Answers
Part 1
[tex]x = g(y), \ c \le y \le d\\\\\\x = 3+4y^2, \ 1 \le y \le 2\\\\\\\frac{dx}{dy} = 8y, \ 1 \le y \le 2\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+[g'(y)]^2}dy\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+\left[\frac{dx}{dy}\right]^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+(8y)^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+64y^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}\sqrt{1+64y^2}*ydy\\\\\\\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\[/tex]
In the last two steps I let u = 1+64y^2, so du/dy = 128y which leads to ydy = du/128.
Note the change in the limits of integration. If y = 1, then u = 1+64y^2 = 65. If y = 2, then 1+64y^2 = 257
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Part 2
[tex]\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\displaystyle A = 2\pi*\frac{1}{128}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\left(\frac{2}{3}u^{3/2}+C\right)\Bigg]_{65}^{257}\\\\\\\displaystyle A = \frac{\pi}{64}\left(\left(\frac{2}{3}(257)^{3/2}+C\right)-\left(\frac{2}{3}(65)^{3/2}+C\right)\right)\\\\\\\displaystyle A = \frac{\pi}{64}*\frac{2}{3}\left((257)^{3/2}-(65)^{3/2}\right)\\\\\\[/tex]
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Part 3
[tex]\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^3}-\sqrt{65^3}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2*257}-\sqrt{65^2*65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2}*\sqrt{257}-\sqrt{65^2}*\sqrt{65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(257\sqrt{257}-65\sqrt{65}\right)\\\\\\[/tex]
[tex]\displaystyle A = \frac{\pi}{96}*257\sqrt{257}-\frac{\pi}{96}*65\sqrt{65}\\\\\\\displaystyle A = \frac{257\pi\sqrt{257}}{96}-\frac{65\pi\sqrt{65}}{96}\\\\\\\displaystyle A = \frac{-65\sqrt{65}\pi}{96}+\frac{257\sqrt{257}\pi}{96}\\\\\\[/tex]
Related Questions
please help :D I understand them but I need someone to check them :)
Answers
six times jason collection of books and one third of nathan collection add up to 134 books. one third of jason collection and nathans entire collection add up to 31 books
Answers
Answer:
j = 21 and n = 14
Step-by-step explanation:
we have the equations:
6j + n/3 = 134
j/3 + n = 31
54j + 3n = 1206
j + 3n = 93
53j = 1113
j = 21
(21)/3 + n = 31
7 + n = 31
n = 14
What is the equation of the line that is perpendicular to and has the same y-intercept as the given line
Answers
Answer:
y = 5x + 1
Step-by-step explanation:
Visually you can see the slope is -1/5, perpendicular just means opposite inverse so -1/5 becomes 5. Line crosses the y-intercept at point (0, 1).
y = mx + b
y = 5x + 1
Answer:
C.
Step-by-step explanation:
Just took the test
The statement "If a = 6, then 6 = a." illustrates which property?
Answers
Answer
Symmetric law
Step-by-step explanation:
This means that even if you swap the numbers the answer stays the same.
HOPE IT HELPED
HAVE A GOOD NIGHT/DAY
Hello Please Answer Quickly:
Answers
Answer:
17 1/30
Step-by-step explanation:
Answer:
The answer is 1/6.
53/6 is the largest and -26/3 is the smallest.
20 twenty-sevens minus 1 twenty-seven
Answers
Answer:
-100
Step-by-step explanation:
27-127=-100
(-12,8), (9,1)
What is the point-slope form of the equation of the line?
Answers
Answer:
y-y1 = m (x-x1)
where
m is the slope
and (x1,y1) is one of the points given.
You have been given 2 points (-12,8) and (9,1). You can call one of them (x1,y1) and the other (x2,y2). It doesn't matter which one is which.
But before we go further, we need to determine the slope.
We can do this from the points as well.
y2-y1
m = ---------
x2-x1
Let's say
(x1,y1) = (-12,8)
(x2,y2) = (9,1)
This gives us a slope of
y2-y1 1-8 -7 -1
m = --------- = ---------- = ---- = ---
x2-x1 9-(-12) 21 3
Now that we have everything we need
y-8 = (-1/3)[x-(-12)]
Distribute the -1/3
y-8 = (-1/3)x -4
If we add 8 to both sides we have the equation in the slope intercept form (y=mx+b)
y = (-1/3)x + 4
Estimate the total of 3,933+790+3,528+1,830 by adding the numbers and then rounding the result to the thousands place.
Answers
Answer:
The answer to your problem is 10000
Answer: 11,000
Step-by-step explanation:
Rounding to the nearest thousand first gives us,
4,000+1,000+4,000+2,000=11,000.
Can you help plz I need this
Answers
Answer:
110 square cm
Step-by-step explanation:
Answer:
i think it's c. 110 cm
Step-by-step explanation:
hope you pass your test ;)
The record low temperature in Pittsburgh, PA is -22°F. The record high is 103°F. What is the difference in the record high and the record low temperatures?
Answers
Answer:
The difference in the record high and the record low temperatures is 125°F
Step-by-step explanation:
Given a quantity T that varies in time, say T1 and T2, being T1 the initial value and T2 the final value.
The change or difference between the final and the initial values is:
T=T2-T1
The record low temperature in Pittsburgh, PA is T1=-22°F while its record high is T2=103°F
The difference is:
T=103°F - (-22°F)
Note both negative signs multiply to produce a positive sign, and a sum instead of a subtraction:
T=103°F + 22°F = 125°F
The difference in the record high and the record low temperatures is 125°F
Janine opens a savings account with a deposit of $850. The account pays 1.75% interest,
compounded daily. What is the first day's interest? Round to the nearest cent.
Answers
Answer:?????
Step-by-step explanation:
Need Help please i will mark brainliest when it lets me
Answers
Answer:it’s the second one
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
I asked my brother and he said it was that one
I need help with this :/
Answers
Answer:
Plz mark me brainliest!!!!
Step-by-step explanation:
0
90
180
270
380
You had planned to go out for pizza with your friends Saturday night. You’ve all gathered at your place but when you’re about to leave, it starts to snow heavily, so you decide to have a pizza party at your place. The pizza delivery guy shows up with your order much sooner than you expected. The bill is $133.32. How much would you tip him? Explain your reasons for deciding how much to tip.
Answers
Answer:
$20
Step-by-step explanation:
the delivery guy show up early and that guy deserve 20bucks
solve equation with variable on both sides
2(3r-4)=4r=3
Answers
Step-by-step explanation:
your problem can't have two equal however if you mean 2(3r-4)=4r + 3 its equal to 11/2. but if you mean 2(3r-4)=4r(3) its equal to -4/3
What is the domain of this function?
Answers
Domain = inputs = x = { 1 , 2 , 3 }
Range = outputs = y = { 2 , -1 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Of the 1,400 students enrolled at Berkmar Middle School, 40% of students enrolled are in the 6th grade. How many students are enrolled in 6th grade? Show your work.
ASAP
Answers
Answer:
3500
Step-by-step explanation:
1400 divided by 40% = 3500
Anyone have the guided notes answers from this point up to the unit test ? Geometry A
Answers
Answer:
vvhcfggfcc
Step-by-step explanation:
ccgvvhhh I don't I need more points buddy
I need your help! there’s a photo above ^^
Answers
Answer:
1. c 2. No, its not the original figure. Its 270 degree turn.
Step-by-step explanation:
Answer:
1.) C 2.) choice d flipped left to right.
The three sides of a triangle are: 16, 12 and 22. Is the triangle Acute, Right, or Obtuse?
Answers
Evaluate the expression when x = 12 and y = 2.
x above 3y
38
2
125
8
Answers
12/3(2)
12/6
2!!!!!!
Identify all the numbered angles that are congruent to the given angle.
Justify your answers.
Answers
Answer/Step-by-step explanation:
The reasons for the stated numbered angles that are congruent to the given angles are written in the parentheses as follows:
7. <7 ≅ 65° (alternate interior angles)
<4 ≅ 65° (corresponding angles)
<1 ≅ 65° (vertical angles)
8. <4 ≅ 51° (alternate interior angles)
<5 ≅ 51° (corresponding angles)
<7 ≅ 51° (vertical angles)
9. <1 ≅ 120° (corresponding angles)
<3 ≅ 120° (alternate angles)
what is the answer? pls help
Answers
Answer:
for the line to have a constant slope, the difference of every y- ordinate with the last ordinate has to be equal
to check this, we will use the following formula
y4 - y3 = y2 - y1
if both the LHS and the RHS are equal, the slope is constant and is irregular otherwise
5 - 8 = 7 - 3
-3 = 4
LHS ≠ RHS
Since LHS is not equal to RHS, the slope is NOT constant and hence keeps increasing or decreasing irregularly
Therefore, option 4 (Not a line) is correct
Answer:
it is not a constant line
Step-by-step explanation:
each x value increases by 1, but the y values are all over the place and are in no order.
What is the slope of the line that passes through points (-3,5) and (11,5)
Answers
Answer:
slope = -3/14
Step-by-step explanation:
y1 - y2 / x1 - x2
They gave you one value, two total coordinates
5-5 = 1
-3 - 11
-14
1/-14
y=1/-14 + b
11= 1/-14(-3) + b
11 = -3/14 + b
17 + 14
b = 15 3/14
4) 41 25h+6
十十十十十十十十十十十十十>
3210 12 3 4 5 6 7 8 9
Answers
Step-by-step explanation:
buena suerte con todo....
At pizza express it takes 6 cups of cheese to make 15 pizzas. At perfect pizza it takes 4 cups of cheese to make 6 pizzas. If the number of pizzas,y,is proportional to the cups of cheese,x, which pizza place has a larger constant of proportionality?
Answers
Pizza Express has a larger constant of proportionality than Perfect Pizzas because 1.6 > 1.5
15/6 6/4
Simplify
5/3 > 3/2
PE: 5/3 or 1.6
PP: 3/2 or 1.5
I had this on my math test
THIS IS ALGEBRA 1 PLEASE HELP IM IN MIDDLE SCHOOL
Answers
Answer:
1.80 + 3.72 (0.25 x b) = 13.02
Step-by-step explanation:
First, combine the "one-time" costs (the medium pendant and the medium chain)
1.80 + 3.72 = 5.52
Now, multiply the cost of the beads by the amount of beads you want
0.25 x 30 = 7.50
Now combine both costs to get the total cost
5.52 + 7.50 = 13.02
It would cost Tamara $13.02 to make a medium length necklace
The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.58 to 32.51 fluid ounces. Find the standard deviation in volumes of quart-size Hellmann's mayonnaise jars (in fluid ounces). NOTE: There are 32 fluid ounces in a quart.
Answers
Answer:
0.27
Step-by-step explanation:
The standard deviation of a uniform distribution is:
σ² = (b − a)² / 12
σ² = (32.51 − 31.58)² / 12
σ² = 0.0721
σ = 0.268
Rounded to the hundredths place, the standard deviation is 0.27.
To solve this question, we use concepts of the uniform probability distribution.
Using this, we get that the standard deviation in volumes of quart-size Hellmann's mayonnaise jars is of 0.2685 fluid ounces.
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.58 to 32.51 fluid ounces.
This means that [tex]a = 31.58, b = 32.51[/tex]
Find the standard deviation in volumes of quart-size Hellmann's mayonnaise jars (in fluid ounces).
[tex]S = \sqrt{\frac{(32.51 - 31.58)^2}{12}} = 0.2685[/tex]
Thus, the standard deviation is of 0.2685 fluid ounces.
A similar example is given at https://brainly.com/question/15855314
how can I do this someone explain me
Answers
Answer: Converse: If the candy has 350 calories, the candy is chocolate, False. There is another 350 calorie candy.
Inverse: If the candy does not have 350 calories, the candy is not chocolate. True In this case, the evidence in the chart supports this. The inverse is not always true.
Contrapositive: If the candy does not have 350 calories, the candy is not chocolate. True The evidence in the chart supports this statement, and the Contrapositive is generally considered a logical equivalent of the original.
Step-by-step explanation:
You need to have a basic frame for converting the original statement to the other forms such as
Original: If P, then Q
Converse: If Q, then P Just reverse the parts
Inverse: If not P then not Q In the same order, make both negative, add "not"
Contrapositive: If not Q then not P Reverse the order of the original and make both negative.
Seven friends bought pizza. Each friend pitched in the same amount. If the pizza came to a total of $14.49, how much did each friend pay?
Answers
Answer: 7p = $14.49
Step-by-step explanation: BRAINLIEST MEEE
