Answer:
Step-by-step explanation:
General form of the linear differential equation can be written as:
[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]
For this case, we can rewrite the equation as:
[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]
Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]
To find the solution (y(x)), we can use the integration factor method:
[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]
Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]
So, we can find:
[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]
Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:
[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]
To check our solution is right or not, put your y(x) back to the ODE:
[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]
[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]
[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]
(it means your solution is right)
Help with tthis photo pls T.T
Answer:
1. False
2. Not sure
3. True
Statement A
A = bh/2
34 = (10)h/2
68/10 = h
h = 6.8
FALSE The actual height of the triangle is the hypotenuse of the fake outer triangle. 6.8 is not used to calculate the area.
Statement B
A = (d1 + d2)/2
56 = (d1 + d2)/2
112 = d1 + d2
I have no idea for this one. There is no way that I know of to verify the area if I don't have at least one diagonal.
Statement C
A = (a + b)(h)/2
24 = (7 + 9)(3)/2
48 = (7 + 9)(3)
16 = 7 + 9
16 = 16
TRUE Area of the trapezoid = 24 in².
Pls help asap, have a great day
find, w: x: y: z:
Answer:
See below ↓
Step-by-step explanation:
Finding w and x [both are equal]
Take the cos function of one of the 45° angles, which is the ratio of the adjacent side to the hypotenusecos(45°) = [tex]\frac{1}{\sqrt{2} } = \frac{w}{6}[/tex]⇒ w = [tex]\frac{6}{\sqrt{2} } = \frac{6}{\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} } = \frac{6\sqrt{2} }{2}[/tex]⇒ w = 3√2 and x = 3√2Finding y
Take the cos ratio of the 60° angle to find ycos(60°) = [tex]\frac{1}{2} = \frac{y}{x} = \frac{y}{3\sqrt{2} }[/tex]⇒ y = [tex]\frac{3\sqrt{2} }{2}[/tex]Finding z
Take the sin ratio of 60° angle of the triangle, which is the ratio of the opposite side to the hypotenusesin(60°) = [tex]\frac{\sqrt{3} }{2}= \frac{z}{x} = \frac{z}{3\sqrt{2} }[/tex]⇒ z = [tex]\frac{3\sqrt{6} }{2}[/tex]what are two variables that might be positively related to academic success?
A spherical balloon has a 16-in diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon
c. What is the radius of the half-inflated balloon?
Answer:
a. 2144.66 cubic inches
b.1072.33 cubic inches.
c. 16 inches
Step-by-step explanation:
hello, to answer this question we have to calculate the volume of sphere:
Volume of sphere: 4/3 π r³
Since diameter (d) = 2 radius (r)
Replacing with the value given:
16 =2r
16/2=r
r= 8 in
Back with the volume formula:
V = 4/3 π r³
V =4/3 π (8)³
V = 2144.66 cubic inches
The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.
2144.66/2 = 1072.33 cubic inches.
To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=1072.33
1072.33 = 4/3 π r³
Solving for r
1072.33 / (4/3 π)= r³
256= r³
16 = r
r = 16 inches
Classify each of the following lines as parallel, transversal or perpendicular.
Answer:
5. Perpendicular
6. Parallel
7. Transversal
8. Perpendicular
9. Parallel
10.Transversal
Step-by-step explanation:
Mr. Sanchez’s class sold fruit pies for $1.73 each and Mr. Kelly’s class sold bottles of fruit juice for $1.44 each. Together, the classes sold 83 items and earned $130.83 for their school. Write and solve a system of equations that models this problem.
The system of equation that models the problem is as follows;
x + y = 83
1.73x + 1.44y = 130.83
The number of fruit pies sold is 44 and the number of fruit juice sold is 39.
How to solve a system of equation that models a problem?
Mr Sanchez class sold fruit pies for $1.73 each and Mr Kelly's class sold bottles of fruit juice for $1.44 each.
