Answer:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
Step-by-step explanation:
The correct format for the equation given is:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
By the application of the general differential equation:
⇒ Mdx + Ndy = 0
where:
M = 6xy+y²+6y
[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]
and
N = 6x +2y
[tex]\dfrac{\partial N}{\partial x}= 6[/tex]
∴
[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]
f(x) = 1
Now, the integrating factor can be computed as:
[tex]\implies e^{\int fxdx}[/tex]
[tex]\implies e^{\int (1)dx}[/tex]
the integrating factor = [tex]e^x[/tex]
From the given equation:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
Let us multiply the above given equation by the integrating factor:
i.e.
[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]
[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]
[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]
By rearrangement:
[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]
Let assume that:
[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]
and:
[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]
Then:
[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]
[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]
By integration:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
PLS HELP ME ON THIS QUESTION!!!
Answer:
210 in³
Step-by-step explanation:
length = 10 in
Width = 7 in
Height = 3 in
Volume of rectangular prism = length * width * height
= 10 * 7 * 3
= 210 in³
Answer: Option D
210 in³
Volume of Rectangular prism = lwh
Height = 3in
Width = 7in
Length = 10in
Volume = 10(7)(3)
Volume = 210 in³
Must click thanks and mark brainliest
11. solve for x!
please help:(
[tex]\\ \sf\longmapsto 2(4x-1)+3(3-2x)=0[/tex]
[tex]\\ \sf\longmapsto 8x-2+9-6x=0[/tex]
[tex]\\ \sf\longmapsto 8x-6x-2+9=0[/tex]
[tex]\\ \sf\longmapsto 2x+7=0[/tex]
[tex]\\ \sf\longmapsto 2x=-7[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7}{2}[/tex]
find the exact value of the indicated trigonometric functions for the acute angle a:
Given: cot a= 3 3/7, find: cos a and tan a?
Answer:
cot a = 3 3/7
or, cot a = 24/7
or, tan a = 7/24
So,
cos a = 24/25
tan a = 7/24
Answered by GAUTHMATH
The sum of two integers equals twelve, while their product equals thirty-five. Which two numbers are they?
Answer: 5 and 7
Step-by-step explanation:
Given
Sum of the integers is 12
Product of the integers is 35
Suppose the integers are [tex]x[/tex] and [tex]y[/tex]
[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]
[tex]\therefore \text{y can be }7\ or\ 5[/tex]
Hence, the numbers are 5 and 7.
HELP FAST! D: TWENTY POINTS
A group of friends goes Sky diving, using a parachute to fall in a straight line from (1,45) to (3,36). If they keep going in a straight line, at what coordinates will they land on the x-axis?
Answer:
0 =-4.5X +49.5
x = 11
Step-by-step explanation:
x1 y1 x2 y2
1 45 3 36
(Y2-Y1) (36)-(45)= -9 ΔY -9
(X2-X1) (3)-(1)= 2 ΔX 2
slope= -4 1/2
B= 49 1/2
Y =-4.5X +49.5
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the
probability of a tornado is 0.15.
. The number of tornadoes in any calendar year is independent of the number of tornados in any other
calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 19 year period.
Answer:
.441320612
or
44.132%
Step-by-step explanation:
This is binomial
fewer than 3 is equal to p(0)+p(1)+p(2)
[tex]p(0)={19\choose0}*.15^0*(1-.15)^{19}=.045599448\\p(1)={19\choose1}*.15^1*(1-.15)^{18}=.152892268\\p(2)={19\choose2}*.15^2*(1-.15)^{17}=.242828896\\p(0)+p(1)+p(2)=.441320612[/tex]
Identify a transformation of the function f(x) = x by observing the equation of
the function g(x) = VX+3.
Answer:
1st option
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Here g(x) = [tex]\sqrt{x+3}[/tex]
The base graph f(x) has been shifted left 3 units
15) A new BMW decreases in value exponentially after it is purchased. If a new BMW is valued at $55,000 and
depreciate at a rate of 22% a year, what is the value after 4 years? After 8 years)
The values of BMW after 2, 4 and 8 years according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.
Using the parameters given, we define an decreasing exponential function :
[tex]A = A_{0} (1 - r)^{t}[/tex]
Where,
[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount
Value after 2 years :
t = 2
A = 55000(1 - 0.22)²
A = 55000(0.78)²
A = $33,462
Value after 4 years :
t = 4
A = 55000(1 - 0.22)^4
A = 55000(0.78)^4
A = $20,358.28
Value after 8 years :
t = 4
A = 55000(1 - 0.22)^8
A = 55000(0.78)^8
A = $7,535.63
Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.
Learn more about Exponential functions :
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Which function is represented by this graph?
Answer:
it is an absolute function
or more precisely
y = - I x - 1 I + 8 (shown in the screenshot)
Which is the correct answer?
