]
Evaluate
m = 11750.3097415
Approximate
m = 11750
(b) t = 10 days and a day later
This means that:
t = 10 and t = 100
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
In (a), we have:
N(10) = 100000
Next, calculate N(11)
[tex]N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}[/tex]
Evaluate
N(11) = 88249.6902585
The slope is then calculated using:
[tex]m = \frac{N(11) - N(10)}{11 - 10}[/tex]
This gives
[tex]m = \frac{88249.6902585 - 100000}{11 - 10}[/tex]
Evaluate
m = -11750.3097415
Approximate
m = -11750
Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
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Which measure of central tendency can be used in finding the average of your grades in a quarter?
Halp me
Me too dum to know pls halp
Answer:
Coordinate pair for Friday (3, 55). This means the length of the eruption was 3 minutes, and the wait time between the eruptions was 55 minutes.
Paulo and Jason wear smaller shoe sizes than Carmen.
Jason and Carmen scored more runs than Paulo.
Step-by-step explanation:
Paulo wears size 5 and Jason wears size 4. Carmen wears size 10, therefore the players wear smaller shoe sizes than he does
Jason scored 10 runs, and Carmen scored 11. Since Paulo only scored 5 runs, the other players scored more than him