The solution to the differential equation dy / dx = 2 · x · y³ · sin x² is equal to - [1 / (2 · y²)] = - cos x² - 3 / 2.
How to solve a separable variable differential equation
In this problem we find a differential equation with separable variables, that is, an ordinary differential equation whose variables can be separated on each side of the equivalence and solved by integrals. First, write the complete expression:
dy / dx = 2 · x · y³ · sin x²
Second, separate the variables:
dy / y³ = 2 · x · sin x² dx
Third, integrate the equation:
∫ dy / y³ = ∫ sin x² · (2 · x) dx
- [1 / (2 · y²)] = - cos x² + C
Fourth, find the value of the constant of integration:
- 1 / 2 = 1 + C
C = - 3 / 2
Fifth, write the solution to the differential equation:
- [1 / (2 · y²)] = - cos x² - 3 / 2
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Two find the point in the solution set for both these functions equation the two functions (f(x)=g(x)) and solve for x. See full process below.
Explanation:
Two find the point in the solution set for both these functions equation the two functions (f(x)=g(x)) and solve for x.
Therefore:
2x−1=−43x+9
We can now solve for x:
2x−1+43x+1=−43x+9+43x+1
2x+43x−1+1=−43x+43x+9+1
2x+43x−0=0+9+1
2x+43x=10
(33×2)x+43x=10
63x+43x=10
103x=10
310×103x=310×10
3
10×103x=310×10
x=3 is the point which lies in the solution set for both functions.
PLEASE HELP DUE TONIGHT
Answer: $1.46 less
Step-by-step explanation:
Lets find how much each bottle is first for Store B, to do that divide 29.10 divided by 15 and you should get 1.94 meaning each bottle of juice is $1.94. Next, lets find how much each bottle costs in store A. You can take any number from the total cost and divide it by the bottles and you should get the same thing. Lets do the first one 2.40 divided by 5 equals 0.48. If you want to check you can multiply 0.48 by any number of bottles and you should get the total cost. Now we have to find how much less Store A costs, to do so we subtract store B (1.94) and store A (0.48) and you should get $1.46.
The sum of three consecutive odd numbers is 39. What is the value of the least number?
Answer: 11
Step-by-step explanation:
The three integers are 11, 13, and 15.
Explanation:We shall consider the integers as x,
(x+2), and (x+4).
The sum of these is 39, so we can write:
x+(x+2)+(x+4)=39
Open the brackets and simplify.
x+x+2+x+4=393x+6=39
Subtract 6 from each side.
3x=33
Divide both sides by 3.
x=11
Therefore:
(x+2)=13
and
(x+4)=15
Suppose you conduct an experiment with 24 subjects and your t-obt turns out to be 2.92, which is statistically significant. Which of the following is the correct way to report your results?
A. t-obt=2.92, p<0.05
B. t(24)=2.92, p<0.05
C. t(23)=2.92, p>0.05
D. t(23)=2.92, p<0.05
The correct way to report the results of this experiment is t(23)=2.92, p<0.05.
Therefore answer is D.
The notation 't(24)=2.92, p<0.05' indicates the degrees of freedom (24), the value of the test statistic (2.92), and the level of significance (p<0.05).
The notation "t(23)" indicates that the t-value was calculated with 24 degrees of freedom, which is the number of subjects minus 1. The level of significance (p<0.05) means that the probability of obtaining a t-value of 2.92 or greater by chance alone is less than 5%. This indicates that the results are statistically significant and unlikely to be due to random chance.
Option A is incomplete because it does not indicate the degrees of freedom. Option B is incorrect because it states that the degrees of freedom is 24. Option C is incorrect because it incorrectly states that the probability is greater than 0.05, which would mean that the results are not statistically significant. Therefore the correct answer is option D.
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Solve for v.
37=-v+182
Explain how you would find the volume of chicken feed that would fill the giant triangular prism structure.
g is a trigonometric function of the form � ( � ) = � cos ( � � + � ) + � g(x)=acos(bx+c)+dg, left parenthesis, x, right parenthesis, equals, a, cosine, left parenthesis, b, x, plus, c, right parenthesis, plus, d. Below is the graph of � ( � ) g(x)g, left parenthesis, x, right parenthesis. The function has a maximum point at ( 3.5 , − 4 ) (3.5,−4)left parenthesis, 3, point, 5, comma, minus, 4, right parenthesis and a minimum point at ( − 1 , − 5 ) (−1,−5)left parenthesis, minus, 1, comma, minus, 5, right parenthesis. Find a formula for � ( � ) g(x)g, left parenthesis, x, right parenthesis. Give an exact expression. � ( � ) = g(x)=g, left parenthesis, x, right parenthesis, equals A graph of a trigonometric wave on an x y coordinate plane. The x axis scales by two and the y axis scales by one. There is a point on the graph at the minimum at (negative one, negative five) and a point on the maximum next to the mentioned point at (three and one half, negative four).
