The volume of the solid formed by rotating the region about the y-axis is 6π/7 cubic units.
To find the volume of the solid formed by rotating the region bounded by the curves y = x³/4, x = 0, y = 1 in the first quadrant about the y-axis, we can use the method of cylindrical shells.
The formula for the volume using cylindrical shells is:
[tex]\mathrm V = \int\limits^a_b {2\pi \mathrm x \times \mathrm f(x)} \, dx[/tex]
Where:
a and b are the limits of integration (in this case, a = 0 and b = 1 since we are rotating in the first quadrant).
f(x) is the height of the shell at the given x-value.
2πx is the circumference of the shell at the given x-value.
In this case, we need to express y = x³/4 in terms of x to find the function f(x).
Given: y = x³/4
To find the function in terms of x, solve for x:
[tex]x = (4y)^{(1/3)[/tex]
Now, the function f(x) becomes:
[tex]\mathrm f(x) = (4x)^{(1/3)[/tex]
Now, let's calculate the volume using the cylindrical shell method:
[tex]\mathrm V = \int\limits^1_0 {2\pi \mathrm x \times \mathrm 4x^{1/3}} \, dx[/tex]
[tex]\mathrm V = 2\pi \int\limits^1_0 { x^{4/3}} \, dx[/tex]
To integrate, add 1 to the exponent and divide by the new exponent:
[tex]\mathrm V = 2\pi \times (3/7) \times x^{(7/3)} |^0_1[/tex]
Now, evaluate the expression at the limits of integration:
[tex]\mathrm V = 2\pi \times (3/7) \times (1)^{(7/3)} - 2\pi \times (3/7) \times (0)^{(7/3)[/tex]
[tex]\mathrm V = 2\pi \times (3/7) - 0[/tex]
[tex]\mathrm V = 6\pi/7[/tex]
So, the volume of the solid formed by rotating the region about the y-axis is 6π/7 cubic units.
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A video game awards points each time a player finds a diamond. The players' point total increases with each additional diamond the player finds, as shown in the table below.
If n represents the number of diamonds found and p represents the total number of points, write an equation that models the points awarded for finding diamonds in this video game. Use the on-screen keyboard to type the equation in the box.
Answer:
15x-5=y
Step-by-step explanation:
The equation of the line will be written as y = 15x - 5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The given data is,
The number of diamonds Total number of points earned
1 10
2 25
3 40
4 55
5 70
The slope of the line will be,
Slope = ( 25 - 10 ) / 1
Slope = 15
The y-intercept of the line,
y = mx + c
y = 15x + c
10 = 15 + c
c = -5
The equation will be written as,
y = mx + c
y = 15x - 5
Therefore, the equation of the line will be written as y = 15x - 5.
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I’m giving first answer brainliest so hurry it up ya know
Answer:
ummmmmm
Step-by-step explanation:
1. Suppose Alice eats 3 ounces of base 2 cake (doubles her height for each ounce eaten) at each meal. a) What will her height be multiplied by after two meals? b) After three meals? c) After four meals? d) After M meals?
Answer:
a)64
b)512
c)2^12
d)2^3m
Step-by-step explanation:
At every meal, 3 ounces of the cake is eaten
a) After 2 meals, the number of ounces consumed is 6 ounces
For each ounce, height is doubled , for 6 ounces, we have 2 * 2 * 2 * 2 * 2 * 2
Her height is multiplied by 64
b) After three meals
Total consumption is 3 * 3 = 9 ounces
So her height will be multiplied by 2^9 = 512
c) After four meals
Total ounces is 4 * 3 = 12
So her height will be multiplied by 2^12
d) After M meals
Number of ounces is m * 3 = 3m ounces
Her height will be multiplied by 2^3m
Solve the following inequality.
7(6 - 4n) + 4n > 138
Answer:
n <−4
42 - 28n + 4n >138
42 - 24n >138
-24n > 138 - 42
-24n >96
n <−96/24
N <−4
Someone help plz right answer gets to be brainliest
PLEASE HELP ME WITH THIS ASAP
9514 1404 393
Explanation:
1. ΔABC ≅ ΔDEF . . . . . 1. SAS postulate*
_____
The two given congruent sides are either side of the given congruent angle, so the SAS postulate applies. The objective appears to be irrelevant.
Your friend offers to pay you $10 plus $2 per day if you will watch his dog while he’s on vacation. Another friend offers you $15 plus $1 per day to watch her dog during the same time. You cannot do both jobs. Tell which job you would choose and explain why.
Answer:
the first one
Step-by-step explanation:
you get lower down payment but higher fee payment
Answer:
their correct
Step-by-step explanation:
help me and get brainiest, like, and 5 starts!
please help me i’ve tried so many of these and i can’t figure out how to do it
Answer:
15.4%
Step-by-step explanation:
Calculate the volume of both containers.
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
[tex]V_{A}[/tex] = π × 10² × 11 = 1100π ft³
[tex]V_{B}[/tex] = π × 7² × 19 = 931π ft³
Subtract volume of B from volume of A to find quantity left in A
quantity left in A = 1100π - 931π = 169π ft³
To calculate the percentage left in A after B has been filled
[tex]\frac{left}{full}[/tex] × 100%
= [tex]\frac{169\pi }{1100\pi }[/tex] × 100%
= [tex]\frac{169}{1100}[/tex] × 100%
= 15.4% ( to the nearest tenth )
1) Which ordered pair is the solution to the system of linear equations shown on the graph? A) (2,6) B) (2,7) C) (7.2) D) (0.-4)
Answer:
A) (2, 6)
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
The solution set of the systems of equations would be where the 2 lines intersect. According to the graph, the equations intersect at (2, 6). Therefore, our answer is A.
in the state of Texas is about 3/100 of the population lives in the city of fort worth. The population of huston textas is about 3 times tge population of fort worth texas
There are three choices of jelly beans: sour apple, cherry, and blue
raspberry. The probability of getting a cherry is 1/4, blue raspberry is 2/5,
what is the probability of getting sour apple?
Answer:
7/20
Step-by-step explanation:
Total probability=1
Total probability of selecting either cherry or raspberry=¼+²/5=13/20
Probability of getting sour apple=1-13/20=7/20
One brand of cookies is sold in three different box sizes small medium and large the small box has half the volume of the Box the volume of the medium box the volume of the medium boxes X if someone buys one of each size which expression shows the combined volume of the three boxes?
Answer:
3.5x
Step-by-step explanation:
the medium box would be 1x, if small is half the size, its 0.5x, and large is 2x since its 2x the size of medium. add all of them up and its 3.5x size
Is SAM - DEL? If so, identify the similarity postulate or theorem that
applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
Step-by-step explanation:
C
The theorem that applies is Similar SAS.
The correct option is C.
What are similar triangles?Those triangles look the same but are different in size.
And in similar triangles,
the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.
Given information:
SM = 27, angle SMA = 31 degrees, MA = 15, DL = 9, LE = 5 and Angle DLE = 31 degrees.
From the given information, we know that angle SMA is congruent to angle DLE because they both have a measure of 31 degrees. However, we do not have any information about the other angles in the two triangles.
To check if the corresponding sides are proportional, we can compare the ratios of the corresponding side lengths:
SM/ DL = 27/9 = 3
MA/LE = 15/5 = 3
Since the ratio of SM to DL is equal to the ratio of MA to LE, we know that the corresponding sides are proportional.
Therefore, we can use the Similarity-SAS (Side-Angle-Side) postulate to conclude that the triangles are similar. The postulate states that if two pairs of corresponding sides are proportional and the included angles are congruent, then the triangles are similar.
The answer is (C) Similar - SAS.
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im stressing and im losing points. i need help please
Answer:
I think it is X or Y. I might be wrong.
Answer:
∠Y = 85° , side XZ
Step-by-step explanation:
180 = 5x - 1 + 8x + 5 + 4x + 6
180 + 1 - 5 - 6 = 5x + 8x + 4x
170 = 17x
x = 170 / 17
x = 10
∠X = 5(10) - 1 = 49°
∠Y = 8(10) + 5 = 85°
∠Z = 4(10) + 6 = 46°
therefore, the longest side of a triangle is the opposite site of
∠Y = 85° , side XZ
Sas a ribbon that is 5/6 yard long. She cuts off 3/5 of that ribbon and uses it to tie her hair back. She gives the rest to her sister. How much of the original ribbon did she give to her sister?
Answer:
7/30
Step-by-step explanation:
5/6 = 25/30 3/5 = 18/30
25/30 - 18/30 = 7/30
Sas gives 7/30 of the ribbon to her sister.
Hope this helps! :3
PLEASE ANSWER FAST ITS FOR A BIG TEST!!! Find an expression which represents the difference when (−6x+5) is subtracted from (−x−8) in simplest terms. ILL GIVE BRAINLIEST
Answer:
5x-13
Step-by-step explanation:
PLEASE HELP
due today in 20 minutes
i will mark you brainliest
Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year. If no deposits or withdrawals are made during the year, how much money will be in her account after one year?
Answer:
FV= $1,545
Step-by-step explanation:
Giving the following information:
Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year.
To calculate the nominal value of the account after one year, we need to use the following formula:
FV= (P*r*t) + P
FV= future value
P= principal
r= interest rate
t= 1
FV= (1,500*0.03*1) + 1,500
FV= $1,545
Solve the system using substitution. Check your solution.
2x - y= 65
5y = x
Answer:
The solutions to the system of equations are:
[tex]x=\frac{325}{9},\:y=\frac{65}{9}[/tex]
Step-by-step explanation:
Given the system of the equations
[tex]\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}[/tex]
isolate 'x' for 2x-y
[tex]2x-y=65[/tex]
Add y to both sides
[tex]2x-y+y=65+y[/tex]
[tex]2x=65+y[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}[/tex]
[tex]x=\frac{65+y}{2}[/tex]
[tex]\mathrm{Subsititute\:}x=\frac{65+y}{2}[/tex]
isolate 'y' for [tex]5y=\frac{65+y}{2}[/tex]
[tex]5y=\frac{65+y}{2}[/tex]
[tex]10y=65+y[/tex]
subtract y from both sides
[tex]10y-y=65+y-y[/tex]
[tex]9y=65[/tex]
Divide both sides by 9
[tex]\frac{9y}{9}=\frac{65}{9}[/tex]
[tex]y=\frac{65}{9}[/tex]
[tex]\mathrm{For\:}x=\frac{65+y}{2}[/tex]
[tex]\mathrm{Subsititute\:}y=\frac{65}{9}[/tex]
[tex]x=\frac{65+\frac{65}{9}}{2}[/tex]
[tex]x=\frac{325}{9}[/tex]
The solutions to the system of equations are:
[tex]x=\frac{325}{9},\:y=\frac{65}{9}[/tex]
The solution to a system of equations is (5,-19) choose two equations that might make up the system
A. y=-3x-6
B. y=2x-23
C. y=-7x+16
D. y=x-17
E. y=-2x-9
Answer:
E
Step-by-step explanation:
By definition,
Linear equationLinear or first degree equations are of the type ax + b = y, with a≠0, or any other equation in which when operating, transposing terms and simplifying they adopt that expression.
A solution to an equation is a number that can be entered into the variable to make a true number statement.
This caseIn this case, you know that the solution to a system of equations is (5,-19). This is, x=5 and y=-19.
Replacing the value of x in linear expressions, I can calculate the value of y and I must get that y=-19.
A. y=-3×5 -6 → y= -15 -6 → y= -21
B. y=2×5 -23 → y= 10-23 → y= -13
C. y=-7×5+16 → y= -35 +16 → y= -19
D. y=5-17 → y= -12
E. y=-2×5-9 → y= -10 -9 → y= -19
Observing the solutions obtained, the equations that satisfy the solution and make uo the system are option C. and E.
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PLEASEEEEE HELP ME
yes, hl
yes, asa
no not enough info
yes, sas
Answer:
a) Yes, HL
Step-by-step explanation:
[tex]We\ know\ that:\\Both\ triangles\ are\ right\ triangles. (90\ degree)\\They\ share\ a\ common\ side.\\They\ have\ their\ hypotenuses\ corresponding.\\Hence,\\Through\ HL(If\ the\ hypotenuse\ and\ any\ leg\ of\ the\ triangles\ are\ corresponding,[/tex][tex]then,\ the\ two\ triangles\ are\ congruent.)[/tex]
[tex]We\ can\ hence,\ conclude\ that\ the\ given\ triangles\ are\ congruent.[/tex]
What is the decrease percentage of 62 to 31
Answer:
50%
Step-by-step explanation:
Answer: 50%
Step-by-step explanation:
31 is half of 62, so it was a 50% decrease.
(30 points!) Powers of i worksheet
Answer:
x+7=14
x=7
(7)+7=14
Step-by-step explanation:
The equation 2x-7=5+x has exactly one solution. True or false
Answer:
True
Step-by-step explanation:
x=5+7=12
The only solution is x=12.
What is the y-intercept of the equation?
Answer:
5
Step-by-step explanation:
Y=-3x+5
what is 3,910 divided by 25 using the power of 10
A: 25
B: 250
C: 25,000
Answer:
izuocha is superior
Step-by-step explanation:
Answer:
ochaochaochaocha
Step-by-step explanation:
sorry i trying to get attention from someone
find the value of x.
4.
122°
100°
to
144
Answer:
84 degrees i think
Step-by-step explanation:
polygons have their interior angles add up to 540, so you just add up all the angles given and subtract them from 540, then you get your answer.
I need help by score is going down
Answer:
JUST DO IT!
Step-by-step explanation:
Motivation
I will give u a thank you
Answer:
The first one
Step-by-step explanation:
3x6=18
3.6x5=18
