Answer:
the answer should be e^3
Step-by-step explanation:
i hope it helps you
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V by slicing & find V by cylindrical shells.
Explanation:
Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by
[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]
Integrating this expression, we get
[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]
or
[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is
[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]
[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]
[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]
[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]
Using Eulers formula, how many edges does a polyhedron with 9 faces and 14 vertices have?
F + V = E + 2
SolutionF = 9V = 14E = ?Substuting the values⇨ 9 + 14 = E + 2
⇨ 23 = E + 2
⇨ 23 - 2 = E
⇨ 21 = E
Hence , the number of edges in polyhedron is 21.
The number of edges of a polyhedron with 9 faces and 14 vertices have will be 21.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
here, we have,
Using Euler's formula, the number of the edges does a polyhedron with 9 faces and 14 vertices have
We know the formula for the edges of the polyhedron will be
By Euler's Formula
F + V = E + 2
The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.
Then we have
Solution
F = 9
V = 14
E = ?
Substuting the values
⇨ 9 + 14 = E + 2
⇨ 23 = E + 2
⇨ 23 - 2 = E
⇨ 21 = E
Hence , the number of edges in polyhedron is 21.
More about the polygon link is given below.
brainly.com/question/17756657
#SPJ2
A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.
Answer:
The sample proportion of students who prefer vanilla ice cream is 0.56.
Step-by-step explanation:
Sample proportion of students who prefer vanilla ice cream:
Sample of 375 students.
Of those, 210 said they prefer vanilla ice cream.
The proportion is:
[tex]p = \frac{210}{375} = 0.56[/tex]
The sample proportion of students who prefer vanilla ice cream is 0.56.
Look at the image for the question
Answer:
Does the answer help you?
Add .003, 265.8, 83.04
and 1972
IS THSI RIGHTTTTTTTT??????????????
Answer:
No. It is EF and GH
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The answer will be EF and GH, both are 7 units long.
I need help ASAP thank you
Answer:D) Under-root 25.Under-root 3
Step-by-step explanation
Under-root 25 = 5
Answer:
Answer D and B.
Step-by-step explanation:
[tex]{ \bf{5 \sqrt{3} }} \\ = { \bf{ \sqrt{ {5}^{2} } \times \sqrt{3} }} \\ = { \bf{ \sqrt{25} . \sqrt{3} }}[/tex]
for the vector (-9,3), find 1/2V, -V, and 4V
9514 1404 393
Answer:
1/2V = <-9/2, 3/2>-V = <9, -3>4V = <-36, 12>Step-by-step explanation:
The scalar multiplier multiplies each of the components.
1/2V = <-9×1/2, 3×1/2> = <-9/2, 3/2>
-V = <(-9)(-1), (3)(-1)> = <9, -3>
4V = <-9×4, 3×4> = <-36, 12>
In the statements below, V is a vector space. Mark each statement true or false. Justily each answer a. The set R is a two-dimensional subspace of R3.Choose the correct answer below O A. False, because R2 is not closed under vector addition. O B. True, because R2 is a plane in R3 Ос. False, because the set R2 is not even a subset of R3 OD. True, because every vector in R2 can be represented by a linear combination of vectors inR3 b. The number of variables in the equation Ax 0 equa's the dimension of Nul A. Choose the correct answer below O A. False, because the number of free variables is equal to the dimension of Nul A. O B. True, because the number of variables in the equation Ax 0 equals O C. True, because the dimension of Nul A equals the largest any solution to O D. False, because the number of plvot columns is equal to the dimension of Nud A. c. A vector space the number of columns in A and the number of columns in A equa's the dimension of Nul A. number of Os in any solution to the equation Ax -b, and the equation Ax- 0 always has the trivial solution, so the number of variables is infinite-dimensional if it is spanned by an infinite set Choose the correct answer below O A. True, because the dimension of a vector space is equal to the number of elements in a set that spans O B. Faise, because a basis for the vector space may O C. True, because the dimension of a vector space number of O D. Faise, because all vector spaces are finite-dimensional. d. If dim Van and it S spans V, then S is a basis of V. Choose the correct answer below. the vector space. have only finitely many elements, which would make the vector space finite-dimensional is the number of vectors in a basis for that vector space, and a vector space spanned by an infinite set has a basis with an infinite number of vect O A. False, because the set S must have less than n elements O B. True, because if a vector space is finite-dimensional, then a set that spans t is a basis of the vector space O C. False, in order for S to be a basis, it must also have n elements O D. True, because if a set spans a vector space, regardiess of the dimension of the vector space, then that setis a basis of the vector spaoe e. The only three-dimensional subspace of R3 is R3 itself. Choose the correct answer below Faise, because False, because any subspaces of R3 which contain three-element vectors are three-dimensional, but most of these most three-dimensional subspaces of R3 are spanned by a linearly dependent set of tree vectors, but R can only be sparned by thre Inearly independent vectors subspaces do not contain all of R
D. True, because any three linearly dependent vectors in R3 span all of R3, so there is no three-dmensional subspace of R' that is not R
Answer:
A. False
B. True
C. False
D. True
Step-by-step explanation:
Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.
