Step-by-step explanation:
Let's first consider a rotation about a vertical axis (x=0 or x=a).
Using washer method, the volume is:
∫ᵧ₁ᵞ² π (x₂² − x₁²) dy
∫ᵧ₁ᵞ² π ((x₂ − a)² − (x₁ − a)²) dy
Using shell method, the volume is:
∫ₓ₁ˣ² 2π x (y₂ − y₁) dx
∫ₓ₁ˣ² 2π (x − a) (y₂ − y₁) dx
First, notice that with washer method, the differential dy is parallel to the axis of rotation. With shell method, the differential dx is perpendicular to the axis of rotation.
Also, notice that the limits of integration must match the differential.
Choosing the best method will depend on the function.
If x² can be written in terms of y, and integrated, then washer method is the one to use.
If y can be written in terms of x, and integrated, then shell method is the one to use.
In other words, use washer method if x = f(y) is simple to integrate. Use shell method if y = f(x) is simple to integrate.
If instead we rotate about a horizontal axis (y=0 or y=a), the volume with washer method is:
∫ₓ₁ˣ² π (y₂² − y₁²) dx
∫ₓ₁ˣ² π ((y₂ − a)² − (y₁ − a)²) dx
Using shell method, the volume is:
∫ᵧ₁ᵞ² 2π y (x₂ − x₁) dy
∫ᵧ₁ᵞ² 2π (y − a) (x₂ − x₁) dy
We choose washer method when y² = f(x) is easy to integrate.
We choose shell method when x = f(y) is easy to integrate.
So here's the takeaway:
If the axis of rotation is x = 0 or x = a, and x² = f(y) is easy to integrate, use washer method.
If the axis of rotation is y = 0 or y = a, and y² = f(x) is easy to integrate, use washer method.
Otherwise, use shell method.
Class Scheduling Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 80 students, and each section of Applied Calculus has 70 students. The department will offer a total of 150 sections in a semester, and 11,200 students would like to take a math course. How many sections of each course should the department offer in order to fill all sections and accommodate all of the students
Answer:
70 section of Finite math and 80 section of Applied calculus
Step-by-step explanation:
As in each section, finite math has 80 student and applied calculus has 70 students
80x + 70Y = 11,200................(i)
There are 150 sections in a semester
x + y = 150..................................(ii)
Multiply equation (ii) by -70
-70x - 70y = 10,500
Add equation (i) and equation (iii)
80x + 70Y = 11,200
-70x - 70y = 10,500
10x = 700
x = 700/100
x= 70
Substitute x in equation (ii)
x + y = 150
70 + y = 150
y = 150 - 70
y = 80
Hence, 70 section of finite math and 80 section of applied calculus should the department offer in order to fill all sections and accommodate all of the students.
PLZ HELP FAST I'm pretty sure that the stuff i put in the boxes is correct
Answer:
3(x + 4)- X= 12
Step-by-step explanation:
John's extremely generous mother gave him $150 to spend on new school clothes. Shirts cost $15 each and a pair of pants cost $25. If John spent all $150 and bought 5 shirts, how many pairs of pants did he buy?
Answer: 3 pairs of pants
Step-by-step explanation:
Answer: he can still buy 3 pairs of pants
Step-by-step explanation: 15x5=75
75 + 75 = 150
he can buy 5 shirts
and 3 pairs of pants
187/100 in simplest form. I mark BRAINLIESTTTTTT and giving 20 POINTS
Answer:
[tex]\frac{187}{100}[/tex]
Step-by-step explanation:
This can't be simplified. It's already in its simplest form.
ASTRONOMY
Mmars= 6.42 x 10^23kg, RMars
3397 km)
Calculate the acceleration of gravity on the surface of Mars
Express your answer with the appropriate units.
Given :
Los Angeles and Las Vegas.
Mass of Mars , [tex]M=6.42\times 10^{23}\ kg[/tex].
Radius of Mars ,
[tex]R=3397\ km\\\\R = 3.397\times 10^6\ m[/tex]
To Find :
The acceleration of gravity on the surface of Mars.
Solution :
Acceleration due to gravity is given by :
[tex]g_m = \dfrac{GM_m}{R_m^2}\\\\g_m =\dfrac{(6.67\times 10 ^{-11}\ m^3\ kg^{-1}\ s^{-2})(6.42\times 10^{23}\ kg) }{(3.397\times 10^6\ m)^2}\\\\g_m = 3.71\ m/s^2[/tex]
Therefore, the acceleration of gravity on the surface of Mars is 3.71 m/s².
Hence, this is the required solution.
2. The students in PE have spent 17/20 of their class period playing basketball.What decimal is equivalent to 17/20?
Answer:
.85
Step-by-step explanation:
just divide 17 by 20
Answer:
0.85 or .85
Step-by-step explanation:
Hope this helps.!!111111
YW
use words to describe what a variable is
Answer: :) If u in college I have to know this already
Step-by-step explanation: :)
PLSSS HELP , ILL MARK BRAINLIST !!! HAVE TO GET IT RIGHT
Answer
It is 6 .
Explanation:
Just plug − 1 in for x in the equation and it gives you the answer
f ( − 1 ) = − 4 × ( − 1 ) + 2 = 4 + 2 = 6
Show all you work plzz
Answer:
[tex]-16+40k[/tex]
Step-by-step explanation:
[tex]8\left(-2+5k\right)[/tex]
Use the distributive law: [tex]a(b+c)=ab+ac[/tex]
[tex]8\times\left(-2\right)+8\times5k[/tex]
[tex]-16+40k[/tex]
Two numbers total 44 and have a difference of 12. Find the two numbers
Answer:
I think an answer is 32 and 12
Step-by-step explanation:
Lauren would like to find the midpoint of a line segment that has endpoints at (–0.5, 3) and (4, 7.5). Which statements are true? Check all that apply. Lauren could solve to find the x-coordinate. Lauren could solve to find the y-coordinate. Lauren could solve (4 + 0.5) – 0.5 to find the x-coordinate. Lauren could solve (7.5 + 3) + 3 to find the y-coordinate. Finding the midpoint is equivalent to partitioning a line segment in a 1:1 ratio.
Answer:2 and 3 and 5
Step-by-step explanation:
Answer:
answers 2,3,5 are correct
Step-by-step explanation:
1) 6x – 5y – 3z = 15
2x – 3y – 4z = 2
y = 4z - 4
Step-by-step explanation:
6x - 5y -3z=15 ...................(1)
2x - 3y - 4z =2 ...................(2)
there are 3 orange fish, 3 red fish, 1 white fish I the fish tank. how many fish are in the fish tank
Answer:
7
Step-by-step explanation:
I went to school once
Answer:
7
Step-by-step explanation:
i read it wrong at first
COEFFICIENT IN THE TERM 20 IS ?
(2+2)^2=2^2∙2^2 true or false
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
U probably don't need my answer anymore
One dozen is 12 items. A bakery made 1,200 cupcakes in one day. Write an equation to show how to find how many dozen cupcakes the bakery
made.
The product of Goran's score and 3 is 39.
Use the variable g to represent Goran's score
Solve v 5x + 11 = 9
O x = -1.6
O x = 4
O x = 14
x = 18.4
Answer:
hope this helped you
please mark as the brainliest (ㆁωㆁ)
A factory that makes can openers has fixed costs for building, fixtures, machinery, etc. of $26,000. The variable cost for
material and labor for making one can opener is $2.75.
What is the total cost of making 20,000 can openers?
Answer:
I think it's B 81,000
Step-by-step explanation:
20000 x 2.75 is 55000
55000 + 26000 is 81000
Answer:is B
Step-by-step explanation:
How would you answer this question?
Answer:
Positive; P increases
Step-by-step explanation:
When gasoline prices go up, the demand for push lawn mowers increases, so the sign of the cross-elasticity is positive.
