Answer:
For revolution about the y-axis:
shell: dV = 2π·x·(f2(x) -f1(x))·dxdisk: dV = π·(f2(y)^2 -f1(y)^2)·dyFor revolution about the x-axis, swap x and y.
Step-by-step explanation:
The methods for computing the volume of revolution of a plane figure are ...
cylindrical shelldiskThe name of the method describes the shape of the differential of volume.
__
Cylindrical shell
For revolution about the y-axis, the differential of volume is a cylindrical shell of radius x, thickness dx, and height y2 -y1, where y2 = f2(x) and y1 = f1(x). (y2 > y1) Integration is over x.
dV = 2π·x·(f2(x) -f1(x))·dx
For revolution about the x-axis, the variables x and y are interchanged.
__
Disk
For revolution about the y-axis, the differential of volume is a donut or disk of inner radius f1(y) = x1 and outer radius f2(y) = x2 (x1 ≤ x2). The thickness is dy. Integration is over y.
dV = π·(f2(y)^2 -f1(y)^2)·dy
For revolution about the x-axis, the variables x and y are interchanged.
__
The preferred method is the one that gives simple integrable functions over a single range of integration. For some geometries, the integration range must be split, because the shape of the differential volume cannot be described by a simple rectangle whose length is the difference of functions of the integration variable.
When the differential of volume can be drawn either way, the choice of methods may be arbitrary. I usually choose the method that gives the simplest integrand.
_____
Additional comment
When the axis of revolution is something other than a coordinate axis, the radius of revolution becomes a different function than a simple x (or y). For example, if the axis of revolution is x=a, the radius of the cylindrical shell will be a-x (for x ≤ a) or x-a (for a ≤ x).
Here's an example of the use of the disk method.
https://brainly.com/question/17446389
Please help! I am confused and cannot get the correct answer.
Answer:
520
Step-by-step explanation:
I used big brain
-
65.8 percent of what number is 14
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{21.27}}}}}[/tex]
Step-by-step explanation:
Let the number be x
Create an equation
[tex] \sf{65.8\% \: of \: x = 14}[/tex]
[tex] \longrightarrow{ \sf{ \frac{65.8}{100} x = 14}}[/tex]
[tex] \longrightarrow{ \sf{x = \frac{14}{ \frac{65.8}{100} } }}[/tex]
[tex] \longrightarrow{ \sf{x = 14 \times \frac{100}{65.8}}} [/tex]
[tex] \longrightarrow{ \sf{x = 21.27}}[/tex]
Hope I helped!
Best regards! :D
which statement is false A: every irrational number is also a real number B: every integer is also a real number C: every integer is also an irrational number D: no irrational number is rational
Answer is D
I say this because I can't be a cause international numbers real
B every integers a real number
C every integers is also an interration number.
Muna is making a scale drawing of a gecko. The gecko is 1:2 inch wide and 5 inches long. she decides to make her drawing of the gecko 1 inch wide. How long will the drawing be ? show your work
Answer:
L= 0.83 in
Step-by-step explanation:
Width= 1.2 in when length = 1 in
Required
Determine the length when width = 1 in
First, we need to determine the ratio
Ratio = [tex]\frac{Width}{Length}[/tex]
Ratio = [tex]\frac{1.2}{1}[/tex]
Ratio = 1.2 ---(1)
Let the required length be represented with L
So:
Ratio = [tex]\frac{Width}{Length}[/tex]
Ratio = [tex]\frac{1}{L}[/tex] ---(2)
Equate (1) and (2)
[tex]\frac{1}{L}[/tex] = 1.2
Multiply through by 1.2
L * [tex]\frac{1}{L}[/tex] = 1.2 * L
1 = 1.2 * L
Divide through by 1.2
L = [tex]\frac{1}{1.2}[/tex]
L = 0.83 in (Approximated)
What is the answer to 24/3x-2
Answer:
=8x−2
Step-by-step explanation:
I hope this helps you
Do the binary numbers “0011” and “000011” have the same value or different values? Explain.
Using binary to decimal conversion, it is found that the numbers have the same values.
----------------------------------
0011
Converting from decimal, the number is given by:
[tex]0011 = 1\times2^0 + 1\times2^1 + 0\times2^2 + 0\times2^3 = 1 + 1 + 0 + 0 = 2[/tex]
----------------------------------
000011
Converting from decimal, the number is given by:
[tex]000011 = 1\times2^0 + 1\times2^1 + 0\times2^2 + 0\times2^3 + 0\times2^4 + 0\times2^5 = 1 + 1 + 0 + 0 + 0 + 0 = 2[/tex]
In both cases, the result of conversion is 2, thus, they have the same value.
A similar problem is given at https://brainly.com/question/7978210
To transform a binary number to a decimal number we need to multiply each of the components of the binary number by 2 to the power of the place value minus one, and sum all of that.
Based on this, we will see that 0011 and 000011 have the same value.
For example, the number 01 will be:
[tex]0*2^1 + 1*2^0 = 1[/tex]
The number 1010 will be:
[tex]1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 1*8 + 1*2 = 10[/tex]
Now let's convert the two given numbers to decimals:
0011
[tex]0*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 3[/tex]
000011
[tex]0*2^5 + 0*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 3[/tex]
So exactly like in decimal numbers, adding zeros to the left side does not affect the value.
If you want to learn more, you can read:
https://brainly.com/question/19802955
What is this called?
MATH
Answer and I will give you brainiliest
Answer:
injective function where range can't have many domain
Step-by-step explanation:
If Jonny and Suzy share a $10 burger, how much does each owe?
Answer: $5
Step-by-step explanation:
10/2=5
2 people x $10 = $5
Sleeping in college. A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 25 students. On average, the sampled students slept 6.25 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.
Answer:
Sample mean = 6.25 hours per night.
Population mean = 5.5 hrs of sleep each night.
Step-by-step explanation:
A sample mean is the mean of the sample collected. The 25 students surveyed by the student is the sample. The average sleep time derived from the sample is the sample mean.
A population mean is the mean of all the population. Here the population are college students. The population mean is the mean derived from studying the sleep duration of all the population - college students
what is 2,340 divided by 36
Answer:
65.
Step-by-step explanation:
You could honestly just use a calculator for this, but okay.
10 10 times as much as what
Answer:
100
Step-by-step explanation:
10x10
10 times 10 is equal to 100.
Does anyone know if this is right if not which one is it
Answer:
Step-by-step explanation:
The answer is actually the last one :)
Use the figure to write the segment addition postulate, write an equation and solve for x.
Answer:
5). x = -1
6). x = 2
Step-by-step explanation:
5). AC = (x + 10)
AB = 5
BC = (2x + 6)
By segment addition postulate,
AC = AB + BC
(x + 10) = 5 + (2x + 6)
x + 10 = 2x + 11
2x - x = 10 - 11
x = -1
6). AC = 19
AB = 9x + 7
BC = -3x + 20
By segment addition postulate,
AC = AB + BC
39 = 9x + 7 + (-3x + 20)
39 = (9x - 3x) + (7 + 20)
39 = 6x + 27
6x = 39 - 27
6x = 12
x = 2
x = 2
Find the general solution of the given system.
dx dt = 6x − y
dy dt = 36x − 6y
Answer:
[tex]y = 6x + C[/tex]
Step-by-step explanation:
Given the system of equations
dx/dt = 6x − y ............. 1
dy/dt = 36x − 6y ............ 2
Divide equation 2 by 1;
[tex]\dfrac{dy/dt}{dx/dt} = \dfrac{36x-6y}{6x-y} \\\\\dfrac{dy/dt}{dx/dt} = \dfrac{6(6x-y)}{6x-y}\\ \\\dfrac{dy/dt}{dx/dt} = 6\\\\\dfrac{dy}{dt}* \dfrac{dt}{dx} = 6\\\dfrac{dy}{dx} = 6[/tex]
cross multiply
[tex]dy = 6dx\\[/tex]
integrate both sides of the expression
[tex]\int\limits {dy} = \int\limits {6} \, dx \\\\y = 6x + C[/tex]
Hence the general solution to the system of equation is [tex]y = 6x + C[/tex]
Using the distributive property, which of the following is an equivalent expression for 3(9 + 15)
Answer:
3 x 9+3 x 15
Step-by-step explanation:
I already know the answer but Brainliest for best explanation 3973-2937
Answer:
1036
Step-by-step explanation:
Working each column from right to left
3 9 7 3
− 2 9 3 7
7 is greater than 3 so you must regroup:
Take 1 from 7, so 7 becomes 6.
Add 10 to 3, so 3 becomes 13.
6 13
3 9 --
− 2 9 3 7
13 minus 7 is 6
6 13
3 9 --
− 2 9 3 7
6
6 minus 3 is 3
6 13
3 9 --
− 2 9 3 7
3 6
9 minus 9 is 0
6 13
3 9 --
− 2 9 3 7
0 3 6
3 minus 2 is 1
6 13
3 9 --
− 2 9 3 7
1 0 3 6
Hope this helps! Plz award Brainliest : )
Answer:
1036
Step-by-step explanation:
Use the Squeeze Theorem to show that [tex]\lim_{t \to \infty} \frac{cos5t}{5t}[/tex]
Complete the following argument: for t arbitrary large and positive.
Im not sure how to break this problem down using the Squeeze Theorem, could anyone help?
Recall that [tex]\cos x[/tex] is bounded between -1 and 1 for all real [tex]x[/tex], so that
[tex]-1\le \cos(5t)\le 1[/tex]
[tex]\implies-\dfrac1{5t}\le\dfrac{\cos(5t)}{5t}\le\dfrac1{5t}[/tex]
Now take the limit of each side of the inequality:
[tex]\displaystyle\lim_{t\to\infty}\left(-\dfrac1{5t}\right)\le\lim_{t\to\infty}\dfrac{\cos(5t)}{5t}\le\lim_{t\to\infty}\dfrac1{5t}[/tex]
The bounding limits are both 0, so by the squeeze theorem the desired limit is also 0.
The definition of a circle uses the underfined term
Arc.
Line.
Plane
Ray
Josh wrote a whole number using the digits 8,4,7,2,9 and 0. Josh's number has a seven in the thousands and a 2 in the tens place. Josh's number is less then 500,000. Is Josh's number greater than 480,000?
Answer:
Step-by-step explanation:
Using the digits 8,4,7,2,9 and 0 to write a whole Number with 7 in the thousands place and 2 in the tens place :
The whole number is 6 digits long
100 thousand
10 thousand
Thousand = 7
Hundred
Tens = 2
Unit
Also the whole number is less than 500,000
Hence, number in the 100 thousand place is less Than 5,
Hence digit in the 100 thousand place = 4
Placing either 8 or 9 in the ten thousand place will mean That Josh's whole number is greater than 480,000
On a map, 1 cm represents 300 km. What does 3/5 cm represent?
Answer:
180 km
Step-by-step explanation:
3/5 times 300 is 180
Answer
180 km
Step-by-step explanation:
Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
x < 5
0-6x-5 < 10 - X
0-6x + 15 < 10 - 5x
-3 -2 -1
0
1
2
2
3
4
5 6 7
+
口……
-7 -6 -5
-4
-3
-2
-1
0
1
2
3
Answer:
what is this??
Step-by-step explanation:
I really don't understand this question can someone please explain to me
Simplify 2(9* 5+3^2) + 4
Answer:
112
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
2(9 × 5 + 3²) + 4
Step 2: Exponents
2(9 × 5 + 9) + 4
Step 3: Multiplication
2(45 + 9) + 4
Step 4: Parenthesis
2(54) + 4
Step 5: Multiply
108 + 4
Step 6: Add
112
the admission fee to an amusement park is $17. It costs an additional c dollars to rent a locker to hold your belongings. the total cost for 10 to enter the amusement park and each rent a locker is $260 how much does it cost for one person to rent a locker
Answer:
$9
Step-by-step explanation:
$260-$170=90
90/10=9
We know that $17 * 10 = $170
c = amount of money to rent a locker.
$170 + 10c = $260
Subtract $170 from both sides.
10c = $90
Divide both sides by 10
c = $9
It cost $9 for one person to rent a locker.
The total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch. If a 48-cubic-inch rock weighs w pounds, write an equation that shows the proportional relation.
Answer:
[tex]d = \frac{w}{48}[/tex]
If [tex]\frac{1}{48} \\[/tex] is constant, say k
Then,
[tex]d = kw[/tex]
∴ d ∝ w
Hence, weight is proportional to the density
Step-by-step explanation:
From the question,
Let w denote the weight of the rock in pounds
s denote the size of the rock in cubic inches and
d denote the density of the rock in pounds per cubic inch.
First, we will write the equation connecting w, s, and d.
We get
[tex]density (pounds/inch^{3} ) = \frac{weight(pounds)}{size (inch^{3}) }[/tex]
That is,
[tex]d = \frac{w}{s}[/tex]
Now, given a 48-cubic-inch rock with weight w pounds, to show the proportional relation between the weight and the density, we will write
[tex]d = \frac{w}{48}[/tex]
If [tex]\frac{1}{48} \\[/tex] is constant, say k
Then,
[tex]d = kw[/tex]
∴ d ∝ w
Hence, density is proportional to the weight OR weight is proportional to the density
Crystal Rollerbladed 150 feet in 15 seconds, while Gavin rollerbladed 150 feet in 10 seconds. Without doing any calculations, who is faster? Why?
Crystal was faster because her distance was less than Gavin's.
Crystal was faster because her time was less than Gavin's.
Gavin was faster because his distance was less than Crystal's.
Gavin was faster because his distance was less than Crystal's.
Answer: Gavin was faster because his time was less than Crystal's.
Step-by-step explanation: They rollerbladed the same distance but Gavin did it in less time.
Hope this helped!
Mark Brainliest if you want!
Answer:
i belive the answer is D tell me if im doing it wrong
Step-by-step explanation:
When the polynomial:
[tex]h(x) ={dx}^{3}+{fx}^{2} - 7x - 6[/tex]
is defined by
[tex]x - 1[/tex]
its remainder is
[tex] - 10[/tex]
and when it is divided by
[tex]x - 3[/tex]
the remainder is
[tex]36[/tex]
find the values of the constant d and f
What is the simplified value of the expression below? StartFraction 4 (negative 8 + 4.5) over 6.25 + (negative 8.25) EndFraction –25 –7 7 25
Answer: -10.49.
Step-by-step explanation:
Using order of operations PEMDAS:
4(-8+4.5)/ 6.25 + (-8.25)
= 4 * -3.5 / 6.25 - 8.25
= -14/6.25 - 8.25
= -2.24 - 8.25
= -10.49.
Answer:
The answer should be -10.49
Step-by-step explanation:
To prevent illness and Injury, employers must make standardized health and safety Information for the chemicals
they produce avallable to employees for all chemicals on the job and train employees to find this Information. true or false?
Answer:
true
Step-by-step explanation:
if they wash there hands the customers and employees can be safe
Math need help fast.............................
Answer: B) 3 times
Step-by-step explanation:
write an equation
2/3x=2
Muktpily 3/2 on both sides
Youll get 3
E
OV
Question 3/18
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Mrs. Scarbrough and her dog drove 204 miles to grandma's house. The trip took them 3 hours.
What was their average speed in miles per hour?
miles per hour