find the measure of c
Answer:
B is the correct answer of this question
Which letter on the diagram below represent a diameter of the circle
Answer:
where is your diagram?
Step-by-step explanation:
Find the length of BC
Answer:
53.68
Step-by-step explanation:
tan54 = bc/39
bc = 39tan54
Step-by-step explanation:
Hey there!
From the given figure;
Angle CAB = 54°
Side AC = 39
To find: side BC
Taking Angle CAB as reference angle;
Perpendicular (p) = BC = ?
Base (b) = AC = 39
Hypotenuse (h) = AB
Taking the ratio of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan(54) = \frac{bc}{39} [/tex]
Simplify it;
1.376381*39 = BC
Therefore, BC = 53.678.
Hope it helps!
Need help pleaseeee!!!
Answer:
C is wrong!
Step-by-step explanation:
The explanation is in the picture!
A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents. The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces. What is the value of the test statistic
Answer:
The value of the test statistic is 59.75.
Step-by-step explanation:
The test statistic for the population standard deviation is:
[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
In which n is the sample size, [tex]\sigma_0[/tex] is the value tested and s is the sample standard deviation.
A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents.
This means that [tex]n = 45, s^2 = 1.1[/tex]
The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces.
0.9 is the value tested, so [tex]\sigma_0 = 0.9, \sigma_0^2 = 0.81[/tex]
What is the value of the test statistic
[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
[tex]\chi^2 = \frac{44}{0.81}1.1 = 59.75[/tex]
The value of the test statistic is 59.75.
i keel asking for the dang answer why wont anyone tell me it a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
In 1815, Sophie Germain won a mathematical prize given by the Institut de France for her work on the theory of elasticity. The prize was a medal made of 1 kilogram of gold. How much is the medal worth today in U.S. dollars and in euros
Answer:
gold price : $58.72/gram
$58,720 per kilo(1000) grams
Step-by-step explanation:
Help me because I dont understand
Answer:
105 sq ft + 31 sq ft
Step-by-step explanation:
= 136 sq ft
Hope it helps✌✌
Divide 500 in the ratio 4:5:1
Answer:
200 : 250 : 50
Step-by-step explanation:
Sum the parts of the ratio, 4 + 5 + 1 = 10 parts
Divide the amount by 10 to find the value of one part
500 ÷ 10 = 50 ← value of 1 part of ratio , then
4 parts = 4 × 50 = 200
5 parts = 5 × 50 = 250
500 = 200 : 250 : 50
Answer:
200, 250 and 50.
Step-by-step explanation:
First find the 'multiplier'.
4 + 5 + 1 = 10
500/10 = 50 = multiplier.
So the answer is
4*50 = 200
5 * 50 = 250
and 1 * 50 = 50.
Simplify the given expression.