If gasoline prices go up, and demand for push lawn mowers goes up, then the price for push lawn mowers will also go up.
solve for b
A=h(a+b)2
Answer:
B = (A/(2h)) - a
Step-by-step explanation:
A = h(a+b)2
divide both sides of the equation by 2h
A/(2h) = a+b
subtract a from both sides
(A/(2h)) -a = b
robert has a piece of rope 12 1/2 feet long. he cut rope into pieces that are 1 1/4 feet long. How many of the shorter pieces will he have?
Answer:
divide 25.5 by 6
or change them to fractions
51/2 divided by 6 = 51/2 x 1/6 = 51/12 = 4 3/12 = 4 1/2 feet each
Step-by-step explanation:
Answer:
He will have 10 shorter pieces
To find this, divide 12.5 from 1.25
To check your answer, multiply the answer, 10, by 1.25 and you should get 12.5.
Hope this helped
Simplify.
1/2 (x – 6) + 3/2 (x + 2)
2x + 6
2x
2x-4
2x + 3
What is the slope of the line on the graph?
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Find 2 points
(0, 2) y-int
(-4, 0) x-int
Step 2: Plug into slope formula to find slope m
[tex]m=\frac{2-0}{0-(-4)}[/tex]
[tex]m=\frac{2}{0+4}[/tex]
[tex]m=\frac{2}{4}[/tex]
[tex]m=\frac{1}{2}[/tex]
The graphs below have the same shape. What is the equation of the red
graph?
g(x) = ?
fix) = -X?
Explain what SOHCAHTOA means.
Answer:
It's a mnemonic device to help you remember the three basic trig ratios used to solve for missing sides and angles in a right triangle. It's defined as: SOH: Sin(θ) = Opposite / Hypotenuse. CAH: Cos(θ) = Adjacent / Hypotenuse.
Answer:
SOH CAH TOA is a mathmatical acronym used in triginometry. It helps find missing angels and sides of a triangle.
Step-by-step explanation:
Sine = Opposite side over Hypotenuse ---> SOH
Cosine = Adjacent side over Hypotenuse ---> CAH
Tangent = Opposite side over Adjactent ---> TOA
You use SOHCAHTOA to find the angle. You use the inverses to find the measures.
Which statement is true regarding the graphed functions?
On a coordinate plane, a red curved line with an upward arc, labeled g of x, crosses the x-axis at (negative 2, 0), and the y-axis at (0, 4). A blue curved line with an upward arc, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Answer:
B
Step-by-step explanation:
I take p a p algebra
Answer:
f(0)=g(0)
Step-by-step explanation:
2020 Edg.
In the diagram what is the measure of angle WRS
Answer:it’s 25
Step-by-step explanation:
Why not
Can yall help plz.........................
Answer:
6^-8 or 1/ 6^8
Step-by-step explanation:
When there is a fraction with the same base, then subtract the exponent of the denominator from the exponent of the numerator.
6^-3 / 6^5 = 6^(-3-5) = 6^-8
Which of the following is correct? Multiple Choice When the sample size increases, both α and β may decrease. Type II error can only occur when you reject H0. Type I error can only occur if you fail to reject H0. The level of significance is the probability of Type II error.
Answer:
(A) When the sample size increases, both α and β may decrease.
Step-by-step explanation:
Which of the following is correct?
(A) This option is right.
When a sample's size increases, the values for alpha and beta may decrease; if and only if sample size is the denominator in the slope equation (in each case) and the numerator stays the same (that is, ceteris paribus; all other things being equal). The larger the denominator, the smaller the slope value for alpha and beta.
(B) This option is wrong
Type 2 error can only occur when you fail to reject a true H0
(C) This option is wrong
Type 1 error can only occur if or when you don't reject a false H0
(D) This option is wrong
The level of significance is the probability of a Type 1 error, not the probability of a Type 2 error.
