The first equation is a first-order nonlinear equation, the second equation is a second-order linear equation, and the third equation is a first-order nonlinear equation.
1. Equation: 12x³y - 7ry' = 4e^y
This equation is a first-order nonlinear equation because it contains the product of the dependent variable y and its derivative y'. Additionally, the presence of the exponential function e^y makes it nonlinear.
2. Equation: 17x³y = -y²x³ dy
This equation is a second-order linear equation. Although it may appear nonlinear due to the presence of y², it is actually linear because the highest power of the dependent variable and its derivatives is 1. It can be rewritten in the form of a linear second-order differential equation: x³y + y²x³ dy = 0.
3. Equation: -3y = 5y³ + 6da + (z + sinθ)
This equation is a first-order nonlinear equation. It contains both the dependent variable y and its derivative da, making it first-order. The presence of the nonlinear term 5y³ and the trigonometric function sinθ further confirms its nonlinearity.
To summarize, the first equation is a first-order nonlinear equation, the second equation is a second-order linear equation, and the third equation is a first-order nonlinear equation.
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helpp!!! i don't understand this
Help pls I don’t understand WILL GIVE BRAINLIEST FOR FIRST ANSWER
Step-by-step explanation:
sin if -7.2 = -0.79 approximately -0.8
Hope you understand and hope this helps.
Good luck ✅.
Sydney purchases a new car for $27,500. The value of the car decreases at rate of 15% each year. In approximately will the $1,254?
Answer:
Time taken n = 19 years (Approx)
Step-by-step explanation:
Given:
Amount of car P = $27,500
Decrease rate r = 15% = 0.15
Final amount A = $1,254
Find:
Time taken n
Computation:
A = P[1-r]ⁿ
1,254 = 27,500[1-0.15]ⁿ
0.0456 = [0.85]ⁿ
Time taken n = 19 years (Approx)
Answer: 5 years
Step-by-step explanation:
the region bounded by and is rotated about the line . using cylindrical shells, set up an integral for the volume of the resulting solid. the limits of integration are:
The volume generated by revolving this region around line x = 3 is 135/2 cubic unit.
Now,
y = 9−x² is an inverted parabola with vertex at (0,9)
It cuts positive x- axis at x = 3
In the region enclosed is rotated about x = 3
Considering the cut with a plane perpendicular to the y axis, we obtain a circular ring with interior radius 3−x and exterior radius 3.
Its area is \(\pi (3^2(3-x)^2)\)
Consider a disk of this area and this height dy. The sum of the volume of all these slices from y = 0 to y = 9 gives the desired volume. The summation is performed by integration.
\(V=\int\limits^9_0 {\pi (3^2(3-x)^2)} \, dx\)
and, y = 9-x²
⇒ dy = -2xdx, where the limits are from 0 to 9.
Now,
\(V=\int\limits^9_0 {\pi (3^2(3-x)^2)} \, (-2xdx)\)
⇒ \(\pi (4x^3-\frac{x^4}{2}\) ) limits are from 0 to 3
⇒ \(\pi (4.3^3-\frac{3^4}{2})\)
= 135/2 cubic unit.
Complete Question:
Consider the region enclosed by the curves y = 9 − x 2 , x = 0, y = 0 in first quadrant. What is the volume generated by revolving this region around line x = 3?
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Zane's cats love tuna fish, so he always mixes a little into their food at dinnertime. For his small cat, he adds 2 ounces of tuna fish to 10 ounces of cat food. For his large cat, he adds 3 ounces of tuna fish to 12 ounces of cat food. Which cat's meal tastes more like tuna fish?
Large cat's meal tastes more like tuna fish
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Zane's cat loves tuna fish
so he adds 2 ounces of tuna fish to 10 ounces of cat food for small cat
and he adds 3 ounces of tuna fish to 12 ounces of cat food for large cat
to know whose meal tastes as tuna fish calculate their percentages
for small cat 2% is added to 10%
that means (2/12)*100=16.6
for large cat 3% is added to 12%
that means (3/15)*100=20
by this we can conclude that, large cat's meal tastes more like tuna fish
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Please help ASAP it’s a alrightveasy question
Answer:
57 here ahgy allsoe fhal
Answer:
1330.5
Step-by-step explanation:
The equation for volume of a cylinder is:
\(V=r^{2} h\)
Now, we have to input our values
\(V = 5.5^{2} (14)\)
And solve!
\(5.5^{2} = 30.25\)
30.25 × 14 = 1330.46
Finally we have to round to the 1 decimal place
1330.46 = 1330.5
(Wondering why I used 5.5 instead of 11 for the radius? Well, the radius of a circle/cylinder is from the center point to the end so 11/2 = 5.5)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
URGENT, pls answerr!!