Answer:
a reflection in the y axis followed by a translation 1 unit down
Step-by-step explanation:
Reflection over the y-axis then a unit down
help me to solve tan^3 2x-3tan2x+2=0
Answer:
Step-by-step explanation:
let tan 2x=y
y³-3y+2=0
y³-y-2y+2=0
y(y²-1)-2(y-1)=0
y(y+1)(y-1)-2(y-1)=0
(y-1)[y(y+1)-2]=0
(y-1)(y²+y-2)=0
(y-1)(y²+2y-y-2)=0
(y-1)[y(y+2)-1(y+2)]=0
(y-1)(y+2)(y-1)=0
y=1,1,-2
tan 2x=1=tanπ/4=tan (nπ+π/4)=tan π/4(n+1)
2x=π/4(n+1)
x=π/8(n+1)
where n is an integer.
tan 2x=-2
[tex]2x=tan^{-1}(-2)\\x=\frac{1}{2} tan^{-1}(-2)[/tex]
Apples are cut into 8 pieces to be shared among some children. Twenty-two bags of seven apples are used. How many pieces of apple are cut?
Answer: 1232 pieces
Work Shown:
1 bag = 7 apples
22 bags = 22*7 = 154 apples
So we have 154 apples to work with in total.
Each of those apples is cut into 8 pieces, giving us 8*154 = 1232 pieces
We can write it as one single calculation to say 22*7*8 = 1232
A father is now twice as old as his son. If the sum of their ages ten years ago was fifty two, how old are they today?
Answer:
24 and 48
Today, the son is 24 years old, and the father is 48 years old.
Step-by-step explanation:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
The father is 2 times his son's age.
2x
= 2(24)
= 48
So, the son is 24 and the father is 48.
10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.
Answer:
So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.
Step-by-step explanation:
If the son’s age is x, the father’s age is 2x.
Ten years ago:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
2x = 48
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=6.00, b=7.56, y = 54°
Answer:
c=6.31, a=50.28 degrees, B=75.72 degrees
Step-by-step explanation:
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.
Now, Using the law of cosine, we can write,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]
[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]
c = √39.8297
c = 6.311
Now, using the sine law the ratio of the sides and angles can be written as,
[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]
[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]
α = 50.2775°
[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
β = 75.726°
Hence, the remaining parts of the triangle can be found as shown.
Learn more about Sine Rule here:
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There are 3200 students at Lake High School and 2/5 of these students are sophomores. If 3/8 of the sophomores are opposed to the school forming a crew team and 1/8 of the remaining students (not sophomores) are also opposed to forming a crew team, how many students are in favor of this idea?
Answer:
4
Step-by-step explanation:
2/5*3000 = 1200 seniors
then
3000 - 1200 = 1800 students not seniors
therefore
4/5* 1200 = 960 do not like rock climbing
and
9/10** 1800 = 1620 also do not like it:
"how many students are in favor of this idea?"
subtract the "don't likes" from 3000
3000 - (960+1620) = 420 like rock climbing:
3x-x+2=4
Step-by-step explanation:
here's the answer to your question
Find the number of possible ways one can choose marbles from a bag containing three marbles: a) if the order is important b) if the order is not important.
Answer:
There are 3 marbles, that we assume are different.
Let's define them as marble 1, marble 2, and marble 3.
a) If the order is important, and we select the 3 marbles, then:
for the first marble, we have 3 options.
For the second marble, we have 2 options (because one is already taken)
for the third marble is only one option.
The total number of combinations is equal to the product between the numbers of options, so in this case, we have:
C = 3*2*1 = 6 combinations.
Now, if we only select 2 marbles from the bag, we have:
for the first marble, we have 3 options.
For the second marble, we have 2 options
Here the number of different combinations is:
C = 3*2 = 6 combinations.
And if we select only one marble from the bag, we have:
for the first marble, we have 3 options.
Then here are only 3 combinations.
the total number of combinations is:
C' = 6 + 6 + 3 = 15 different combinations.
b) If the order is not important, then there is only one combination when we draw the 3 marbles.
When we draw one marble there are 3 combinations (one for each marble)
When we draw two marbles, again there are 3 combinations (one for each marble that we do not draw)
then the total number of combinations in this case is:
C = 1 + 3 + 3 = 7
A fruits seller bought some lemon for Re 1 for 15 lemon. if he sold all lemons at 25% profit, how many lemons were sold for Rs 1.
Answer:
12 lemons
Step-by-step explanation:
CP of 15 lemon = ₹ 1
Profit = 25 %
SP of 15 lemons = [tex]\frac{100+profit}{100}*CP[/tex]
[tex]= \frac{125}{100}*1\\\\= \frac{5}{4}[/tex]
SP of 15 lemons = ₹ [tex]\frac{5}{4}[/tex]
Number of lemon for ₹ [tex]\frac{5}{4}[/tex] = 15
Number of lemons for ₹ 1 = 15 ÷ [tex]\frac{5}{4}[/tex]
[tex]= 15 *\frac{4}{5}\\\\= 3*4\\\\= 12[/tex]
Ai đó giúp mình với. Bài này mình không nghĩ ra cách giải
Answer:
-3 -2. 1 0 2 3 -2 3Step-by-step explanation:
please make it a brainliest answer.
what is the probability of choosing a green marble from a jar containing five red, 6 green, and four blue marbles
Answer:
6/15
Step-by-step explanation:
add all the marbles up and you get 15
6 green ones out of 15 marbles
Answer:
2/5
Step-by-step explanation:
6 green+5 red+4 blue = 15 marbles
P(green) = number of green/ total
= 6/15 = 2/5
Please help me out with math will mark like brainlist if answers ASAP
Answer:
13/16
Step-by-step explanation:
To add these two fractions multiply the first fraction by 2 to get equivalent denominators so 6/16+7/16 then add the numerators to get 13/16.
Answer:
13/16
Step-by-step explanation:
3/8 + 7/16
Get a common denominator
3/8*2/2 + 7/16
6/16 + 7/16
13/16
Find the approximate side length of a square game board with an area of 128 in2. HELP PLZ
Answer:
The side length is approximately 11.3 inches
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
128 = s^2
Take the square root of each side
sqrt(128) = sqrt(s^2)
11.3137085= s
The side length is approximately 11.3 inches
Answer:
11.3
Step-by-step explanation:
Formula for square: x^2 = A
Plug in:
x^2 = 128
√x^2 = √128
x = 11.3
Hope this helped.
Lucy's dog sleeps 14 hours a day. What percent of the day does her dog spend sleeping?
Answer:
58.3333
Step-by-step explanation:
make 14/24 into a fraction with a denominator of 100, and you get 58.333333 over 100
Lucy's dog sleeps for 58.3% of the whole day.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Lucy's dog sleeps 14 hours a day, we need to find that how much percent of the total day, her dog sleeps.
We know, there are 24 hours in a day,
Percentage = 14% of 24
= 24x14/100
= 58.3333333333 ≈ 58.3%
Hence, Lucy's dog sleeps for 58.3% of the whole day.
Learn more about percentage,
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HELP ILL GIVE BRAINLIEST
Answer:
linear increasing
Step-by-step explanation:
For the section labeled B, the line goes up as x increases. This means the line is increasing
Answer:
Linear increasing
Step-by-step explanation:
The slope of interval B is constant since it's a straight line, which makes it linear. The line in interval B is pointing upward so it's increasing.
PLS HELP ME RN I AM FAILING AND NEED HELP ITS PYTHAGOREAN THEOREM
Answer:
9.89949 or 9.9
Step-by-step explanation:
7^2 + 7^2 = c^2
49+49=98
square root of 98 = 9.89949
Find the area of this circle. Use 3 for .
A = r2
12 cm
[?] cm2
Answer:
452.16 cm²
Step-by-step explanation:
Given :-
Radius = 12cm .To find :-
Area of circle .Solution :-
As we know that ,
A = πr² A = 3.14 * (12 cm)² A = 3.14 * 144cm² A = 452.16 cm²Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you[/tex]
This two-way frequency table shows the results of a survey of users of the mass-transit system in a city. People were asked their age and whether they used the system regularly (three or more times per week).
Answer:
if Q={1,3,5,7,9}Express it in description methods
Answer: With the condition that age is 30 or under, the sample space is restricted to the first column. This simplifies the problem to:
P(uses mass transit |age is 30 or under) = 125/575=0.217
Step-by-step explanation:
edmentum
Anyone here who can help me with this?
Answer:
D. 16 years old
Step-by-step explanation:
Step 1: Let T be Tien's age and J as Jordan's age (today),
[tex]T=\frac{1}{4}J[/tex]
Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),
[tex]T+2=\frac{1}{3} (J+2)[/tex]
[tex]T=\frac{1}{3}(J+2)-2[/tex]
Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,
[tex]\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16[/tex]
A diameter of a circle is 12 inches. What's the distance when rotate 3 circle ?
Answer:
36π inches which is 113.10 inches to the nearest hundredth
Step-by-step explanation:
The circumference = 12 * π
Rotating 3 times the distance moved is 3 * 12π.
Use the identity property to answer the question.
Answer:
3k + 0 = 3k
Step-by-step explanation:
Identity property of addition states that the sum of 0 and the term would result in the term.
∴ in this case, 3k + 0 will result in 3k.
~
What is the value of the expression below when w=2 and x=2
9w - x
Here, all we need to do is subtitute w = 2 and x = 2 into the expression, by multiplying and adding. First, we will muliply 9w:
9w
9 · w =
9 · 2 =
18
Now, all we have to do is use our answer for 9w, and subtract x from it:
9w - x
18 - (2) =
18 - 2 =
16
So, our answer is 16.
Let me know if you have any other questions! :)