The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.
Describe Function?A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.
From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).
The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.
Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.
Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.
To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.
To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.
Substituting these values into the equation for g(x), we have:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4
Therefore, the exact expression for g(x) is:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.
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Let’s say Bob wants to offer an insurance package to his employees that will cover any outpatient surgery charges, tooth sealants, and glasses. His total annual cost for providing these insurance plans will be $ 5659 per employee for the year. Let’s assume that Schmidt wants to cover his employees’ expenses in case of disability. He also wants to ensure that the family of an employee is provided for in the event of an employee’s loss of life. The total annual cost for providing these insurance plans will be $ 12500 per employee.
His total annual cost for providing these insurance plans will be $ 5, 659 per employee for the year.
The total annual cost for providing these insurance plans will be $ 12, 500 per employee.
How to find the annual cost of insurance ?The annual cost of insurance to Bob for the insurance package that he wants to offer his employees is:
= Health Insurance + Dental Insurance + Vision Insurance
= 5, 179 + 360 + 120
= $ 5, 659
The total cost of the insurance plans per employee would be:
= Life Insurance + Disability insurance
= 9, 500 + 3, 000
= $ 12, 500
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The full question is:
Let's say Bob wants to offer an insurance package to his employees that will cover any outpatient surgery charges, tooth sealants, and glasses. His total annual cost for providing these insurance plans will be $ ____ per employee for the year. Let's assume that Schmidt wants to cover his employees' expenses in case of disability. He also wants to ensure that the family of an employee is provided for in the event of an employee's loss of life. The total annual cost for providing these insurance plans will be $ _____ per employee.
How many coefficients are in the expression 5x³ 2x²2 +6x-4?
There are three coefficients present in the expression: 5 for the x³ ; 2 for the x² and 6 is for x.
Explain about the coefficients?The integer or constant quantity put before a variable is known as a coefficient.
The multiplicative numbers directly preceding a variable, such as x or y, are called coefficients. A quantity in a solution is not regarded as a coefficient if it is not linked to a variable. It is referred to be a constant instead. Decimals, fractions, whole numbers, as well as positive or negative, real or imaginary coefficients are all possible.The coefficient in the expression 5x is 5. The above coefficient is a real, positive whole number.The coefficient for the expression -3y is -3. The above coefficient is a genuine, entire, negative number.Thus, there are three coefficients present in the expression: 5 for the x³ ; 2 for the x² and 6 is for x.
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Complete question-
How many coefficients are in the expression 5x³ + 2x²+6x-4?
DUE TODAY, I WILL MARK BRAINLIEST
screenshot provided!!
Answer:
6% for open side up
14% for closed side up
80% for landing on side
A=3\sqrt[n]{(1,0a)^{3} +(0,0b)^{3} }
The answer is approximately 4.08 But again, it's hard to say for certain without more information about what you're trying to do with this equation
Sure, I'd be happy to help!
The equation you've given is a bit tricky to interpret without more context, but here's my best attempt:
It looks like you're trying to find the value of "A" based on an expression involving some kind of radical, and two terms "a" and "b".
Specifically, it seems like you're taking the cube of two coordinate points (1,0) and (0,b), and then adding those cubes together. Finally, you're taking the nth root of the resulting sum (where "n" is some unspecified number).
So if we plug in some values for "a" and "b", and assume that "n" is equal to, say, 2, we might get something like:
A = 3√[(1,0)^3 + (0,4)^3]
= 3√(1 + 64)
= 3√65
. Let me know if there's anything else I can help with!
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How can you make x the subject in the equation?
The equation solved for the variable x is:
[tex]x = e^{ W(ln(y))}[/tex]
How to make x the subject in the equation?In any equation of the form:
y = f(x), to make x the subject of the equation, we need to isolate x in one of the sides of the equation, then we will get:
x = g(y).
In this case we have:
xˣ = y
And we want to make x the subject of the equation.
