(a) See the attached sketch. Each shell will have a radius y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of
2π (radius)² (height) = 4πy
Then the volume of the solid is obtained by integrating over [2, 4]:
[tex]\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}[/tex]
(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of
2π (9 - x)² (8 - x ³) = 2π (648 - 144x + 8x ² - 81x ³ + 18x ⁴ - x ⁵)
so that the overall volume of the solid would be
[tex]\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}[/tex]
I leave the details of integrating to you.
Liam's monthly bank statement showed the following deposits and withdrawals:
$32.35, -−$114.95, $63.09, $98.79, -−$79.41
If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
Answer:
I think it's $62.32?
Step-by-step explanation:
1. $62.45 USD subtracted by ($114.95 + $79.41) = -131.91 USD
2. $-131.91 + ($32.35 + $63.09 + $98.79) = $62.32
Joe reads 24 chapters of a book in 8 hours. What is his rate chapters per hour?
24 chapters in 8 hours = 3 chapters per hour
24 : 8 = 3
Answer:
3
Step-by-step explanation:
The rate formula is to divide the length by the time.
In this, 24 chapters is the length and 8 hours is the time.
Divide:
24/8 = 3
So, the speed is 3 chapters per hour
Hope this helped.
Hytgvvuccuchccucucuvff hxhxhxhxu u uh
Answer:
Angle 6 = 120 (corresponding angles)
Select two ratios that are equivalent to 27: 9.
Choose 2 answers:
Answer:
1. 9:3
2. 3:1
Step-by-step explanation:
Hope it really helps you
I need help please!!!
Worth 10 points will give brainliest if correct!
Answer:
the x coordinate is 1 and the y coordinite is 5
help me plss im timed :(
Answer:
-138u+56
Step-by-step explanation:
(-8×-10u)+(-8×6u)+(-8×-7)-10u
-80u+(-48u)+56-10u
-80u-48u-10u+56
-138u+56
Answer:
22u + 56
Step-by-step explanation:
https://mathsolver.microsoft.com/en/solve-problem/-8%20%60left(%20-10u%2B6u-7%20%20%60right)%20%20-10u
Maths f(x) type of question please help
Since 1 < x < 5, adding each side by a, where a is negative, gives
a > ax > 5a
and adding b to each side gives
a + b > ax + b > 5a + b
or
5a + b < ax + b < a + b
Since 7 < f(x) < 23, it follows that
5a + b = 7
a + b = 23
Solve for a by eliminating b :
(5a + b) - (a + b) = 7 - 23
4a = -16
a = -4
Solve for b :
-4 + b = 23
b = 27
[IMAGE ATTACHED]
I don’t understand this please help.
Answer:
9
Step-by-step explanation:
1. You would make these to equations equal to each other because there are parellel(they have the same angel)
2. EQUAL these 2 equations together to find r.
3. SOLVING for r
7r - 5 = 6r + 4
r = 9
How do you do this. Please give a full answer and explain why.
Law of Exponent
[tex] \displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }[/tex]
Compare the terms.
[tex] \displaystyle \large{ {a}^{ - n} = {( - 2)}^{ - 3} }[/tex]
Therefore, a = -2 and n = 3. From the law of exponent above, we receive:
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ {( - 2)}^{ 3} } }[/tex]
Exponent Def. (For cubic)
[tex] \displaystyle \large{ {a}^{3} = a \times a \times a }[/tex]
Factor (-2)^3 out.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{( - 2) \times ( - 2) \times ( - 2)}}[/tex]
(-2) • (-2) = 4 | Negative × Negative = Positive.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{4 \times ( - 2)}}[/tex]
4 • (-2) = -8 | Negative Multiply Positive = Negative.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ - 8}}[/tex]
If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.
Hence,
[tex] \displaystyle \large \boxed{ {( - 2)}^{ - 3} = - \frac{1}{ 8}}[/tex]
The answer is - 1 / 8
Find the slope and y-intercept of the following line.
- 10 - x= -5
BER
Find the slope of the line. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
B. The slope of the line is undefined.
(Answer quickly)
Answer:
The Slope of the line is undefined
Step-by-step explanation:
Complete the table of values.
find the relative error of the number 8.6 if both of it's digits are correct
Answer:
if the X number is rounded up to N decimal place then EA=12(10-N)
10⁴ has how many zeros?
Answer:
4 zeros
Step-by-step explanation:
10·10·10·10=10000
Answer:
10,000.
Step-by-step explanation:
10 to the power of 4 = 10 x 10 x 10 x 10 = 10,000. hope this helps
what is the solution to 2x+3= -7
2x + 3 = -7
2x = -7 - 3
2x = -10
x = -10/2
Answer:
Step-by-step explanation:
2x + 3 = -7
2x = -10
x = -5
I need help on this problem!
g(h+2/3)=1 for h
Answer:
[tex]g(h + \frac{2}{3} ) = 1 \\ \\ gh + \frac{2}{3} g = 1 \\ \\ gh = 1 - \frac{2}{3} g \\ \\ h = (1 - \frac{2}{3} g ) \div g \\ \\ h = (1 - \frac{2}{3} g ) \times \frac{1}{g} \\ \\ h = \frac{1}{g} - \frac{2}{3} [/tex]
I hope I helped you^_^
x – Зу +8x47+ 15 – 4у
Answer:
X-7y+391
Step-by-step explanation:
First multiply
8x47=376
Now group those that are the same together
X-3y -4y+376 +15
X-7y+391
Answer:
x - 7y + 391
Step-by-step explanation:
[tex]x - 3y + 8 \times 47 + 15 - 4y[/tex]
[tex]x - 3y + 376 + 15 - 4y[/tex]
[tex] - 3y - 4y = (- 3 - 4)y = - 7y[/tex]
[tex]x - 7y + 376 + 15[/tex]
[tex] = x - 7y + 391[/tex]
Find the amplitude of f(x) = 8 sin(6x + 4) – 3.