Answer:
15/16
Step-by-step explanation:
In a dice, there are 3 even and 3 odd numbers.
So, to calculate the required probability, we will have to calculate the probability of getting an odd number in all of them.
Probability of getting odd number in 1 dice = 3/6 = 1/2
Probability of getting odd number in 4 dice =
1/2 x 1/2 x 1/2 x 1/2 = 1/16
Therefore, probability of getting atleast one even number is 1 - 1/16 = 15/16
15/16 is the answer.
Pls mark as brainliest. Cheers
Find the area of quadrilateral ABCD and RST.
Answer:
ABCD is 6 units 2×3=6
im not really sure about RST but i think it would be 4 or 5 units because it just looks like there is about that many inside.
We can see here that the area of quadrilateral ABCD = 12 units².
While the area for triangle RST = 5 units².
What is quadrilateral ?A quadrilateral is a polygon with four sides, four vertices, and four angles. The word "quadrilateral" is derived from the Latin words "quadri" (meaning "four") and "latus" (meaning "side"). Quadrilaterals are classified based on the lengths of their sides, the measures of their angles, and other specific properties.
Area of the parallelogram ABCD = B × H = 3 units × 4 units = 12 units².
Area of the triangle RST = 1/2bh = 1/2 × 5 units × 2 units = 1/2 × 10 units = 10/2 units = 5 units².
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calculate the value of 1/3 a = -5
Answer:
- 15
Step-by-step explanation:
\( \frac{1}{3} a = - 5 \\ \\ a = - 5 \times 3 \\ \\ a = - 15\)
Answer:
-15
Step-by-step explanation:
As you can see, the denominator of 1/3 is 3. 1 third of a is -5. So what you do is, you multiply -5 * 3 and that'll give you -15. So, it is equal to -15.
(4 points) 1. Suppose \( f(x) \) is a quadratic function with zeros at \( x=3,9 \) and goes through the point \( (1,32 \) ). Write the equation for this function. \[ f(x)= \] 2. Suppose \( f(x) \) is
Given the quadratic function has zeros at `x = 3` and `x = 9`, we can write the function in factored form as:\(\[f(x) = a(x - 3)(x - 9)\]\) where `a` is a constant.
Since the function goes through the point `(1, 32)`, we can use this to solve for `a`. Plugging in `\(x = 1` and `f(x) = 32`\), we get:\([32 = a(1 - 3)(1 - 9) = -16a\] , `a = -2`.\)
Substituting this back into the factored form, we get:\(\[f(x) = -2(x - 3)(x - 9)\]\)Expanding this gives the equation for the quadratic function: \[f(x) = -2x^2 + 24x - 54\]2.
Since `f(x)` is a quadratic function, it can be written in the form: \[f(x) = ax^2 + bx + c\]We know that `f(-1) = -2`, `f(0) = -1`, and `f(1) = 0`.
Using this information, we can write three equations in terms of `a`, `b`, and `c`:\(\[a(-1)^2 + b(-1) + c = -2\]\)\\([a(0)^2 + b(0) + c = -1\]\)Simplifying each equation, \(\[f(x) = a(x - 3)(x - 9)\]\)
we get:\[a - b + c = -2\]\[c = -1\]\[a + b + c = 0\] Substituting `c = -1` into the first and third equations gives a system of two equations in two variables:\[a - b - 1 = -2 \ Rightarrow a - b = -1\]\[a + b - 1 = 0 \ Rightarrow a + b = 1\] Solving this system of equations, we get `a = 1` and `b = 0`.
the quadratic function is:\[f(x) = x^2 - 1\]
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If 1=3
2=3
3=5
4=4
5=4
Then, 6=?
Then 6 = 7.
What is a sequence ?
"Sequence and series is one of the basic topics in Arithmetic. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements. An arithmetic progression is one of the common examples of sequence and series.
In short, a sequence is a list of items/objects which have been arranged in a sequential way."
1 = 3
2=3
3=5 ( +2)
4=4
5=4
6= 7
7=5
8=5
9= 7
10= 6
Hence, 6 = 7 in the sequential way.
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A vet recommends using a
dog's food from 8 oz to 6 oz
per feeding. What is the
percent decrease in food per
feeding?
Please help and show work, will give lots of points!
Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read 3/5 of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
y = []x + []
(Use above format to write the equation.)
What does the y-intercept of this linear equation represent?
A. Pages already read
B. Pages in book
C. Pages read each day
D. Days to finish
Answer:
The linear equation is y = 450 - 30 x, where y is the number of pages
Lourdes has left to read after x days
Step-by-step explanation:
Each day, Lourdes reads 30 pages of a 450-page book
- We need to write a linear equation to represent the number of pages
Lourdes has left to read after x days
∵ Lourdes reads 30 pages each day
∵ Lourdes will read for x days
∴ The number of pages Lourdes will read in x day = 30 x
- The left pages will be the difference between the total pages of the
book and the pages Lourdes read
∵ The book has 450 pages
∵ Loured will read 30 x in x days
∴ The number of pages left = 450 - 30 x
- Assume that y represents the number of pages Lourdes has left
to read after x days
∴ y = 450 - 30 x
The linear equation is y = 450 - 30 x, where y is the number of
pages Lourdes has left to read after x days
HELPPPPPPPPPP Lol thankd
Answer:
6 10
Step-by-step explanation:
Answer:
6, 10
Step-by-step explanation:
The first point is on 6, and ending at 10.
please help asap!!!!
Answer:
142 cm
Step-by-step explanation:
7*5 + 7*5 + 3*5 + 3*5 + 7*3 + 7*3
=> 35 + 35 + 15 + 15 + 21 + 21
=> 70 + 30 + 42
=> 100 + 42
=> 142
Help me plssssssssssssssssssss
Can two obtuse angles be supplementary
Answer:
no,
Step-by-step explanation:
two numbers have to equal 180 degrees. The biggest numbers can only be 90+90 and that is a right angle.
Find the measure of each numbered angle
Answer:
m∠1 = 54° m∠2 = 63° m∠3 = 117°
Step-by-step explanation:
We know that 117 + m∠2 = 180°, which when calculated is equal to 63. Now, we know that 63 + 63 + m∠1 = 180°. This comes out to be 54°. Finally, we know that m∠3 has to equal 117° because they are same side interior angles.
The measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively
The sum of angle in a straight line is 180 degrees, hence:
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63 degrees
For the diagram, m<2 - m<3 = 63 degrees (alternate angle.)
Also, the sum of interior angle of the triangle is 180 degrees, hence:
m<2 + m<2 + m<1 = 180
63 + 63 + m<1 = 180
126 + m<1 = 180
m<1 = 180 -126
m<1 = 54degrees
Hence the measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively
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I need some help with this, can someone help me?
Answer:
D. Paul can type 3/4 as fast as Jennifer
Step-by-step explanation:
60/80 = 3/4
Solve system of equations (no solution, one solution, or infinitely many solutions) show work.
Y=5x
2x+3y=34
Answer:
x=2 and y=10
Step-by-step explanation:
Substitute 5 x for y in 2x+3y=34
2x+3y=34
2x+35x=34
17x=34
17x/17=34/17
x=2
Substitute 2 for x in y=5x
y=5x
y=(5)(2)
y=10
x=2 and y=10
Answer: x=2
y=10
I hope tht helped ...
Step-by-step explanation:
What is wrong with the following proof that for every integer n, there is an integer k such that n < k < n+2? suppose n is an arbitrary integer. therefore k = n + 1.
The proof fails to demonstrate that there is an integer k such that n < k < n+2.
The proof you provided is incorrect. Let's analyze the statement and the proof:
Statement: For every integer n, there is an integer k such that n < k < n+2.
Proof (incorrect):
Suppose n is an arbitrary integer.
Therefore, k = n + 1.
The error in the proof lies in step 2. While it is true that k = n + 1 is an integer, it does not necessarily satisfy the condition that n < k < n+2. In fact, if we substitute k = n + 1 into the inequality, we get:
n < n + 1 < n + 2
This simplifies to:
n < n + 1 < n + 2
The inequality is not satisfied since n + 1 is not guaranteed to be less than n + 2. Therefore, the proof fails to demonstrate that there is an integer k such that n < k < n+2.
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tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues to move 1 unit east and 3 units north twelve more times, placing a pin each time. Where will the last pin be placed?
Tomas's last pin on the graph will be placed at (16, 36)
Understanding and Reading graphs:Graphs are used In every aspect of daily life, including weather forecasts, stock market trends, and company reports. They provide data or relationships between variables in a visual manner.
Reading both axes and comprehending what they represent is the first step. The values of the points located along the graph's lines are analyzed in the following phase.
To comprehend the trend of data changes, the rise and fall of the lines are closely watched.