Answer:
8x-21
----------------------
(2x-7)(2x+7)
Step-by-step explanation:
7 4
----------- + ------------
4x^2 -49 2x+7
Factor ( notice that it is the difference of squares)
7 4
----------- + ------------
(2x)^2 - 7^2 2x+7
7 4
----------- + ------------
(2x-7)(2x+7) 2x+7
Get a common denominator
7 4(2x-7)
----------- + ------------
(2x-7)(2x+7) (2x-7)(2x+7)
Combine
7 +4(2x-7)
----------------------
(2x-7)(2x+7)
7 +8x-28
----------------------
(2x-7)(2x+7)
8x-21
----------------------
(2x-7)(2x+7)
Answer:
(8x - 21) / (2x + 7)(2x - 7)
Step-by-step explanation:
7 / (4x^2 - 49)+ 4 / (2x + 7)
= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)
LCM = (2x + 7)(2x - 7) so we have
(7 + 4(2x - 7) / (2x + 7)(2x - 7)
= (8x - 21) / (2x + 7)(2x - 7).
The distance from the green point on the parabola to the parabolas focus is 11. What is the distance from green point to the directrix?
Answer:
answer 11
Step-by-step explanation:
I think it the right answer
Heeeellllllppppp?????
9514 1404 393
Answer:
-1
Step-by-step explanation:
We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...
a17 = (a1 +a33)/2
2a17 -a33 = a1 = 2(10) -21 = -1
a1 = -1
_____
Additional comment
You could go to the trouble to find the general term of the sequence.
an = a1 +d(n -1)
a17 = a1 + d(17 -1) = 10
a33 = a1 + d(33 -1) = 21
Subtracting the first equation from the second, we have ...
16d1 = 11
d1 = 11/16
Using the first equation, we find ...
a1 +(11/16)(17 -1) = 10
a1 = 10 -11 = -1 . . . . same as above.
Determine the product of (46.2 × 10^-1) ⋅ (5.7 × 10^–6). Write your answer in scientific notation.
A)
2633.4 × 10^–5
B)
2.6334 × 10^–7
C)
2.6334 × 10^–1
D)
2.6334 × 10^–5
Step-by-step explanation:
here's the answer to your question
Prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
i. (G.M)²= (A.M)×(H.M)
ii.A.M>G.M>H.M
Answer:
See below
Step-by-step explanation:
we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
(G.M)²= (A.M)×(H.M) A.M>G.M>H.Mwell, to do so let the two unequal positive numbers be [tex]\text{$x_1$ and $x_2$}[/tex] where:
[tex] x_{1} > x_{2}[/tex]the AM,GM and HM of [tex]x_1[/tex] and[tex] x_2[/tex] is given by the following table:
[tex]\begin{array}{ |c |c|c | } \hline AM& GM& HM\\ \hline \dfrac{x_{1} + x_{2}}{2} & \sqrt{x_{1} x_{2}} & \dfrac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } \\ \hline\end{array}[/tex]
Proof of I:[tex] \displaystyle \rm AM \times HM = \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } [/tex]
simplify addition:
[tex] \displaystyle \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
reduce fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{1}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
simplify complex fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{x_{1} x_{2}}{x_{1} + x_{2}} [/tex]
reduce fraction:
[tex] \displaystyle x_{1} x_{2}[/tex]
rewrite:
[tex] \displaystyle (\sqrt{x_{1} x_{2}} {)}^{2} [/tex]
[tex] \displaystyle AM \times HM = (GM{)}^{2} [/tex]
hence, PROVEN
Proof of II:[tex] \displaystyle x_{1} > x_{2}[/tex]
square root both sides:
[tex] \displaystyle \sqrt{x_{1} }> \sqrt{ x_{2}}[/tex]
isolate right hand side expression to left hand side and change its sign:
[tex]\displaystyle\sqrt{x_{1} } - \sqrt{ x_{2}} > 0[/tex]
square both sides:
[tex]\displaystyle(\sqrt{x_{1} } - \sqrt{ x_{2}} {)}^{2} > 0[/tex]
expand using (a-b)²=a²-2ab+b²:
[tex]\displaystyle x_{1} -2\sqrt{x_{1} }\sqrt{ x_{2}} + x_{2} > 0[/tex]
move -2√x_1√x_2 to right hand side and change its sign:
[tex]\displaystyle x_{1} + x_{2} > 2 \sqrt{x_{1} } \sqrt{ x_{2}}[/tex]
divide both sides by 2:
[tex]\displaystyle \frac{x_{1} + x_{2}}{2} > \sqrt{x_{1} x_{2}}[/tex]
[tex]\displaystyle \boxed{ AM>GM}[/tex]
again,
[tex]\displaystyle \bigg( \frac{1}{\sqrt{x_{1} }} - \frac{1}{\sqrt{ x_{2}}} { \bigg)}^{2} > 0[/tex]
expand:
[tex]\displaystyle \frac{1}{x_{1}} - \frac{2}{\sqrt{x_{1} x_{2}} } + \frac{1}{x_{2} }> 0[/tex]
move the middle expression to right hand side and change its sign:
[tex]\displaystyle \frac{1}{x_{1}} + \frac{1}{x_{2} }> \frac{2}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \frac{\frac{1}{x_{1}} + \frac{1}{x_{2} }}{2}> \frac{1}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \rm \frac{1}{ HM} > \frac{1}{GM} [/tex]
cross multiplication:
[tex]\displaystyle \rm \boxed{ GM >HM}[/tex]
hence,
[tex]\displaystyle \rm A.M>G.M>H.M[/tex]
PROVEN
f(x)=3(x+5)+4/xwhat is f (a+2) solve this problem with showing the work
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
Answer:
24 years
Step-by-step explanation:
total ratio =8
older student=40 years
3/8*40 ÷ 5/8=24
2 cans of beans cost 98¢ how many cans can you buy for $3.92?
Diane must choose a number between 49 and 95 that is a multiple of 2, 3, and 9. Write all the numbers that she could choose. If
there is more than one number, separate them with commas?
The set of numbers that Diane can choose is:
{54, 60, 66, 72, 78, 84, 90}
Finding common multiples of 2, 3, and 6:
A number is a multiple of 2 if the number is even.
A number is a multiple of 3 if the sum of its digits is multiples of 3.
A number is a multiple of 6 if it is a multiple of 2 and 3.
Then we only need to look at the first two criteria.
First, let's see all the even numbers in the range (49, 95)
These are:
{50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94}
All of these are multiples of 2.
Now we need to see which ones are multiples of 3.
To do it, we sum its digits and see if that sum is also a multiple of 3.
50: 5 + 0 = 5 this is not multiple of 3.
52: 5 + 2 = 7 this is not multiple of 3.
54: 5 + 4 = 9 this is multiple of 3, so 54 is a possible number.
And so on, we will find that the ones that are multiples of 3 are:
54: 5 + 4 = 9.
60: 6 + 0 = 6
66: 6 + 6 = 12
72: 7 + 2 = 9
78: 7 + 8 = 15
84: 8 + 4 = 12
90:9 + 0 = 9
Then the numbers that Diane could choose are:
{54, 60, 66, 72, 78, 84, 90}
If you want to learn more about multiples, you can read:
https://brainly.com/question/1553674
square root of 12321 by prime factorization
12321-3x3x37x37
(3)^2×(37)^2
square root = 3×37=111
Hope it helps you..!!
Using the applet, explore the results for simulating a group of 30 people and noting whether there is a duplicated birthday (whether at least two people have a matching birthday). Run at least 40 trials. What is the relative frequency of trials that had at least two people with the same birthday
Answer:I just need points
Step-by-step explanation:
Hey
please solve asap thanks
Answer:
A' (-2,3)
B' (-1,1)
C' (-4,0)
Step-by-step explanation:
Given coordinates:
A (3,0)
B (4,-2)
C (1,-3)
We want to find the location of the coordinates after a translation of <-5,3>
Explanation of translation
<-5,3>
Subtract 5 from the x value and add 3 to the y value
Applying translation
A (3,0) ---------> (3-5,0+3) ---------> (-2,3)
B (4,-2) ---------> (4-5,-2+3) ---------> (-1,1)
C (1,-3) ---------> (1-5,-3+3) ---------> (-4,0)
So the new coordinates would be
A' (-2,3)
B' (-1,1)
C' (-4,0)
