The evaluated double integral is (ln(2)) * (2 * e^3 - 1).
To evaluate the double integral of (x * e^x) / y over the region R = [0, 3] x [1, 2], follow these steps:
1. Set up the double integral: ∬(x * e^x) / y dA, where dA = dy dx (since the region is given in terms of x and y).
2. Integrate with respect to y first: ∫(∫(x * e^x) / y dy) dx. The limits for y are from 1 to 2.
3. Calculate the inner integral:
∫(x * e^x * (ln(y))) | from y=1 to y=2 dx.
4. Substitute the limits for y:
∫(x * e^x * (ln(2) - ln(1))) dx.
5. Simplify the expression:
∫(x * e^x * ln(2)) dx, with limits for x from 0 to 3.
6. Integrate with respect to x:
(ln(2)) * (∫x * e^x dx), from x=0 to x=3.
7. Use integration by parts for ∫x * e^x dx, with u=x and dv=e^x dx:
du = dx and v = e^x.
8. Apply integration by parts formula:
uv - ∫v du = x * e^x - ∫e^x dx.
9. Integrate the remaining term:
x * e^x - e^x, evaluated from x=0 to x=3.
10. Substitute the limits for x:
(ln(2)) * ((3 * e^3 - e^3) - (0 * e^0 - e^0)).
11. Simplify the expression:
(ln(2)) * (2 * e^3 - 1).
The evaluated double integral is (ln(2)) * (2 * e^3 - 1).
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Therefore, the integral of xe^x / y da r = [0,3] x [1,2] is 60.2565...
How to calculate the integral?The integral of xe^x / y da r = [0,3] x [1,2] is:∫∫(xe^x / y) dA = ∫1²∫0³(xe^x / y) dxdy = ∫1²(∫0³(xe^x / y) dx) dy
Integration with respect to x:∫0³(xe^x / y) dx = (xe^x / y) |0³ = (3e³ / y) - (0 / y) = 3e³ / y
Thus,∫1²∫0³(xe^x / y) dxdy = ∫1²(3e³ / y) dy= 3e³[ln(y)] |1²= 3e³(ln(2) - ln(1))= 3e³ln(2) - 3e³ln(1)= 3e³ln(2) = 3 * 20.0855...= 60.2565...
Therefore, the integral of xe^x / y da r = [0,3] x [1,2] is 60.2565...
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Solve (x – 3)2 = 49. Select the values of x. A. –46 B. -4 C. 10 D. 52
Answer: If you are meaning for the number to be squared would be ten.
Step-by-step explanation:
49 divided by 2 equals 7, 7 plus 3 =10
The answer would be C. 10
if we want to test for the significance of the model, the critical value of f at a 5% significance level is
To test for the significance of the model at a 5% significance level, the critical F value must be determined using the degrees of freedom and the F distribution table or statistical software. The calculated F value is then compared to the critical F value to determine if the model is statistically significant.
The significance of a model is determined by comparing the calculated F value to the critical F value at a given significance level. The critical F value is determined by the degrees of freedom for the numerator and denominator, and the significance level.
At a 5% significance level, the critical F value can be found using a F distribution table or a statistical software. The critical F value will be the value at which 95% of the F distribution falls below it, and 5% falls above it.
For example, if the degrees of freedom for the numerator are 2 and the degrees of freedom for the denominator are 10, the critical F value at a 5% significance level would be 4.10. If the calculated F value is greater than the critical F value, the model is considered to be statistically significant at the 5% level.
In conclusion, to test for the significance of the model at a 5% significance level, the critical F value must be determined using the degrees of freedom and the F distribution table or statistical software. The calculated F value is then compared to the critical F value to determine if the model is statistically significant.
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Which linear equation describes the line passing through point (10, 3) and has a y-intercept at (0, -1)?10y = -3x +y = -x +y=2- 1= 5*-y=31-x-13*-52
Answer: y = 2x/5 - 1
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
The given points are (0, -1) and (10, 3). thus,
x1 = 0, y1 = - 1
x2 = 10, y2 = 3
m = (3 - - 1)/(10 - 0) = (3 + 1)/10 = 4/10 = 2/5
By substituting m = 2/5 and c = - 1 into the slope intercept equation, the equation of the line is
y = 2x/5 - 1
A television station shows commercials for 7 1/2 minutes each hour how many 45 second commercials can it show per hour
the television station can show 10 45-second commercials per hour.
convert hour into minuteTo convert hours into minutes, you simply multiply the number of hours by 60, since there are 60 minutes in an hour.
So, if you want to convert 3 hours into minutes, you would do:
3 hours x 60 minutes/hour = 180 minutes
Therefore, 3 hours is equivalent to 180 minutes.
There are 60 minutes in an hour, and 7 1/2 minutes is equal to 7.5 minutes.
So, the television station shows commercials for 7.5 minutes per hour.
We can convert 45 seconds to minutes by dividing it by 60:
45 seconds ÷ 60 = 0.75 minutes
To find out how many 45-second commercials the television station can show per hour, we can divide the total number of minutes of commercials by the length of each commercial:
7.5 minutes ÷ 0.75 minutes/commercial = 10 commercials
Therefore, the television station can show 10 45-second commercials per hour.
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Ruby uses 1/4 yard of ribbon to make 2 bows.
Answer:
1/4 ÷ 2
Step-by-step explanation:
Answer:
the first option 1/4 ÷ 2
hope it helped!!!
plz help will give brainliest
Step-by-step explanation:
Hey there!!!!
Your required answer is option A.
The reason is.
When we solve it through elimination method we need to multiply second equation by "2" and then subtract to get "-4y" in 1st equation and "+4y" in 2nd equation cancelled.(As when we multiply equation 2 by 2 and subtract we get "-2y" as "+4y".)
So, it the equation seems like,
\(12 {x}^{2} + 4 {y}^{2} = 22\)
Now, this equation is made after multiplying it by 2 and subtracting the 1st and 2nd equation to solve the equation s.
So, the answer is option A.
Hope it helps...
latifa writes down a number. she says
if i find a cube root of that number and then quadruple the answer, i get 16
what number did latifa write down?
Answer:
8
Step-by-step explanation:
the cubed root of 8 equals 2
if you quadruple 2 (multiply it by 4), you will get 8
If you have a line with a Slope of -4 and a y-intercept of -2, what would be the equation of that line?
Question 6 options:
y = -4x + 2
y = -2x - 4
y = -4x - 2
y = -2x + 4
Answer:
y = -4x - 2
Step-by-step explanation:
y = mx + b where
m = slope, and b = y-intercept
slope = -4 = m
y-intercept = -2 = b
y = mx + b
y = -4x - 2
Answer: y = -4x - 2
solve for x
5x+2=4x-9
Hello !
Answer:
\(\Large \boxed{\sf x=-11}\)
Step-by-step explanation:
We want to find the value of x that satisfies the following equation :
\(\sf 5x+2=4x-9\)
Let's isolate x !
First, substract 4x from both sides :
\(\sf 5x+2-4x=4x-9-4x\\x+2=-9\)
Now let's substract 2 from both sides :
\(\sf x+2-2=-9-2\\\boxed{\sf x=-11}\)
Have a nice day ;)
Hello!
5x + 2 = 4x - 9
5x - 4x = - 9 - 2
x = -11
You are at a restaurant and the check comes to a total of $29. If you want to leave a 19% tip, how much total money should you pay, to the nearest cent?
Answer:
$34.51
Step-by-step explanation:
To find 19% of 29, you first want to change the 19% to a decimal.
19% to a decimal is 0.19
Then you multiply the 0.19 by 29
29•0.19= 5.51
Now just add the 5.51 to the 29 to get the total
5.51+29=$34.51
Write a compound inequality that the graph could represent.
Answer:
k < -4 or k > 13
Step-by-step explanation:
Let's take a look at the graph, we can see that the arrows point towards both directions, both dots are open, meaning that we can only have < and > signs. We can see that the arrow pointing to the left contains numbers that are less than -4, so that part of the compound inequality must be k < -4. And on the other side, they are numbers that are greater than 13, so that part must be k > 13. Thus, the answer must be d.
Hopes this helps.
what is the solution 2/3x + 5 = 1
Answer:
x = -6
Step-by-step explanation:
subtract 5 from both sides
2/3 x = -4
multiply by 3
2x = -12
divide by 2
x= -6
Answer:
2=x
Step-by-step explanation:
2/3x+5=1
2/3 is also like division so lets do it this way:
2÷3x+5=1
-5 -5
______________________-
2÷3x=-4
·3x ·3x
__________________-
2=-4·3x
+4 +4
______________-
6=3x
÷ 3 ÷3
_______________
2=x
Hope this helps
explain roller coaster steps potential and kinetic energy
Answer:
Step-by-step explanation:
Potential energy=stored energy so say when the roller coaster stops somewhere they are storing energy.
In then when they just go down there would now be using kinetic energy.
Hope this helps have a great afternoon:)
In order for the parallelogram to be a square, x=?
Answer:
x=7 Thx pls mark as brainliest
Step-by-step explanation:
In order for a polygon to be a parallelogram, the polygon needs to be a four-sided rectangle type shape, with two sets of parallel sides.
For this square to be a parallelogram, all
4
angles need to be
90
º
. This will give us to the two sets of parallel sides.
Knowing this, and the fact that on of the angles is being bisected, we need only multiply the defined angle by two and set it equal to
90
.
Every rhombus is a rectangle. true or false
Answer: false
Step-by-step explanation:
Explain how you would go about graphing this equation? What would be your first step and how would you go from there? Y=4x+6 *
Step-by-step explanation:
First I would look at the y intercept. In a linear equation, y = mx + b, b is the y-intercept and m is the slope. This means that (0,6) is a point on the line since at a y-intercept, the x value is 0. First you should plot this point.
Next, the slope is 4, meaning that for every 1 unit to the right, the line rises 4 units. You can count 1 to the right and 4 up from the y-intercept, which gives you (1,10), a second point on the line. After this, you can connect the two points and there you go, you have a graph!
Pls help me solve for x ill give 10 points away
Answer:
.53 pounds of dog food each day.
Step-by-step explanation:
Use PEMDAS to solve
If she has enough or not
Answer:
enough is the correct worf
What is the distance between -18 and 10 on a number line?
Answer: 28
The distance between -18 and ten on a number line is 28.
Plz mark brainliest:)
9 - 3 divide 1/3 + 1 =
Answer:
8
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
9 - 3 divide 1/3 + 1
-3 divide by 1/3
9 - 9 + 1
0 + 1
1
It is 1, because you should use the order of pemdas. PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.
PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction.
What is the slope of the line that passes through the points (2, -3) and (1, -2)? Write your answer in simplest form.
Given:-
\( \textsf{( 2 , -3 ) -- point [ i ]}\)\( \: \)
\( \textsf{( 1 , -2 ) -- point [ ii ]}\)\( \: \)
To find:-
\( \textsf{slop of the line = ?}\)\( \: \)
By using formula:-
\( {\color{hotpink}\bigstar} {\boxed{\sf {\green{ slope : m = \: \frac{y_2 - y_1}{x_2 - x_1} }}}}\)
Solution:-
\( \sf \: m = \frac{y_2 - y_1}{x_2 - x_1} \)
\( \: \)
where ,
\( \green \star \underline{ \sf \: 2 = x_1 , -3 = y_1\: }\)\( \: \)
\( \green \star{ \underline{ \sf{ \:1 = x_2 , -2 = y_2 \: }}}\)\( \: \)
\( \sf \: m = \frac{( -2 ) - ( -3 ) }{1 - 2} \)
\( \: \)
\( \sf \: m = \frac{ - 2 + 3}{ \: 1 - 2} \)
\( \: \)
\( \sf \: m = \cancel \frac{1}{ - 1} \)
\( \: \)
\( \underline{\boxed{ \sf{ \blue{ \: m = -1 \: }}}}\)
\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps:)
Find the value of x. * 66 (3x + 21) 57°A)12B)15C)57D)10
We have a triangle with angles: 66 deg, 57 deg and (3x+21).
We have to solve for x.
We know that the sum of the interior angles of a triangles is 180 degrees.
Then, we can write and solve for x as:
\(\begin{gathered} 66+57+(3x+21)=180 \\ 3x+21=180-57-66 \\ 3x+21=57 \\ 3x=57-21 \\ 3x=36 \\ x=\frac{36}{3} \\ x=12 \end{gathered}\)The value of x is 12.
Answer: A) 12
how do you solve the volume of a rectangular prism using the packing cubes method
You have learned that the formula for volume is
V = l w h and that it may also be written as V = B h.
Take note that the formula V = l w h only applies to rectangular prisms and cubes when used in its simplest form.
This is further explained below.
What is the packing cubes method?Generally, It entails the disorganized loading of completed plastic or metal pieces into a container, sometimes a corrugated box. This kind of packing results in clustered containers or closures that have been hurriedly put together with parts rubbing against one another.
The cross-section of a rectangular prism is square. Consists of two sets of mutually parallel bases. There are eight corners and six sides on a rectangular prism. A cuboid, in that it can be described by its width at the base, its height, and its length.
In conclusion, Rectangular prisms and cubes are the only objects for which the version, V = l w h, is true.
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What is the slope of the line that passes throug the points (5,-1) and (-3,3)?
Answer:
negative slope.............
Answer:
c
Step-by-step explanation:
The total surface area of a closed cylinder is 5000cm². Find the dimension of the radius that maximizes its volume and state the maximum volume.
The maximum volume of the cylinder is 27147.355 cm² at the maximum point.
What is volume of cylinder?
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. The substance could be a liquid amount or something else that can be evenly put into the cylinder.
The formula for the volume of the cylinder v = \(\pi r^2\)h,
To find the maximum volume of the cylinder we apply the condition of maxima \(\frac{dv}{dr}\) = 0.
Let r cm be the radius and h cm be the height of the closed cylinder.
Then, Total surface area of the cylinder = \(2\pi r(r+h)\)
5000 = \(2\pi r^{2} +2\pi rh\)
h = \(\frac{5000-2\pi r^{2} }{2\pi rh}\)............(1)
Volume of the cylinder v = \(\pi r^2h\)
Substitute the value of h in the above equation
= \(\pi r^2\) × \(\frac{5000-2\pi r^{2} }{2\pi rh}\\\)
= \(\frac{r}{2}\) × \(5000-2\pi r^2\)
v = \(2500r-\pi x^{3}\) ..............(2)
Now, for the maximum volume of the cylinder dv/dr= 0
\(\frac{d(2500r-\pi x^{3})}{dr}\) =0
\(3\pi r^{2} =2500\)
\(r^{2} =\frac{2500}{3\pi }\)
r=\(\frac{50}{\sqrt{3\pi } }\)
r= 27147.355
Hence, The maximum volume of the cylinder is 27147.355 at the maximum point r= \(\frac{50}{\sqrt{3\pi } }\).
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please help lol im confused i dont know why but please help
Answer:
No, but if it was how many studens school like math then yes
in Step-by-step explanation:
Reed is currently r years old. Which expression represents his age seven years from now
Answer: r+7
Whatever his age is now, we add 7 to it. So we simply add 7 to r getting r+7.
Example: Say he is 10 years old now
r = 10
r+7 = 10+7 = 17
meaning he will be 17 seven years from now
I added a picture below
If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.
What is the Solution to a System of Linear Equations?A solution to a system of linear equations is a set of values for the variables that satisfy all the equations in the system simultaneously. In other words, it is a collection of values for the variables that make all the equations in the system true at the same time.
The solution can be represented graphically as the intersection of the lines or planes defined by the equations in the system, or it can be represented algebraically as a set of values for the variables.
The equation "5 = 0" is false. It means that 5 cannot be equal to 0. This could indicate that the system of linear equations has no solution or that there is an error in the method being used to solve it.
Therefore, the answer is: "none of these statements are true".
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HELP
A plant that manufactures metal plates has a quality control team to check
that the plates are the right size. A rectangular plate with dimensions 5 cm
by 3 cm must have length within 0.25 cm of 5 cm. Write and solve an
absolute value inequality to find the minimum and maximum area of the
plates. (Round to the nearest hundredth)
minimum:
(cm²
maximum:
cm2
Answer:
minimum area: 30.40 cm²
maximum area: 30.52 cm²
Step-by-step explanation:
1. 6x + 1 = -6(1-x)
2. 4(3r + 4) = -8(2r + 5)
3. 11 + 2p = p + 4
4. 2(-6m -3) = 6(5m -1)
5. -3 + 5a = 4a -10
6. -16 + 3n = -8 - 5n
7. -22 + 8v = 7(4v -6)
8. 3(2x – 4) = 2 (3x- 6)
Equations with variable please solve i give brainliest.
Applying the distributive property, the solutions are given as follows:
1. No solution.
2. r = -2.
3. p = -7.
4. m = 0.
5. a = -7.
6. n = 1.
7. v = 1.
8. x = All real values.
What is the distributive property?The distributive property is used when the outside term multiplies each of the inside terms, then if necessary, the like terms are used.
For this problem, the property is used to isolate the variables and find the desired result of the expressions.
Item 16x + 1 = -6(1 - x)
6x + 1 = -6 + 6x
0x = -7
No solution. (division by 0).
Item 24(3r + 4) = -8(2r + 5)
12r + 16 = -16r - 40
28r = -56
r = -2.
Item 311 + 2p = p + 4
p = -7.
Item 42(-6m - 3) = 6(5m - 1)
-12m - 6 = 30m - 6
42m = 0
m = 0.
Item 5-3 + 5a = 4a - 10
a = -7.
Item 6-16 + 3n = -8 - 5n
8n = 8
n = 1.
Item 7-22 + 8v = 7(4v - 6)
-22 + 8v = 28v - 42
20v = 20
v = 1.
Item 83(2x - 4) = 2(3x - 6)
6x - 12 = 6x - 12
0 = 0
x = All real values.
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