Answer:
[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringCalculus
Differentiation
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]Step 3: Integrate Pt. 1
Substitute [Surface Area]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property: [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]Step 4: Integrate Pt. 2
[Integral] Define: [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply: [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]Step 5: Integrate Pt. 3
[Integral] Substitute/Integral - FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply: [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]It is in ft² because it is given that our axis are in ft.
Step 6: Find Amount of Glass
Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.
Convert ft² to in²: [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply: [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]And we have our final answer! Hope this helped on your Calc BC journey!
Mr Lee has a family of 6 people and Mrs Scarlett has a family of 4. They were given 15 kg of chocolate
when they visited a chocolate factory for work. If they decide to share it so that each family
member gets an equal amount, determine the required ratio and hence calculate how much
chocolate Mr Lee and Mrs Scarlett will each take home to their families.
Answer:
Mr. Lee takes home 9 kg of chocolate.
Mrs. Scarlet takes home 6kg of chocolate.
Step-by-step explanation:
Mr. Lee has a family of 6 people, and Mrs. Scarlett has a family of 4 people.
Together, the total number of people is 6 + 4 = 10
If we divide evenly the chocolate between all 10, then each one gets the same amount.
Then we need to do the quotient:
15kg/10 = 1.5kg
This means that each person gets 1.5kg of chocolate.
And Mr. Lee has 6 on his family, then the amount of chocolate that Mr. Lee takes home is 6 times 1.5 kg
6*1.5kg = 9kg
Mr. Lee takes home 9 kg of chocolate.
Mrs. Scarlett has a family of 4 people, then she takes home 4 times 1.5kg of chocolate, this is:
4*1.5kg = 6kg
Mrs. Scarlet takes home 6kg of chocolate.
Write an equation for the line that passes through the points (0, -2) and (-4, 0).
y = - x - 4
y = -2 x - 4
y = -2 x - 2
y = - x - 2
Answer:
y=-1/2x-2
Step-by-step explanation:
I dont think any of those options are the right one so thats the correct answer
Answer: y = -1/2x - 2
Step-by-step explanation:
To first write the equation, we need to find the slope and the y intercept and write it in the form y=mx +b
To find the slope, we will find the difference between the y coordinates and divide it by the difference between the x coordinates.
The y coordinates of the points are , 0 and -2
The x coordinates of the points are -4 and 0
0 - (-2) = 2
-4 -0 = -4
Slope: 2/-4 = -1/2
Now using the formula y=mx+b, you will input the slope and use one of the given point's coordinates to solve for b the y intercept.
We will use the point (0,-2)
-2 = -1/2(0) + b
-2 = b
This means the equation will be y = -1/2x - 2
△XYZ is translated up 3 units to form the image ∆X′Y′Z′.
What are the coordinates of the vertices of ∆X′Y′Z′ ?
Enter your answer by filling in the boxes.
Answer:
The coordinates of the vertices of ∆X′Y′Z′:
X'(-4, 9)Y'(1, 9)Z'(1, 4)Step-by-step explanation:
Given the triangle △XYZ with the vertices
X(-4, 6)Y(1, 6)Z(1, 1)It is stated that △XYZ is translated up 3 units to form the image ∆X′Y′Z′.
Translating 3 units UP means we have to add 3 units to all the y-coordinates of the coordinates of the vertices X, Y, and Z to generate the image ∆X′Y′Z′.
Thus,
THE RULE OF TRANSLATING 3 UNITS UP:
P(x, y) → P'(x, y+3)
Therefore, the coordinates of the vertices of ∆X′Y′Z′ will be:
X(-4, 6) → X'(-4, 6+3) → X'(-4, 9)
Y(1, 6) → Y'(1, 6+3) → Y'(1, 9)
Z(1, 1) → Z'(1, 1+3) → Z'(1, 4)
Thus, the coordinates of the vertices of ∆X′Y′Z′:
X'(-4, 9)Y'(1, 9)Z'(1, 4)Least to greatest
8/9 0.51 3/5
Answer:
0.51 ,8/9, 3/5
Step-by-step explanation:
that is pretty self explanatory, i hope that helps!
