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)) ]
A student taking a Calculus class makes the following statement:
”If f(1) > 0 and f(3) < 0, then there exists a number c, between 1 and 3 such that f(c) = 0.”
Is the statement true? If it’s true, explain why, if it is false, explain why, or give an example that disproves it.
Explanation:
Imagine that f(x) was a road without any gaps. The road can be straight or it can be curved somehow.
Now imagine that a horizontal line is the border between two countries. The country up north is the positive country and the southern country is negative.
f(1) > 0 means we're in the northern country since f(x) is positive here
then f(3) < 0 means we're now in the southern negative country
Somewhere along the road we must have crossed the border at least one time. This must be the case because the road does not have any gaps in it and we cannot teleport. This is what it means to be a continuous function. To draw a continuous curve, you cannot lift your pencil up.
So because f(x) transitions from positive to negative, this means f(x) = 0 at some point at least once. So that's why there exists a c such that f(c) = 0
Can someone pls help me?!?
Answer:
288
Step-by-step explanation:
Answer:
I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.
Step-by-step explanation:
NEED HELP!!!!!!!!!!!!!!!!
Answer:
1=4 being the co interior angle
2=3 being the opposite angle
The largest whale is the blue whale weighing 19,000 kg what is its weight in scientific notation
Answer:
1.9*10^4 kg
Step-by-step explanation:
1.9*10^4 kg
Answer:
1.9 × 10⁴
Step-by-step explanation:
Move the decimal 4 places to the left to get your number less than 10 but greater than one. Every space you moved left is then placed in the position of the exponent for 10.
In the figure, m∠2=(20x+52)° and m∠7=(40x-48)°
For what value of x is m || n ?
Enter your answer in the box.
x = ___
Answer: x=5 m is parallel to n
Step-by-step explanation:
∠2 and ∠7 are alternate exterior angles so they are equal.
So you can create the equation
40x-48 = 20x+52 Subtract 20x from both sides. Add 48 to both sides.
20x = 100
x = 5
if you need m∠2 Substtute 5 for x in 20x+52
20(5) + 52 = 100 +52 m∠2= 152°
m∠7 40(5) - 48 = 200-48 m∠7= 152°
Answer:
x=5 and m is parallel to n
Step-by-step explanation:
give the other person brainliest ^^
Marco need to buy some dog food.at the nearest store,3 bags of dog food costs $10.50.How much would Narco spend on 5 bags of dog food?
Answer:
17.50
Step-by-step explanation:
Answer:
17.50
Step-by-step explanation:
$10.50÷3 = 3.50
3.50×5 = 17.50
HELP!!!!! WILL MARK BRAINLIEST 10 POINTS
Evaluate y5 for y =1.
Answer:
the answer is 5
Step-by-step explanation:
you replace y by 1 and distribute (1)5
Simplify 0.3(x - 2y) + 0.5x - y.
Sorry I would give more points but I really dont have much.
Answer:
0.8x - 1.6y
Step-by-step explanation:
Step 1: Write expression
0.3(x - 2y) + 0.5x - y
Step 2: Distribute 0.3
0.3x - 0.6y + 0.5x - y
Step 3: Combine like terms
0.8x - 1.6y
Answer:
0.8x - 1.6y
-step explanation:
How many terms are in the following:
19x - 4y - 2?
Answer:
3
Step-by-step explanation:
Just count how many terms are there in the expression
Please help thank you!
Answer:
Elimination
Step-by-step explanation:
You can just multiply the bottom equation by 2 and it would cancelled out the ys.
Answer:
Elimination
Step-by-step explanation:
It is elimination because when you eliminate you are adding or subtracting to get one variable. For example, you would do 10y-5y= 5y and 14 + 4 = 18
Did this help!?
simplify 1/2 +1/4 - 1/6
Answer:
look for the LCM of all the denominators, devide the denominators by the LCM and add the numerators( don't forget the signs ), then add and subtract your answers ( by this time the LCM becomes the denominator and the answer from th subtraction and addition of the numerators becomes the present numerator ), then reduce to lowest term the answer gotten
A rental car agency charges a flat fee of $32.00 plus $3.00 per day to rent a certain car. Another agency charges a fee of $30.50 plus $3.25 per day to rent the same car.
Answer:
a rental car agency charges a flat rate fee of $32.00 plus $3.00 per day to rent a certain car
c = 32 + 3d
another agency charges a fee of $30.50 plus $3.25 per day to rent the same car
c = 30.50 + 3.25d
the number of days for which the cost are the same means
32 + 3d = 30.50 + 3.25d
by solving we find d = 6 days
Given: PS=RT, PQ=ST
Prove: QS=RS
Answer:
I) Eq(1) reason: sum of segments of a straight line
II) Eq(2) reason: Given PQ = ST & PS = RT
III) Eq(3) reason: sum of segments of a straight line
IV) Eq(4) reason: Same value on right hand sides of eq(2) and eq(3) demands that we must equate their respective left hand sides
V) Eq(5) reason: Usage of collection of like terms and subtraction provided this equation.