Therefore,
let
x = number of fruit pies sold
y = number of fruit juice sold
Together, the class sold 83 items. Therefore,
x + y = 83
They sold a total of $130.83. Therefore,
1.73x + 1.44y = 130.83
x + y = 83
1.73x + 1.44y = 130.83
1.73x + 1.73x = 143.59
1.73x + 1.44y = 130.83
0.29x = 12.76
x = 12.76 / 0.29
x = 44
Therefore,
y = 83 - 44
y = 39
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=8600(0.11)^x
The function represents a decay of 88.97% per unit increase in x.
What is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
The exponential function can be written in the form of y = [tex]ab^{x}[/tex], where:
a is the initial value or the value of the function when x = 0
b is the base or the factor by which the function changes for each unit increase in x
Comparing this form to the given function, we can see that:
a = 8600
b = 0.11
To determine whether the function represents growth or decay, we need to consider the value of the base (b). If the base is greater than 1, then the function represents growth, and if the base is between 0 and 1, then the function represents decay.
In this case, the base (0.11) is between 0 and 1, so the function represents decay.
To determine the percentage rate of decrease, we can use the formula:
Percentage change = (new value - old value) / old value * 100%
Since the function represents decay, the old value is the initial value (a = 8600) and the new value is the value of the function when x = 1:
y(1) = 8600(0.11)¹ = 946
Plugging in these values, we get:
Percentage change = (946 - 8600) / 8600 * 100% = -88.97%
Therefore, the function represents a decay of 88.97% per unit increase in x.
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For each pair of similar figures, find the ratio of the area of the first figure to the area of the second.
answer:
[tex]\frac{4}{9}[/tex]
explanation:
the area of the larger square is 36 (6*6), and the area of the smaller square is 16 (4*4). to find the ratio of the area, simply just put 16 over 36 and simplify.
[tex]\frac{16}{36} = \frac{4}{9}[/tex]
--
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Help plsss its an emergency
Answer:
-8.05E14
Step-by-step explanation:
If you arent familiar with E notation it means the same thing as [tex]10^x[/tex] where x is the number proceeding the E
3. Evaluate the following:
a.) What value of Syields the coordinate point (1, 3)?
b.) What value of Syields the coordinate point (3, 1)?
c.) x(710)=
d.) y(V10+ V5)= = B С
e.) x(2)=
f.) y(2.5)=
Answer: See below
Step-by-step explanation:
Question 3:
[tex]a) \ $S=1$ \ yields \ $(1,3)$ \\ \\b) \ $S=3$ \ yields \ $(3,1)$ \\ \\ c) \ $x(\sqrt{10})=\sqrt{10}$ \\ \\d) $y(\sqrt{10}+\sqrt{5})=1$ \\ \\e) $x(2)=2$ \\ \\f) $y(2,5)=1$ \\[/tex]
Challenge:
[tex]\begin{aligned}&x(s)=s \quad ,s \in[0,4] \\&y(s)=\left\{\begin{array}{cc}3 s & , s \in[0,1] \\5-2 s &, s \in[1,2] \\1 & s \in[2,4]\end{array}\right.\end{aligned}[/tex]
A mechanic charges his customers $45 for every hour he works. He also charges the cost of parts.
For one job, he works 4.5 hours, and the parts cost $118. What is the total amount of money he
charges for the job?
How many seconds is 3.25 hours
Answer:
a total of 11700 senconds are on 3.25 hours
) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b.
[tex]f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -\dfrac{150}{50}\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\dfrac{27}9\\\\\implies b = -3[/tex]
Which of the numbers listed below are solutions to the equation? Check all
that apply.
x² = -64
O
A. -8
O
B. -64
0 C. 8
1
D. -4
u
E. 64
F. None of these
Answer:
F. None of these
Step-by-step explanation:
A number can never be negative when squared unless an imaginary number is involved. Since none of the answers involve i, the answer must be F. None of these.
PLEASE HELP!! TRYING TO PREPARE FOR A TEST!! TOTAL 50 POINTS WHEN GIVEN BRAINLIEST ANSWER!!
Change the Cartesian integral to an equivalent polar integral, and then evaluate.
∫₋₁₁¹¹ ∫₀√⁽¹²¹⁻ˣ²⁾ dy dx
\int\limits^{11}_{-11} \int\limits^{\sqrt{121-x^{2}} } _{0} dy dx
It looks like the starting integral is
[tex]\displaystyle \int_{-11}^{11} \int_0^{\sqrt{121-x^2}} dy\,dx[/tex]
The key is recognizing the domain of integration as the semicircle centered at the origin with radius 11. In polar coordinates, this integral transforms to
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{11} r \, dr \, d\theta}[/tex]
Jessica needs 658 cups of flour for her recipe. The box she has only has 78 cup of flour left in it.
How many more cups of flour does she need?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
5 3/4 cups.
Step-by-step explanation:
Subtract the two amounts.
6 5/8 - 7/8
Make 6 5/8 an improper fraction by multiplying the 8 and 6 then adding 5.
8 x 6 = 48
48 + 5 = 53
53/8
53/8 - 7/8 = 46/8
Convert back into a mixed number by dividing.
46/8 = 5 6/8
reduce the fraction
5 3/4
You pick a card at random
1) What is P(3)? ?
Answer:
probability=events over the sample space
Step-by-step explanation:
The domain of a function g(x) is x< 2. and the range is y > 0. What range the domain and range of its inverse function, g[tex]g^-1[/tex](x)?
Answer: the answer is b
Step-by-step explanation:
Domain and ranges of inverse functions are swapped.
Domain of the original is the range of the inverse and vice versa.
CAN SOMEONE HELP ME PLEASE
Answer:
the answer is -4
Step-by-step explanation:
you take the points (0,6) and (4,-10), then you subtract -10 by 6 and you get -16. then you take 4 subtracted by 0 and you get 4. -16 divided by 4 is -4.
|x+3/4|= 5 6/7 please help with this question from 6.2 russian mathemetics school
Answer:
143/28 or -185/28
Step-by-step explanation:
Negative case
-(x+3/4))=(41/7)
-x-(3/4)=(41/7)
-x=(185/28)
x=-(185/28)
Positive case
(x+(3/4))=(41/7)
x=(143/28)
lol this was easy r u sure its 6 grade?
Answer:
143/28 or -185/28
Toni is 30 inches less than twice Jordan's height. Toni is 66 inches tall. How tall is Jordan?
Answer:
96 inches
Step-by-step explanation:
66 + 30 = 96
The area of the circle
Answer:
The answer would be 201.06
Step-by-step explanation:1. You need to have the radius and not the diameter so you would divide 16 by 2 to get 8.
2. You would plug 8 into the formula A=π[tex]r^{2}[/tex], meaning it would be A=π[tex]8^{2}[/tex]
3. 8 Squared is equal to 64 so the formula would now be A=π64
4. 64 x π = 201.06 giving you your final answer.
I hope that helps!
Answer:
200.96 mi²
Step-by-step explanation:
Before, finding the area of the circle, first, let us find the radius.
Given that,
diameter ( d ) ⇒ 16 mi
Let us use the below formula to find the radius of the circle.
d = 2r
16 = 2r
Divide both sides by 2.
8 mi = r
And let us find the area of the circle using the below formula.
A = π r²
A = π × 8 × 8
A = 3.14 × 64
A = 200.96 mi²
7
.
Marisela wants to create a trophy in the shape of a rectangular
pyramid with volume 0.1875 cubic foot. Complete the descriptions
by writing in the missing measurements. 7.6.6
Design #1: pyramid height = 1.5 ft; base width = 0.75 ft;
Answer:
Volume of a rectangular pyramid:
[tex]V=\dfrac13lwh[/tex]
where:
[tex]V[/tex] = volume[tex]l[/tex] = length of base[tex]w[/tex] = width of base[tex]h[/tex] = heightGiven:
[tex]V[/tex] = 0.1875 ft³[tex]w[/tex] = 0.75 ft[tex]h[/tex] = 1.5 ftSubstitute given values into the formula and solve for [tex]l[/tex]:
[tex]\implies 0.1875=\dfrac13 \cdot l \cdot 0.75 \cdot 1.5[/tex]
[tex]\implies 0.1875=\dfrac{1.125}{3} l[/tex]
[tex]\implies 0.1875=0.375 l[/tex]
[tex]\implies l=\dfrac{0.1875}{0.375}[/tex]
[tex]\implies l=0.5[/tex]
Therefore, the base length is 0.5 ft
Solve the following equation
X = 2x+8/x
Answer:
2i*sqrt(2), -2i*sqrt(2).
Step-by-step explanation:
x=2x+8/x
x-2x=8/x
-x=8/x
8=-x(x)
8=-x^2
8-(-x^2)=0
8+x^2=0
x^2+8=0
x=2i*sqrt(2), -2i*sqrt(2).
Step-by-step explanation:
[tex]x = \frac{2x + 8}{x} [/tex]
[tex] {x}^{2} = 2x + 8[/tex]
[tex] {x}^{2} - 2x - 8 = 0[/tex]
[tex](x - 4)(x + 2) = 0[/tex]
[tex]x = 4[/tex]
or
[tex]x = - 2[/tex]
AYUDAAA PORFA , se entrega a las 4 porfavorrrrrr
What is the distance between points A and B?
0-6 units
-1 units
O 5 units
O6 units
Step-by-step explanation:
d 6 units .................
The distance between the points A and B is given by D = 6 units
What is the distance between two points?Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )
The distance from A to B is the same as the distance from B to A
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane
Given data ,
Let the distance between 2 points be represented as D
Now , let the first point be P ( -5 , 0 )
Let the second point be Q ( 1 , 0 )
Now , distance D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
On simplifying , we get
D = √ ( -5 - 1 )² + ( 0 )²
D = √ ( 6 )²
D = 6 units
Hence , the distance is 6 units
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Select the correct answer.
What are the roots of this quadratic equation?
help
Answer:
A
Step-by-step explanation:
I took the test it was right
When a certain number is divided by 20, the result is same when number is decreased by 361. What is the number?
Answer:
The number is 380
Step-by-step explanation:
Let the number be 'x'
[tex]\sf \dfrac{x}{20}=x-361\\\\\text{multiply the entire equation by 20}\\\\20*\dfrac{x}{20}=20*(x-361)[/tex]
x = 20x - 20*361
x = 20x - 7220
Now subtract '02x' from both sides
x - 20x = -7220
-19x =-7220
Divide both sides by (-19)
x = (-7220) ÷ (-19)
x = 380
A bag of balloons contains 4 red balloons, 11 green balloons, 15 yellow balloons, and 8 orange balloons. What is the probability that
a randomly selected balloon would be green or orange?
Answer:
There is motlre chance that a green Ballon will be selected because green Ballon are more than orange
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3.
On = 31/2,w=
- 3/2
On - 3√2, w = 3/2
Oh = 12, w = 312
W
Oh=312. W = 2
The dimensions to maximize the area must be:
length = (√3)/2width = (√3)/2How to get the dimensions of the rectangle?The rectangle with the largest area that can be inscribed on a circle of radius 3, will be a rectangle whose diagonal is equal to the diameter of the circle, so we have:
√(x + y) = 6 units.
Where x and y are the dimensions of the rectangle. We also must have that:
x < 6 unitsy < 6 units.Now, because we have limits, the largest area (which is the product of x and y) happens when x and y have the same value x = y, then we have:
√(x + x) = 6 units.
√(2x) = 6 units.
x = (√3)/2 = y
So the rectangle is actually a square of side length = (√3)/2
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