Please help me!! I'll give Brainliest!! Fairly simple Geometry question!
Answer:
Option AStep-by-step explanation:
Let's look at the options
A. Equal side lengths and equal diagonal lengths.
CorrectB. Impossible without angle measure.
Incorrect. Option A gives us solution.C. Equal side lengths and diagonals bisect each other.
Incorrect. This could be a rhombus.D. Equal side lengths and diagonals.
Incorrect. Diagonals will have a greater length.3 1/2 divided by 3/4
The depth of snow melting on a sidewalk changes over time. The equation below represents
the depth (d) in inch(es) as time (t) passes. How many inches deep is the snow just before
it begins to melt?
Answer:
0.5 inch
Step-by-step explanation:
d=0.5t
if you caculate it right you should get 0.5 inch break it apart to get what you need and the answer is up there if you cant figure it out still.
Answer:
7 inches
Step-by-step explanation: My teacher told me:)
Help help please will give brainliest PLEASE
Answer:
its is the 1st one or the thrid one
Step-by-step explanation:
Someone help please I need help!!
Answer:
hello
Step-by-step explanation:
adjacent angles are equal to 180 degrees,
[tex](2x + 9) + (5x + 3) = 180 \\ 8x + 12 = 180 \\ 8x = 180 - 12 \\ 8x = 168 \\ x = \frac{168}{8} \\ x = 21 \\ \\ [/tex]
but, for some reason, does not match the answers…
Can the answers be wrong?
or I miscalculated…
i hope it helps have a nice day
Answer:
24
Step-by-step explanation:
(2x + 9 )+ (5x + 3) = 180
x = 24
(I just guessed and checked. It was multiple choice so why not?)
who else thinks this is kinda a school social media??
Answer: I totally agree. In fact, it's the closest thing to social media I have LOL
How do I find the area of a circle of 5 inches
Answer:
Area =πr2
Step-by-step explanation:
Hope this Helps
Stacia has 28 red and blue marbles. The ratio of red to blue marbles is 1:6. How many blue marbles does Stacia have?
Answer:
The total number of blue marbles = 24Step-by-step explanation:
Total number marbles Stacia has = 28
The ratio of red to blue marbles = 1 : 6
Let 'r' be the number of red marbles.Let 'b' be the number of blue linesAs the total number of marbles is 28. Thus,
r + b = 28
As the ratio of red to blue marbles is 1 to 6.
It means for each red marble 'r', we have 6 blue 'b' marbles. Thus,
b = 6r
now substituting b = 6r in the equation r + b = 28
r + b = 28
r + 6r = 28
7r = 28
divide both sides by 7
7r/7 = 28/7
r = 4
Thus,
The total number of red marbles ⇒ r = 4
The total number of blue marbles ⇒ b = 6r = 6(4) = 24
Therefore,
The total number of blue marbles = 24Can someone help me please!
Answer:
It would be -5
Step-by-step explanation:
MULTIPLE CHOICE 9th grade math: help me find the formula to the nth term:
Answer:
[tex]a_{n}[/tex] = - 5n - 2
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- 12 - (- 7) = - 17 - (- 12) = - 5
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 7 and d = - 5, then
[tex]a_{n}[/tex] = - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2
Solve the formula a(m+r) -t=s for a.
9514 1404 393
Answer:
a = (s +t)/(m +r)
Step-by-step explanation:
Add t, then divide by the coefficient of 'a'.
[tex]a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}[/tex]
what is the inequality of 2.2m < 11
Answer:
m<5
Step-by-step explanation:
Answer:
m < 5
Step-by-step explanation:
what is the square root of 3 multiplied by 1/2 in the simplest radical form?