We can start by apliying the natural logarithm in both sides to get:
ln(xˣ ) = ln(y)
x*ln(x) = ln(y)
We can rewrite:
[tex]x = e^{ln(x)}[/tex]
Then our equation becomes:
[tex]e^{ln(x)}*ln(x) = ln(y)[/tex]
Now the Lambert W function is defined as:
[tex]W(x*e^x) = x[/tex]
So if we apply this in both sides, we will get:
[tex]W(e^{ln(x)}*ln(x)) = W(ln(y))\\ln(x) = W(ln(y))[/tex]
Now apply the exponential in both sides and get:
[tex]ln(x) = W(ln(y))\\\\e^{ln(x)} = e^{ W(ln(y))}\\x = e^{ W(ln(y))}[/tex]
That is the equation solved for x.
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Complete question:
"How can you make x the subject in the equation? xˣ = y"
negative five and one seven divided by negative two and two fifths
Answer:
Step-by-step explanation:
[tex]-5\frac{1}{7} \div 2\frac{2}{5} =-\frac{36}{7}\div \frac{12}{5}[/tex]
[tex]=-\frac{36}{7} \times \frac{5}{12}[/tex]
[tex]=-\frac{3}{7} \times \frac{5}{1}[/tex] (÷ top and bottom by 12)
[tex]=-\frac{15}{7}[/tex]
[tex]=-2\frac{1}{7}[/tex]
Write the equation of the line through (1, 1) that is perpendicular to 6x + y = −10.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]6x+y=-10\implies y=-6x-10\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -6 \implies \cfrac{-6}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-6} \implies \cfrac{1}{ 6 }}}[/tex]
so we're really looking for the equation of a line whose slope is 1/6 and it passes through (1 , 1)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{6}}(x-\stackrel{x_1}{1}) \\\\\\ y-1=\cfrac{1}{6}x-\cfrac{1}{6}\implies y=\cfrac{1}{6}x-\cfrac{1}{6}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{6}x+\cfrac{5}{6} \end{array}}[/tex]
Why do you need to know the height of a cylinder to figure out its surface area?
Answer:
look in explanation
Step-by-step explanation:
The formula to find the surface area of a cylinder is as follows: SA= (2*π*r*h) + (2*π*r²)
You need to know the height of the cylinder in order to input the number into the equation.
Also, if you are using nets, you need to know the height of the cylinder because you cannot calculate the area of the rectangle part of the cylinder's net without that measurement.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
What is the measure of each numbered angle?
We can use various parallel line properties to solve this problem like corresponding angles, alternate interior-exterior angle, Vertically opposite angle, etc.
What is the measure of each of the numbered angles?
Here are the measure of each angle -
Angle 1 = 76 degrees (By using verically opposite angle property)
Angle 2 = 32 degrees (By using linear property)
Angle 3 = 72 degrees (By using verically opposite angle property)
Angle 4 = 32 degrees (By using linear property)
Angle 5 = 72 degrees (By using alternate interior property)
Angle 6 = 108 degrees
Angle 7 = 72 degrees
Angle 8 = 72 degrees
Angle 9 = 76 degrees
Angle 10 = 76 degrees
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You randomly choose a marble from a bag that contains 10 black marbles
8 red marbles, 4 white marbles, and 6 blue marbles. Match each marble
with the correct probability of selection.
Answer: 10/20, 8/20, 4/20, 6/20
Step-by-step explanation:
Black: 10/20
Red: 8/20
White: 4/20
Blue: 6/20
There are 20 marbles in total the amount of colored marbles is the numerator and the denominator is the total.
Have a lovely day!!
Which equation represents a proportional relationship?
(A) y = 1/5x
(B) y = -5x
(C) y = 5x + 1
(D) y = -5 (x + 1)
___
correct answer gets brainliest
Answer:
y = -5x
Step-by-step explanation:
y = -5x;
[tex]\frac{y}{x}[/tex] = -5;
y:x=-5:1
Please help!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!
Golf Skydiving Fishing 100-yard dash
Drag racing
1. Brainstorm: Which of the above sports do you think the graph could represent? Why?
2. Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?
(Photo of graph is added)
Please!!!!! 30 points added!
Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.
Step-by-step explanation:
The scales of a map is 1 inch to 100 miles. The map is 9 x 12 inches in size. Points A and B are 7 1/2 inches apart. If the distance actually traveled is 11% greater than the distance show on the map, how far would a truck actually travel in going from a to b
Answer: one inch measured the the map represented 100 feet on the ground
Step-by-step explanation:
Adalia spent 1/6 of her money on food, 3/5 of the remaining on transport and 1/12 of what still remained on sweets. If she still had $22.00 left, how much was her money?
Answer:
$132
Step-by-step explanation:
Hope this helps!
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the median of the data.
Building Toy Pieces
180
65
285
370
370
65
124
316
285
129
190
228
To find the median of the data, we need to first arrange the numbers in order from smallest to largest:
65, 65, 124, 129, 180, 190, 228, 285, 285, 316, 370, 370
There are 12 numbers in the sample, so the median will be the middle value. In this case, there are two middle values because there are an even number of data points. To find the median, we take the average of the two middle values:
median = (180 + 190)/2 = 185
So the median number of pieces in the sample of building toys is 185.
Core concept
EXAMPLE 4
Using the Distance Formula
Your school is 4 miles east and 1 mile south of your apartment. A recycling center,
where your class is going on a field trip, is 2 miles east and 3 miles north of your
apartment. Estimate the distance between the recycling center and your school.
The estimated distance between the recycling center and your school is approximately 4.47 miles.
WHAT IS DISTANCE?
Distance is a numerical measurement of the amount of space between two points. In physics, distance is often described as the length of a path traveled by an object from one point to another. Distance is a scalar quantity, which means it has magnitude but not direction. It is typically measured in units such as meters (m), kilometers (km), feet (ft), or miles (mi).
Distance is an important concept in many fields, including physics, mathematics, geography, and engineering. It is used to describe the separation between two objects or locations, and to calculate various quantities such as speed, velocity, and acceleration.
To estimate the distance between the recycling center and your school, we can use the distance formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y) represents the coordinates of your school, (x₂, y₂) represents the coordinates of the recycling center, and the √ symbol denotes the square root.
From the problem statement, we know that:
Your school is 4 miles east and 1 mile south of your apartment. Therefore, the coordinates of your school are (4, -1).
The recycling center is 2 miles east and 3 miles north of your apartment. Therefore, the coordinates of the recycling center are (2, 3).
Substituting these values into the distance formula, we get:
distance = √((2 - 4)²+ (3 - (-1))²)
= √((-2)² + (4)²)
= √(4 + 16)
= √20
≈ 4.47 miles
Therefore, the estimated distance between the recycling center and your school is approximately 4.47 miles.
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University car wash purchased new soap
Answer: University Car Wash purchased new soap dispensing equipment that cost $258,000 including installation. The company estimates that the equipment will have a residual value of $28,500. University Car Wash also estimates it will use the machine for six years or about 12,500 total hours.
Step-by-step explanation:
Please help I need in under 10 min I’ll give brainlyest
Answer
Step-by-step explanation:
what's the question?
if it is 5:00 will the clock show a right angel
Answer:
the clock hands do not form a right angle at 5:00.
Step-by-step explanation:
Help me With this please.
m∠NOP = 90° is the value of angle .
What does a math angle mean?
An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.
A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. The Latin word "angulus," which meaning "corner," is the source of the English term "angle". The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.
m∠NOP = 90° is the value of angle .
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
1/4(2^3 + 4^2) = 6
Step-by-step explanation:
I
Approximate the critical numbers.
List the critical numbers at which each phenomenon occurs. (If an answer does not exist, enter DNE.)
relative maxima X =
relative minima x =
absolute maxima x=
absolute minima x =
The answer of the given question on the listing the critical numbers is the critical numbers as x = 3, 6, and 9. and the function has an absolute maximum at x = 9. and the function has an absolute minimum at x = 2.
What are Absolute maximum?an absolute maximum occurs at the highest point on the graph of a function over its entire domain. It can be a local maximum or a global maximum, depending on whether there are any other points in the domain that have higher function values. Finding the absolute maximum of a function is important in optimization problems, where we want to find the maximum or minimum value of a function subject to certain constraints.
Based on the graph provided, we can approximate the critical numbers as x = 3, 6, and 9.
To determine whether there is relative maximum, relative minimum, absolute maximum, or absolute minimum at each critical number, we need to examine behavior of function near each critical number.
At x = 3, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.
At x = 6, the function has a relative minimum, since the graph changes from decreasing to increasing at that point.
At x = 9, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.
Since the graph increases without bound as x approaches 10 from the left, but approaches a finite value as x approaches 10 from the right, the function has an absolute maximum at x = 9.
Since the graph decreases without bound as x approaches 2 from the right, but approaches a finite value as x approaches 2 from the left, the function has an absolute minimum at x = 2.
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the complete question is attached below.if u help i will aprestait u
Answer:
d is the correct option
Step-by-step explanation:
when powers are raised to powers
they got multiplied
Answer:
Step-by-step explanation:
NOTE:
[tex](x^p)^q=x^{p\times q}[/tex]
As a result of this law the correct solution is (d). )