Answer: the area of the resulting surface is π/16 [ 4√(17) + In( 4 + √( 17)) ]
Step-by-step explanation:
Given that;
y = e^(-4x), x ≥ 0
then, dy/dx = -4e^(-4x)
now, √( 1 + (dy/dx)² ) = √( 1 + ( -4e^(-4x))²) = √( 1 + 16e^(-8x)
so the surface area of the surface obtaining by rotating the curve y = e^(-4x) on ( 0, ∞ ) about x-axis is,
S = ₀∫^∞ 2πy √( 1 + (dy/dx)² ) dx
S = ₀∫^∞ 2πe^(-4x) . √( 1 + 16e^(-8x) dx
S = 2π. ₀∫^∞ e^(-4x) . √( 1 + 16e^(-8x) dx
so LET 4e^-4x = u ⇒ -16e^(-4x) dx = du
⇒e^-4x dx = du/ -16
so whenx = 0, then u =4 and when x → ∞ then e^(-4x) → 0 so u →0
therefore
S = 2π ₄∫⁰ √(1 + u²) . du/-16
= π/8 ₀∫⁴ √(1 + u²) . du
= π/8 [ u/2√(1 + u²) + 1/2 In ( u + √( 1 + u²) ]₀⁴
WE MAKE USE OF
∫√( a² + u²) du = u/2√(a² + u²) + a²/2 In ( u + √( a² + u²)) + C
so
= π/8 [ 4/2√(1 + 16) + 1/2 In ( 4 + √( 1 + u16 ]
= π/8 [ 2√(17) + 1/2 In ( 4 + √( 17)) ]
= π/16 [ 4√(17) + In( 4 + √( 17)) ]
therefore the area of the resulting surface is π/16 [ 4√(17) + In( 4 + √( 17)) ]
In the figure, m∠1=(2x+40)° and m∠8=(12x−20)° . PLEASE HELP
For what value of x is m∥n ?
Enter your answer in the box.
x =
Answer: x = 6
Step-by-step explanation:
Angles 1 and 8 are alternate exterior angles, so they are equal.
so you can create an equation to solve for x
12x−20 = 2x+40 Subtract 2x from both sides. Add 20 to both sides
10x = 60
x = 6
if you need the m∠1, Substitute 6 for x. (2x+40)° 2(6) +40= 12+40 m∠1= 52°
m∠8=(12x−20)° 12(6) - 20 = 72-20 m∠8 = 52°
Whats 2x2 i will give you 14 points
Answer:
4
Step-by-step explanation:
2×2=4
hope that helped
Answer: 4
Step-by-step explanation: 2 x 2 = 4 dummy
Solve for x: 6(2x - 4) = 7(21 - 8)
Answer:
[tex]9 \frac{7}{12} [/tex]
Step-by-step explanation:
Expand:
[tex]6(2x) + 6( - 4) = 7(13) \\ 12x - 24 = 91[/tex]
+24 on both sides:
[tex]12x = 91 + 24[/tex]
Simplify:
[tex]12x = 115[/tex]
÷12 on both sides:
[tex]x = 115 \div 12 \\ x = 9 \frac{7}{12} [/tex]
Answer:
x = 9.583 or 115/12
Step-by-step explanation:
Hope this helps!!
Brian bought 14 packs of 9 tickets each he also found 6 more tickets how many tickets does he have in all
Answer:
756
Step-by-step explanation:
14x9x6=756
Answer:
it is 132
Step-by-step explanation:
14x9+6
PLEASE HELP URGENT !
Write a compound inequality for the graph shown below. Use x for your variable.
x < -7 or x ≥ 7
I hope this helps!
THIS IS DUE IN 1 HOUR I WILL MARK BRAINLIEST
Jack has 24 game cards. He divides them between his brother, his sister, and himself in the ratio 2:1:5. How many cards does each get?
THERE IS 15 POINT WAITING FOR YOU
Answer:
brother gets 6 cards
sister gets 3 cards
he gets 15 cards
Answer:
8
Step-by-step explanation:
(1/5) ^ 3 * (1/5) ^ 4 * (1/5) =
9514 1404 393
Answer:
(1/5)^8
Step-by-step explanation:
The applicable rules of exponents are ...
a = a^1
(a^b)(a^c) = a^(b+c)
__
(1/5)^3 · (1/5)^4 · (1/5) = (1/5)^(3+4+1) = (1/5)^8
= 1/390625
How many times do you need to regroup to add 873 + 465 ? Explain .
Answer:
2
Step-by-step explanation:
To find the answer to this question, we need to add the numbers according to their place. Etc if 1 and 4 are together in a hundreds place, we add them together. If both numbers add up together results in a number bigger than 9, we have to regroup.
First, let us find the ones place.
3+5=8
Since the result is not more than 9, we do not have to regroup.
Secondly, we find the tens place.
7+6=13
Since the result is more than 9, we have to regroup.
Regrouping counter:1
Thirdly, we find the hundreds place.
8+4=12
Regrouping counter:2
Hence, your final answer is 2.
The number of times we need to group when summing 873 and 465 is 2.
During addition of two numbers, values are added based on their place values, such that digits with the same place value are added together.
The highest single value that can be obtained when summing values without needing to regroup is 9.
Hence, each time two digits are added such that the value of the sum exceeds 9, then regrouping is required.
Adding 873 + 465
H __ T __ U
8 __ 7 __ 3
4 __ 6 __ 5
(3 + 5) = 8 ( NO NEED TO REGROUP)
7 + 6 = 13 (WE NEED TO REGROUP) SUM exceed 9
(8 + 4 + 1) = 13 (WE NEED TO REGROUP) SUM exceed 9
Hence, the number of times we need to regroup is 2.
Learn more : https://brainly.com/question/5117026
Sarah and Jane both brought new storage containers for packing away winter clothing. Sarah’s storage containers are cubic meters, of the storage container. Jane’s containers are prism shaped, and the height of each in her set can be determined by the following graph.
Answer: the answer is Sarah
Step-by-step explanation:
Just got it correct on Plato
Find the midpoint of the segment with the following endpoints.
(-6, 4) and (-1,-6)
Answer:
Hello
Midpoints of (-6,4),(-1,-6)
P(a,b)=(x1+x2/2),(y1+y2/2)
=(-6+-1/2),(4+-6/2)
=(-7/2),(-2/2)
=(-7/2),(-1)
Midpoints of the segment with endpoints (-6, 4) and (-1,-6) are (-7/2),(-1)
Hope it helps you......
What is the slope of the line on the graph?
Answer:
2/4
Step-by-step explanation:
You would have to count the number of units (rise over run)
Answer:
the slope is 1/2 .
Step-by-step explanation:
3 + |-7| I would like some help
Answer: The answer will be -4
You baked a total of 270 cookies for your school using three shapes:
stars, circles, and hearts. You have four times as many stars as
circles. The number of hearts is ten less than five times the number
of circles. How many hearts are there?
Answer: They are only 5 heart remaining.
Step-by-step explanation:
Please help with these two questions, 20 points
Answer:
1. Coefficient
2. Variable
44% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
A Ferris wheel has a radius of 65 feet. What is the
circumference of the wheel? (This is the distance each
passenger will travel in one complete revolution.)
Round to the nearest tenth, and use
T 3.14
Answer:
408.41 feet
Step-by-step explanation:
C = 2πr
C = 2π(65)
C = 408.41 feet
show your work and please hurry
−16 + x = −15
Answer:
x-1
Step-by-step explanation:
-16+1 16-15=1
To get -15 move 1 in the positive direction or backwards
or if this helps ignor the - and just subtract 16 from 15
Answer:
x = 1
Step-by-step explanation:
Add 16 to each side, so it now looks like this: x = 1I hope this helps!
Given f(x) = {(4 - x), what is the value of f(16)?
Answer:
f(16)= 4-16
f(16)= -12
what is y + 1=x in slope intercept form?
Answer:
My answer is in the equation
Step-by-step explanation:
where m is the slope and b is the y-intercept. Subtract x from both sides of the equation. Multiply both sides by −1
write an equation to solve for x your only writing the equation 7x +9 5x +3 will mark brainiest
Answer:
-3
Step-by-step explanation:
7x+9=5x+3
2x+9=3
2x=-6
x=-3
Answer:
equation is 7x +9 = 5x +3x = -3Step-by-step explanation:
7x +9 = 5x +3
combine like terms
7x - 5x = 3 - 9
2x = -6
x = -6/2
x = -3
proof:
7x +9 = 5x +3
7(-3) +9 = 5(-3) +3
-12 = -12 ---- ok
You are at a restaurant and the check comes to a total of $23. If you want to leave a 20% tip, how much total money should you pay, to the nearest cent?
Answer:
$27.60
Step-by-step explanation:
23×1.2=27.60 is the answer
An auto mechanic earns $498.75 in 35 hours during the week. His pay is $2.50 more per hour on weekends. If he works 6 hours on the weekend in addition to 35 hours during the week, how much does he earn?
Answer:
$513.75
Step-by-step explanation:
An auto mechanic earns $498.75 in 35 hours during the week. His pay is $2.50 more per hour on weekends.
$498.75 + $2.50 × x
If he works 6 hours on the weekend in addition to the 35 hours during the week:
$498.75 + $2.50 × 6
= $498.75 + $15
= $513.75
Percent decrease from 275 to 242
A cube has a volume of 8 cubic inches. What is the length of each edge of the cube?
Answer:
2in
Step-by-step explanation:
because 2x2x2=8
Please help I’m not sure if my answer is correct!!!
Answer:
i would say it is GOOD JOB
Step-by-step explanation:
A chicken traveled 4.5 miles in 30 minutes . A squirrel traveled 4 miles in 20 minutes . Which animal traveled at a faster rate ?
Answer:
The squirrel
Step-by-step explanation:
4.5/30 is 0.15 per minute while the squirrel is 4/20 which equals 0.2 per minute. 0.2 is greater than 0.15 making the squirrel faster. Hope this helps!
What Is 3 times blank equelas 27?
Answer:
3 * 9 = 27
Step-by-step explanation:
3 * 9 = 27
Answer:
3 times 9 equals 27
Step-by-step explanation:
3x1=3
3x2=6
3x3=9
3x4=12
3x5=15
3x6=18
3x7=21
3x8=24
3x9=27
porcentaje de 70 y 35
Answer:
50%
Step-by-step explanation:
35/70 = 50%
Answer:
debe ser 30 porque la distancia entre 70 y 35 es 40.
Step-by-step explanation:
70 - 35 = 35
Show all work to multiply quantity 6 plus the square root of negative 64 end quantity times quantity 3 minus the square root of negative 16 end quantity
Answer:
2
Step-by-step explanation:
(6 + square root of -64) - (square root of -16)
6 - 8 + 4
2
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression [6 + √(-64)] [3 - √-16] when simplified is equal to 50.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
What is a complex number?A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = -1; every complex number may be represented as a + bi, where a and b are real numbers.
The given expression can be written as,
[6 + √(-64)] [3 - √-16]
= (6 + 8i)(3 - 4i)
= 18 - 24i + 24i - 32i²
= 18 - 32(-1)
= 18 + 32
= 50
Hence, The given expression [6 + √(-64)] [3 - √-16] when simplified is equal to 50.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ2
The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities. He charges $200 for these events, and the club is charging 51.50 for
tickets with a chance to have the psychic read the ticket holder's mind.
Let x represent the number of tickets sold and y represent money. Fill in the items below for the linear model
Y=? X +?
How much would the club gain or lose by selling 100 tickets?
How many tickets are needed to break even? (Round to nearest whole ticket)