Here we have
Tamas is at (3, 0) intially
He moves 1 unit toward the east and 3 units toward the north
If we observe the pattern,
Tamas moves 1 unit to the East for each move
Initially, he is at 3
After 1st move, he is at 4
He continued like this and moved 12 more times i.e 13 moves
On continuing the above pattern After 13 moves, he will be at 13 +1(3) = 16
Tamas moves 3 units to the North for each move
Initially, he is at 0
After 1st move, he is at 3
After 2nd move, he is at 6
He continued like this and moved 12 more times i.e 13 moves
On continuing the above pattern After 13 moves,
he will be at 13(3) = 36
From the observation, we can conclude that
Tomas's last pin be placed at (16, 36)
Therefore,
Tomas's last pin on the graph will be placed at (16, 36)
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What’s the surface. area
Answer:
138.61 square centimeter
(Please tell me if I'm wrong)
Two-fifths of a gallon
of deck stain covers
one quarter of a deck.
How much stain is
needed for the entire
deck?
Answer:
8 / 5
Step-by-step explanation:
Since 2/5 gallons cover 1/4 of the deck you would have to multiply 2/5 times 4 to so how much it would take to cover the whole deck so your answer is 8/5 gallons
Answer quicklyy please
Answer:
B
Step-by-step explanation:
Because to have the problem fully divided she would have to subtract 40 once more time to get 1 as a remainder.
Hopes This Helps :)
Help I need to find area and it’s due by 8
Answer:
20 1/2
Step-by-step explanation:
because area equals length times width
Answer and Step-by-step explanation:
First, let's split the figure into two common shapes that we know the area formula for.
The top shape can become a triangle, while the bottom shape can become a rectangle.
We know the area of a triangle is
\(A = \frac{bh}{2}\)
and the area of a rectangle is
A = lw
Where:
A = Area
b = Base length (length)
h = Height
l = Longer length of a side
w = Smaller length of a side
Area of a Triangle:
b = 3
h = 3
A = \(\frac{3 * 3}{2}\)
A = 4.5
Area of a Rectangle:
w = 3
l = 8
A = 3 × 8
A = 24
Now we add together the areas to get the area of the figure.
Area of the Figure:
A = 4.5 + 24
A = 28.5
The area of the figure is 28.5 \(units^{2}\).
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5 of 8
What single percentage change is equivalent to a 11% increase followed by a 13% increase?
Answer:
25.43
Step-by-step explanation:
Correct trust me!
When you are analyzing the relationship between two continuous variables, how should you plot the data?.
Answer:
Scatterplot.
Step-by-step explanation:
Scatterplots help in analyzing the relationship between two continuous variables
4/2n+5/3c=1
Solve for c.
-Multiply both sides by (blank) to clear fractions.
Answer:
We conclude that:
\(c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2\)
Step-by-step explanation:
Given the expression
\(\frac{4}{2n}+\frac{5}{3c}=1\)
Let us solve for 'c'
\(\frac{4}{2n}+\frac{5}{3c}=1\)
Least Common Multiplier of 2n, 3c: 6nc
Now multiply both sides by LCM = 6nc
\(\frac{4}{2n}\cdot \:6nc+\frac{5}{3c}\cdot \:6nc=1\cdot \:6nc\)
Simplify
\(12c+10n=6nc\)
Subtract 10n from both sides
\(12c+10n-10n=6nc-10n\)
Simplify
\(12c=6nc-10n\)
Subtract 6nc from both sides
\(12c-6nc=6nc-10n-6nc\)
Simplify
\(12c-6nc=-10n\)
Factor 12c - 6nc = 6c(2-n)
\(6c\left(2-n\right)=-10n\)
Divide both sides by 6(2-n); n≠2
\(\frac{6c\left(2-n\right)}{6\left(2-n\right)}=\frac{-10n}{6\left(2-n\right)};\quad \:n\ne \:2\)
simplify
\(c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2\)
Therefore, we conclude that:
\(c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2\)
Select which of the following are surds
A) √17 B) √36 C) √100 D) √15 E) √30
\(\sqrt{17}\), \(\sqrt{15}\) and \(\sqrt{30}\) are surds among the given options.
According to the question,
We have the following information:
A) √17 B) √36 C) √100 D) √15 E) √30
Now, among these options we have to find which of them is a surd.
We know that surds are defined as numbers which can not expressed as rational numbers or in the form of p/q where q should not be equal to 0.
In this case, 6 is the perfect square root of \(\sqrt{36}\). So, it can not be classified as a surd.
10 is the perfect square root of \(\sqrt{100}\). So, it can also be expressed as a rational number.
However, among these 5 options \(\sqrt{17}\) can not be expressed as a perfect square root of any number. So, it is a surd.
\(\sqrt{15}\) and \(\sqrt{30}\) also can not be expressed as a rational number.
Hence, the correct options are A, D and E.
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