9514 1404 393
Answer:
8
Step-by-step explanation:
The amplitude is the coefficient of the sine function: 8.
Answer:
8
Step-by-step explanation:
Amplitude is the onehalf of highest value minus the lowest value
since sine function has maximum 1 and minimum -1, then the highest value of f(x) is 8(1) - 3 = 5 and the minimum value is 8(-1)-3 = -11.
Therefore the amplitude is (1/2) ( 5 +11) = 8.
2____+2_____=5_____
what are the nouns
Answer:
nous hkgjgjdoyufslhddigxupfFuDdyYofzufzplud
Number 2? I’m so confused..
Answer:
answer is 4. each square is 0.5
Step-by-step explanation:
Determine if each term is synonymous to SLOPE.
Answer:
A to C and B to D
Step-by-step explanation:
Thats how it works dude/Bro
Error Analysis jeremy incorrectly says that 2 1/8 is the same as 2.18 Convert 2 1/8 to a decimal correctly. Then explain 's likely error.
Answer:
1 divided by 8 = 0.125 let's replace the 0 with a 2 since 2 is the whole number = 2.125 is correct
Step-by-step explanation:
Jeremy has mistaken 2 1/8 as 2.18 probably because he thought 1/8 was 0.18
The correct decimal value is 2.13.
We have Jeremy who incorrectly said that [tex]2\frac{1}{8}[/tex] is the same as 2.18.
We have Convert [tex]2\frac{1}{8}[/tex] to a decimal correctly.
How will you convert the mixed fraction - [tex]5\frac{2}{3}[/tex] to normal fraction?The method to convert the mixed fraction to normal fraction is -
[tex]5\frac{2}{3}\\[/tex] = [tex]\frac{3\times 5 +2}{3} = \frac{17}{3}[/tex]
According to question, we have -
Mixed fraction = [tex]2\frac{1}{8}=\frac{17}{8}[/tex] = 2.125 = 2.13
Hence, the correct decimal value is 2.13.
To solve more questions on Error analysis, visit the link below -
https://brainly.com/question/11152559
#SPJ2
Plsssssssssssssssssssss help me fast
Answer:
The answer is 95cm2
Step-by-step explanation:
A=b×h
=19×5
= 95 cm2
please mark me the brainliest
Please help review this explain why its wrong and tell me whats right pls
Answer:
for 1st one B is corret
for 2nd one D is correct
Step-by-step explanation:
Arrange the following integers in ascending order, putting the smallest first. Look at the negative numbers first. The smallest negative number is -35, then -2. Then look at the positive numbers.
Simplify 6^9/6^3
20 characters :/
Answer:
=46,656
Step-by-step explanation:
=6^9 =6^3
=10,077,696 =216
=10,077,696 / 216
=46,656
Solve this problem and show the steps please because I’m so confused
Answer:
= 77
Step-by-step explanation:
{3 × [tex]2^{2}[/tex] - 3} -2 × 11
Solve the brackets first
{ 3 × 4 - 3} -2 × 11
{12 - 3 } -2 × 11
9 -2 × 11
9 -22
= -13
Answer:
-13
Step-by-step explanation:
Solve in the bracket first
(3*4 -3) -2 * 11
(12 - 3) -22
9 - 22
-13 is the final answer
write a decimal equivalent to the fraction
[tex]-\frac{7}{10}[/tex]
9514 1404 393
Answer:
-0.7
Step-by-step explanation:
7 goes in the tenths place. That's what seven tenths means. Of course, the decimal number has the same negative sign.
-0.7
A rectangle has sides measuring (4x + 5) units and (3x + 10) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answer:
PART A :
AREA OF RECTANGLE = LENGTH × BREADTH
A = (4x + 5) (3x + 10)
A = 12(x^2) + 55x + 50
PART B: The above is a trinomial with the second degree. Trinomial because it has 3 terms and second degree because the variable(x) is squared.
PART C : Closure under addition and multiplication. Look at the signs.
Find the value of 9 ÷ 2/5
Answer:
22(½)
Step-by-step explanation:
9 ÷ 2/5
9 × 5/2
45/2
22(½)
Answer:
❁ Hello! ❁
9 ÷ 2/5 = 9 × 5/2 = 45/2
Order the following decimals from least to greatest (separated by
commas).
0.33 0.83 0.2 0.57 0.5
Answer:
0.2, 0.33, 0.5, 0.57, 0.83
f(x)=x2
g(x)=x−3
Find the composition of the two functions and show your process:
f(g(x))
Answer:
x²-6x+9
Step-by-step explanation:
f(x) = x²
g(x) = x-3
f(g(x)) = (x-3)²
=(x-3) (x-3)
= x²-3x-3x+9
= x²-6x+9
Answer:
[tex]f(x) = {x}^{2} \\ g(x) = x - 3 \\ f(g(x) = f(x - 3) = {(x - 3)}^{2} \\ = {x}^{2} - 2 \times x \times 3 + {3}^{2} \\ = {x}^{2} - 6x + 9 \\ thank \: you[/tex]