Step-by-step explanation:
We are given that;
PS = RT and that PQ = ST
Now, we want to prove that QS = RS.
From the diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
PQ + QS = PS - - - - (eq 1)
Now, from earlier we saw that PQ = ST & PS = RT
Thus putting ST for PQ & PS for RT in eq 1,we have;
ST + QS = RT - - - - (eq 2)
Again, from the line diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
RS + ST = RT - - - - -(eq 3)
From eq(2) & eq(3) we can see that both left hand sides is equal to RT.
Thus, we can equate both left hand sides with each other to give;
ST + QS = RS + ST - - - (eq 4)
Subtracting ST from both sides gives;
ST - ST + QS = RS + ST - ST
This gives;
QS = RS - - - - (eq 5)
Thus;
QS = RS
Proved
lester hears a strange noise from the house across the street. he Lester hears a strange noise from the house across the street he hurries back into the house and watches from the window. which character trait best describes lester?
blondness
cautiousness
lack of curiasody
kindness
Answer:
cautousness because he is aware of his surroundings
8) Your sister also tries to make a cake for her mom. The recipe requires 3 3/5
cups of flour. If she only wants 3/4 of the recipe, how many cups of flour should
she use to make the cake?
Answer:
2.7 cups of flour
Step-by-step explanation:
75% of 3.6 is 2.7
Help meeee it's math ::Simplify an expression for the perimeter of the rectangle shown
For the equation y=3x+2 if we were to add 7 What effect would it help on the equation.
If you make a copy of a puzzle peice using a scale factor of 0.2 will the copy be larger smaller or the same size
Answer:
sMaLlEr (not sure so sorry please don't hate me dude or dudett
Which of the following shows 2.736 correctly rounded to the tenths place?
Answer:
2.7 is the correct answer
Step-by-step explanation:
Answer:
2.7
Step-by-step explanation:
Does anyone know what the answer is?
Answer:
0.974.
Step-by-step explanation:
You have to use a correlation calculator.
8=2+3d u got to get d. i need this asap
Answer:
d = 2
Step-by-step explanation:
8 - 2 = 6
6 / 3 = 2
plz mark brainliest
Answer:
d=2
Step-by-step explanation:
Switch the left and right sides
2+3d=8
Rearrange the expression
3d+2=8
Separate the constants and variables
3d=8−2
Add or subtract the numbers
3d=6
divide both sides by 3
3d/3=6/3
d=2
hope it helps :)
Given m|n, find the value of x.
(3x+5)*(x-25)
Answer:
-31.5
step-by-step explanation
Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of n components can be viewed as the n trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 1%. Suppose a random sample of five items from a recent shipment is tested.
a. Assume that 1% of the shipment is defective. Compute the probability that no items in the sample are defective.
b. Assume that 1% of the shipment is defective. Compute the probability that exactly one item in the sample is defective.
c. What is the probability of observing one or more defective items in the sample if 1% of the shipment is defective?
d. Would you feel comfortable accepting the shipment if one item was found to be defective? Why or why not?
Answer:
A. 0.9510
B. 0.0480
C. 0.0490
D. No, I would not feel comfortable accepting the shipment if one item was found defective, because the probability is quite small to obtain 1 or more defective items.
Four cups of pure water are added to a 20-cup bowl of punch that is 75% juice. What percentage of the new punch is juice?
Answer:
C
Step-by-step explanation:
Answer:
That would be 62.5%
Step-by-step explanation:
That's what I put and it said it was right...
please give the answer to this
Answer:
l;k
Step-by-step explanation:
qwdefr
Answer:
a= -7, b= 4
Step-by-step explanation:
Please see the attached picture for the full solution.
A line passes through the point (-6,4) and has a slope of 3/2. Write an equation in point slope form for this line.
Answer:
y-4=3/2(x+4)
Step-by-step explanation:
If you plug the numbers into the equation (y-y1=m(x-x1)), you get y-4=3/2(x+4).
Answer: y=3/2x+13
Step-by-step explanation: y-4=3/2(x-(-6))
y-4=3/2x+9
y=3/2x+13
the price of a bookcase including 8% sales tax is $378 what is the price of the bookcase before sales tax
Answer:
$347.76
Step-by-step explanation:
sales tax= $30.24
378 - 30.24 = 347.76
Multiply
g(x) = x2 + 3x
h(x) = 2x - 2
Find (g* h)(2)
Answer:
10
Step-by-step explanation:
At first, (goh)(x)= g{h(x)}
= g{2x-2}
={2x-2}^2 +3x
[tex] = 4 {x}^{2} - 8x + 4 + 3x \\ = 4 {x}^{2} - 5x + 4 \\ then \: \:(goh)(2) = 4 \times {2}^{2} - 5 \times 2 + 4 \\ = 16 - 10 + 4 \\ = 10[/tex]
hope u got it.....
Find the inverse:
[
0 8
-1 -5
Answer:
Hi there!
Your answer is:
D: [ -5 -8
1 0 ]
Step-by-step explanation:
To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc)