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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What is equivalent to -(-2)
what is the answer to x - 8 < -2
Answer:
X < 6
Step-by-step explanation:
Add 8 to both sides
x < 6
Answer:
X<6
Step-by-step explanation:
x-8<-2
So first off, you want to get X by itself. To do that you have to do the opposite of what the number is. If the number is negative you add it. If the number is positive, you subtract it. What you do on one side, you do on both.
x-8<-2
+8 +8
X<-2+8
Next, You need to add alike terms.
X<6
A box of oat cereal costs $4.37 for 19 ounces. A box of rice cereal costs $3.77 for 13 ounces.
Which box of cereal costs less per ounce? Complete the explanation and give your answer.
Answer:
Oat cereal cost less per oz.
Step-by-step explanation:
OC: 4.37/19=0.23
RC: 3.77/13=0.29
oat cereal shows up as less for one ounce
If 11 + 11 = 22 and 10 + 12 = 22 then which of the following is true?
A. 11 + 10 = 11 + 12
B. 11 + 11 = 10 + 12
C. 11 + 11 = 12 + 12
D. 10 + 11 = 12 + 13
show your work
Answer:
B. 11+11=10+12
Step-by-step explanation:
11+11 is 22
And 10+12 is 22
So the statement is true because both sides are equal
Evaluate the expression shown for x = 9.
-5/6x +7.
A.-13 1/3.
B.-1/2.
C.7 1/3.
D.9 2/3
Answer:
B. 1/2
Step-by-step explanation:
Make 9 an improper fraction, then multiply by -5/6.
-5/6 times 9/1 = -45/6.
-45/6 cannot be simplified, so you make it a mixed number.
-7 1/2.
Add the 7 to -7 1/2 and that cancels out to 1/2
I will give brainliest to the best answer.
A random two digit number (10-99) is drawn. Find each probability
1. p(32)
2. p(odd number)
3. p(a multiple of 5)
My teacher gave an assignment on this and didn't even teach how to do it.
Given that two digit numbers are used and one digit is drawn randomly.
Sample space = {10,11,...99}
n(S) = 90
32 is only one number favorable
Hence P(32) = 1/90
----------------------------
Odd numbers are exactly 45.
Hence prob (odd number) = 45/90 = 1/2
-------------------------------------
Multiples of 5 are 10,15,.....95
There are exactly 18 numbers.
Hence P(a multiple of 5) = 18/90 =1/5
Have an amazing day! <3
Please help!
if the ball family has a child in 8 years how much can I expect to spend to raise a child per year from birth to 5 years of age ?
A). $22,800
B). $21,530
C). $20,890
D).$18,240
Answer: 22,800
Step-by-step explanation: Depends on what you do that year
What is the distance between A(3,7) and B(4,2)?
Round your answer to the nearest tenth.
A. 5.1
B. 4.9
C. 11.4
D. 7.9
Answer:
A. 5.1Step-by-step explanation:
[tex]d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\A(3,7)\quad\implies\quad x_A=3\,,\ y_A=7\\\\B(4,2)\quad\implies\quad x_B=4\,,\ y_B=2\\\\d=\sqrt{(4-3)^2+(2-7)^2}= \sqrt{1^2+(-5)^2}= \sqrt{1+25}= \sqrt{26}\approx5.1[/tex]
What is the y-intercept of the equation?
Answer:
6
Step-by-step explanation:
We need to make the 2y into just y, so divide the whole equation by 2. Now you have
y = 3x + 6. Since 6 represents B in the equation, and b is the y-intercept, the y-intercept is 6
~theLocoCoco
I have no clue how to answer this?
is 2/4 greater then 5/6?
Answer:
No 5/6 is greater
Step-by-step explanation:
2/4 is half. Half of 6 is 3.
Equations
6) 2x + 3y = -1
3x + 4y = -4
Answer:
x = -8
y = 5
Step-by-step explanation:
2x = -3y-1
x = (-3y-1)/2
3x + 4y = -4
3[(-3y-1)/2]+4y = -4
(-9y-3/2)+4y = -4 (x2 all)
-9y-3+8y = -8
-9y+8y = -8+3
-y = -5
y = 5
3x+4.5 = -4
3x+20 = -4
3x = -24
x = -8
checking:
2.(-8)+3.5 = -1
-16+15 = -1 (checked)
Does anyone know how to do this?
Step-by-step explanation:
I just solved this problem you can see my answers of this question
PLEASE ANSWERRRRRRRR!!!
What is the value of, when x^2+5=21?
Have a good day!!
Answer:
x= 4 or -4
Step-by-step explanation:
take the root of both sides then solve
hope this helped♥
Will mark brainliest for whoever answers
Answer:
Uh is it B, what kind of question is this
Step-by-step explanation:
Answer:
i think it is b
Step-by-step explanation:
14. Graph
y>-1/2x-4
Y
Answer:
Step-by-step explanation:
both of those equations that are in the system are lines
first line it has a y-intercept at (0, -4) and a slope -1/2 so you can use that to
find another point ( 2 ,-5)
Since the equation has ≥ DRAW a solid line trough points (0, -4) and (2,-5)
Now highligt above the line since (0,0) cheks for the equation
second line goes troughh the points (0,1) because of y-intercept and point (1,2) because the slope is m=1
draw a solid line trough those points and highlight under the line
the intersection of the 2 highlighted ares is your solution
Which statement describes the term salary?
A.
Salary refers to the fixed amount paid on a daily basis.
B.
Salary refers to the varying amount paid on a daily basis.
C.
Salary refers to the fixed amount paid on a weekly, bi-weekly, or monthly basis.
I need the answer please
Answer: i'm sorry i can not answer your question cos i can't see the last part of the problem but i riley wish i could but since i cant i'll thank you and rate you with 5 stars if you want to be friends we can just follow me and friend me you don't have to if you don't want to so stay safe around others
Step-by-step explanation:
I'd really appreciate your help, please no joke answers
Find the distance from (7, -4) to y+3x - 5
Procedure would be apreciated
Image attached and an explaination I don't fully understsand
Answer:
d= 2√10
Step-by-step explanation:
y= 3x - 5
3x - y - 5=0
d= | 3* 7 +(-1) * (-4) + (+5) |
________________
[tex]\sqrt{3^{2} } + (-1)^{2}[/tex]
d = | 20 | / [tex]\sqrt{10}[/tex]
d = 20 / [tex]\sqrt{10}[/tex]
d = 2[tex]\sqrt{10}[/tex]
The original price of a marker is $5.00 What will the new price be after a
15% increase ? *
Answer:
5.75
Step-by-step explanation:
for a 15% increase, you multiply 5.00 x 1.15. you then get 5.75. hope this helps!
Answer:$5.75
Step-by-step explanation:
Complete the table.
$80,20%
what is the sale price
Answer:
if the shoes are $80 and you take 20% off it is $64Step-by-step explanation:
What is the product of this multiplication?
Answer:
69
Step-by-step explanation:
just cause
Geometry...Please help as soon as possible please and Thank you!!!
Answer:
Step-by-step explanation:
Statement1. ST║UV
Reason 1. Given
Statement 2. ∠U≅∠T (A)
Reason2. Alternate interior angles
Statemnt 3. ST≅UV (S)
Reason3. Given
Statement 4. ∠S≅∠V (A)
Reason 4. Alternate interior angles
Statment5. ΔSTW≅ΔVUW
Reason5. ASA theorem of congruency
Answer:
GOOD LUCK ❤️
Step-by-step explanation:
.........
Monday: 10 apples and 5 bananas
cost £4.20
Friday: 8 apples and 10 bananas
cost £5.40
Find the cost of each.
Answer:
An apple costs £0.25
A banana costs £0.34
Step-by-step explanation:
HELP PLS I JUST HAVE 10 MIN ILL PICK BRIALIAST
Answer:
0.6
Step-by-step explanation:
Brainliest please
10 points
This morning, Suzie took a history test. There were 74 multiple-choice
problems on the test and Suzie answered 50% of them correctly. How
many problems did Suzie get right?
565 miles in 12 hours
Does -45 belong in natural numbers or whole numbers (giving brainliest)
Answer:
Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.
Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…
Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…
Step-by-step explanation:
Victoria uses
3/16
cup of flavored syrup to make an Italian soda. She has 2 cups of flavored syrup left. How many Italian sodas can she make?
A.
9 3/8
B.
10 2/3
C.
11 1/4
D.
12 1/2
Answer:
B. or 10 2/3
Step-by-step explanation: Because if she had only 2 cups left then 1 cup can make 5 drinks so 10 then the rest would be a fraction.
She can make 32/3 of Italian sodas with 2 cups of flavored syrup.
What is a fraction?
A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Victoria uses 3/16 cups of flavored syrup to make an Italian soda.
Assume that 3/16th of x is 1.
∴ (3/16)x = 1.
3x/16 = 1.
3x = 16.
x = 16/3,
Now from 2 cups of flavored syrup, we can make 2x of Italian soda.
Which is (16×2)/3.
= 32/3
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PLEASE HELP I KNOW ITS EASY BUT I FORGOT!!!! PLEASE HELP!! Write -3/8 as a decimal.
Answer:
-0.375
Step-by-step explanation:
You can write fractions as equations and solve for a decimal.
-3/8 = -3 ÷ 8
-3 ÷ 8 = -0.375
Answer:
I got you bro
Step-by-step explanation:
-0.38