Answer:
usbqjqnamallqnbajabqjqnqkqlqlqllqqlqoqoqnajajhchhsgavbsujwhwjwjqqbq.
hshsjwhwjwjuwubwbwwuwhquuwqjqjqkqbqv pangit mo potang ina mo bulok wlang silbe wag kana mag ajabajajajqkqjbqiqiq
Fill in the blanks to complete the equation that describes the diagram.
What would the equation of the line be that passes through the points (-2,3) and (0,2)?
the side pieces of a dog house are 10 1/4 inches long.How many pieces can be cut from a board measuring 61 1/2
Answer:
Step-by-step explanation:
all of them
I need answers for those two questions please.
Answer:
Step-by-step explanation:
1.
sin R=15/39=0,3846
R≈23°
2.
tan 52°= 1,2799
Given the following equation:
y+3= -3(x-2)
m: point: ( , )
Help pliss
Answer:
y= 3x+3
Let's solve for x.
y+3=−3(x−2)
Step 1: Flip the equation.
−3x+6=y+3
Step 2: Add -6 to both sides.
−3x+6+−6=y+3+−6
−3x=y−3
Step 3: Divide both sides by -3.
−3x
−3
=
y−3
−3
x=
−1
3
y+1
Answer:
x=
−1
3
y+1
A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.
What is the approximate probability that exactly one of the four characters will be a number?
1%
11%
28%
44%
The approximate probability that exactly one of the four characters will be a number is 44% option fourth is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9.
Total letters = 26
Total numbers = 10
Total = 10 + 26 = 36
Total possibilities = 36×35×34×33 = 1413720
Password with one number = C(10, 1) = 10
With three letters = C(26, 3) = = 2600
Outcomes = 2600×10 = 26000
Favorable outcomes = 26000×4! = 624000
Probability = 624000/1413720 = 0.44 = 44%
Thus, the approximate probability that exactly one of the four characters will be a number is 44% option fourth is correct.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ5
3. Ramona drank 1 5/8 liters of water during soccer practice. She drank 1 1/4
liters of water on the ride home. Which expression could be used to
determine the amount of water, in liters, Ramona drank altogether?
Answer:
The expression x = [tex]\frac{13}{8}+\frac{5}{4}[/tex] could be used to determine the amount of water drank altogether.
Step-by-step explanation:
Given that:
Amount of water drank during practice = [tex]1\frac{5}{8} = \frac{13}{8}[/tex] liters
Amount of water drank on the ride home = [tex]1\frac{1}{4} = \frac{5}{4}[/tex] liters
Let,
x be the total amount of water drank by Ramona.
x = Water drank during practice + Water drank on the ride home
x = [tex]\frac{13}{8}+\frac{5}{4}[/tex]
Hence,
The expression x = [tex]\frac{13}{8}+\frac{5}{4}[/tex] could be used to determine the amount of water drank altogether.
Help me plzzzzzzz!!!!! ASAP!!!!!!!
Answer:
3/4
Step-by-step explanation:
12/16 = 3/4
7
There are 9 pencils in Bryce's pencil box. 3/4 of the pencils are mechanical pencils.
How many of his pencils are mechanical?
HELP
Answer: 27 mec. pencils
Step-by-step explanation:
Please help me 7th grade math
Answer:
I believe it is C.
Step-by-step explanation:
Sorry if wrong
|2n|-4=8 solve for n
Answer:
n = ± 6
Step-by-step explanation:
absolute value equations usually produce 2 solutions
to get the positive solution just solve normally: 2n - 4 = 8
2n = 12
n = 6
to get the negative solution you must take what is in the absolute value bars and multiply by negative one: -(2n) - 4 = 8
-2n - 4 = 8
-2n = 12
n = -6
Find the product of 2 and 3 and then take that from 8
Answer:
2
Step-by-step explanation:
2*3=6
8-6=2
2×3=6 8-6=2
Step-by-step explanation:
im was a great place
if a ship was on coordinate (6,5) and it moved 5 units, what coordinate is it on now?
Answer:
Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the y-coordinate is positive, move up; if the y-coordinate is negative, move down.
Step-by-step explanation:
Answer:
well which direction?
Step-by-step explanation: