Answer:
21π/2
Step-by-step explanation:
94.55π is the area of the required surface.
What is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis?[tex]S=\int\limits^{x_1}_{x_2} {2\pi f(x)\sqrt{1+f'(x)^2} \, dx[/tex]
is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis
How to solve the problem?Given,
[tex]x=\frac{1}{3}(y^2+2)^{\frac{3}{2}}[/tex]
[tex]\implies (3x)^\frac{2}{3}=y^2+2\\\implies y^2=(3x)^\frac{2}{3}-2[/tex]
[tex]\implies y=\sqrt{(3x)^\frac{2}{3}-2}[/tex]
Let
[tex]y=\sqrt{(3x)^\frac{2}{3}-2}=f(x)[/tex]
Now, the range of y is given 3≤y≤4
hence, the range of x is [tex](\frac{1}{3}(3^2+2)^{\frac{3}{2}}[/tex],[tex]\frac{1}{3}(4^2+2)^{\frac{3}{2}})[/tex]=(12.16,25.46).
So, [tex]S=\int\limits^{25.46}_{12.16} {2\pi f(x)\sqrt{1+f'(x)^2} dx\\\\=[\frac{\pi}{2}(3x)^{\frac{4}{3}}-\pi (3x)^{\frac{2}{3}}]^{25.46}_{12.16}\\=101.63\pi - 6.99 \pi \\= 94.55 \pi[/tex]
is the area of the required surface.
Hence, 94.55π is the area of the required surface.
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estimate 2,072-581 by first rounding each number to the nearest hundred
Answer:
1490 is the correct answer
Step-by-step explanation:
2070- 580= 1490
Water Street intersects 25th Street and 28th Street at right angles. Highway 47 is parallel to 28th Street. How are 25th Street and Highway 47 related?
Answer:
25th Street is parallel with Highway 47Step-by-step explanation:
Water Street intersects 25th Street and 28th Street at right angles.
Outcome ⇒ 25th Street and 28th Street are parallelHighway 47 is parallel to 28th Street.
Outcome ⇒ 25th Street is parallel with Highway 47GiveN:
Water Street intersects 25th Street and 28th Street at right angle.Highway 47 is parallel to 28th StreetWhat to do?
How are 25th Street and Highway 47 related[tex]?[/tex]Step-wise-Step Explanation:
If wall Street intersects 25th Street and 28th Street at right angle then they will Parallel (||) to each other. Because,
If two lines are perpendicular to the third line then those two lines are parallel to each other as they will never meet.Now Highway 47 is parallel to 28th Street. It means 25th Street is also parallel to Highway 47 because,
If two lines are parallel to the third line then those two lines are parallel to each other as they will never meet.Thus, They are Highway 47 and 25th Street are parallel to each other. (Answer)
Jorge is at the dollar store buying ballqons for a birthday party. For every 5 balloons he
buys, he pays $6. What is the price per balloon?
Answer:
Step-by-step explanation:
Umm idk-
Somebody please help meee
3√2/(√3 - √2) . (√3 - √2)/(√3 - √2)
3√2(√3 - √2)/(3 - 2)
3√2(√3 - √2)
3√6 - 6
3(√6 - 2)
Answer: 3(√6 - 2)
An investment earn 6% simple interest. What amount of principal is need to have $3000 after 5 years
Answer:
The amount of $1000 principal is needed to have $3000 after 5 years.
Step-by-step explanation:
As the interest formula is
[tex]I=Prt[/tex]
Where
P is the principler is the rate in decimalt is the time in yearsSubstituting the following values in the interest formula and solve for P
I=$3000
r = 6% = 6/100 = [tex]0.06[/tex]
t = 5
so the equation becomes
[tex]I=Prt[/tex]
[tex]3000=P\left(0.06\right)\left(5\right)[/tex]
switch both sides
[tex]P\left(0.06\right)\left(5\right)=3000[/tex]
[tex]P\left(0.3\right)=3000[/tex]
[tex]P=10000[/tex] $
Therefore, the amount of $1000 principal is needed to have $3000 after 5 years.
9.2*10^-3 in standard form
Answer:
9.200 × [tex]10^{-3}[/tex]
I hope this helps!
Irina has 3 hours to finish her final math exam. Keeping in mind that there are 60 minutes in 1 hour, how much time, on average, does she have for each question if there are 45 questions on the exam? 1.5 minutes 2.ModifyingAbove 6 with bar minutes 4 minutes 15 minutes
Answer:
4 minutes per question
Step-by-step explanation:
3 hours = 180 mins
180/45 = 4
4 minutes per question
Answer:
an average of 4 minutes on each
Step-by-step explanation:
Alicia received the following seven scores on her math assignments.
80, 90, 10, 75, 90, 95, 99
Find the mean and median. Which measure of center best represents the data?
Answers:
Mean = 77Median = 90The median is the better measure of center=============================================
Explanation:
Part (1) Finding the mean
Add up the values to get
80 + 90 + 10 + 75 + 90 + 95 + 99 = 539
Then divide by 7 because there are 7 values in this list
539/7 = 77
The mean is 77
--------------------------
Part (2) Finding the median
First we'll need to sort the values from smallest to largest
{80, 90, 10, 75, 90, 95, 99}
will sort to
{10, 75, 80, 90, 90, 95, 99}
The middle most value is 90 since we have three items below it {10,75,80} and three items above it {90, 95, 99}.
The median is 90
--------------------------
Part (3) Which is the better measure of center?
Nearly all of the values are clustered from 75 to 99. The value 10 is an outlier since it's far from the main cluster. There are more technical processes used to find out if 10 is actually an outlier or not, but we won't deal with that right now.
The much smaller outlier pulls on the mean to make it smaller than what it should be. The mean 77 is too small to represent what the center should be. The median is not affected by outliers, which is why it's used in applications such as home prices.
The median 90 is the better measure of center.
Answer:
I tried c and i got it wrong
Step-by-step explanation:
its not c
write the equation in point slope form for a line that passes through the points (-2,3) and (6,-1)
Answer:
y - 3 = -1/2(x + 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Point (-2, 3)
Point (6, -1)
Step 2: Find slope m
Substitute: [tex]m=\frac{-1-3}{6+2}[/tex]Subtract/Add: [tex]m=\frac{-4}{8}[/tex]Simplify: [tex]m=\frac{-1}{2}[/tex]Step 3: Write linear equation
Point-Slope Form: y - 3 = -1/2(x + 2)
Answer:
y = -(1/2)x+2
Step-by-step explanation:
What is the equation of the line that passes through the point (-6,-5) and has a slope of 2/3
Answer:
the answer is y=2/3x-5
136/50
as a percentage?
Answer: 272%
Step-by-step explanation: To write 136/50 as a percent have to remember that 1 equal 100% and that what you need to do is just to multiply the number by 100 and add at the end symbol % .
136/50 * 100 = 2.72 * 100 = 272%
And finally we have:
136/50 as a percent equals 272%
Which expression shows the amount of tax on a T-shirt that costs x dollars, if tax is 7%?
A
0.07x
B
0.07
C
7x
D
7
Answer: A or B
Step-by-step explanation:
Help me I need to be done pls
Answer:
im not 100% sure but i think 1.5
Step-by-step explanation:
sry if not
Answer:
-3
___
2
Step-by-step explanation:
9-(4-1)^2
______
8-2^2
9-(16-1)
______
8-4
9-15
_____
4
-6
___
4
=-3
------
2
Solve -2(2x + 5) - 3 = -3(x - 1) (1 point)
Answer:
x=-16
Step-by-step explanation:
hope this helps!
what conjecture can you make about the sum of firs 52 positive even numbers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete. However, the available details is enough to work out a solution.
Considering the first even number: 2
In this case, n = 1
The sum of the first even term is 2.
Represent the sum as a product:
[tex]2 = 1 * 2[/tex]
Considering the first two even numbers: 2 and 4
In this case, n = 2
The sum of the first two even terms is 6
Represent the sum as a product:
[tex]6 = 2 * 3[/tex]
Considering the first three even numbers: 2, 4 and 6
In this case, n = 3
The sum of the first two even terms is 12
Represent the sum as a product:
[tex]12 = 3 * 4[/tex]
Notice the pattern from n = 1 to 3
[tex]2 = 1 * 2[/tex] --- n = 1
[tex]6 = 2 * 3[/tex] --- n = 2
[tex]12 = 3 * 4[/tex] --- n = 3
------------------------------------
It follows that, the sum when represented as a product is: [tex]n * (n + 1)[/tex]
So, the sum of the first 52 even terms would be:
[tex]52 * (52 + 1)[/tex]
Where n = 52
[tex]52 * (52 + 1) = 52 * 53[/tex]
[tex]52 * (52 + 1) = 2756[/tex]
Hence, the sum of the first 52 even terms is 52 * 53 or 2756
Write an expression so that when you divide ¼ by a number the quotient will be greater than 1/4.
40/ 1/4
40 x 4 = 160
160 is greater than 1/4
Any number that is greater than 0.25 can be your answer
Hope this helps :)
A theatre shows four movies, with a break after each one. Movie 1 starts at 11:00 am. When does Movie 3 start? *
Answer:
Movie 3 starts at 4:15 pm
Step-by-step explanation:
11:00 am + 2 hours 30 minutes + 2 hours 30 minutes + 15 minutes
11: 00 am + 5 hours + 15 minutes = 4:00 pm + 15 minutes
Movie 3 starts at 4:15 pm
how do you get a 15 year old girl to like you when you're 13 and how to tell 8f they'll like you
Answer:
you dont
Step-by-step explanation:
Answer:
sing to her and say- "but age aint nothing but a number" and you'll start dating real quick
Pls answer fast i will mark u brainliest
Answer:
-16 3/28
Step-by-step explanation:
sowwy if wrong owo
1. multiply
-2 3/4 * 5 6/7 = -11/4 * 41/7 = -451/28
2. simplify
-451/28 = -16 3/28
Would someone mind helping me? I really need this answer but I'm so confused. I would appreciate any help :) and if you get the answer right, ill give you brainliest.
Answer:
The answer is A.
Step-by-step explanation:
The equation y=mx+b is shown where m is slope and m=-2 and b is the y-intercept, which b=1 (0,1) is the y intercept.
Andre is writing a paper for science class. He can type 30 words per minute. What is the ratio of words to minutes? Write the ratio three ways. Enter the correct answers in the boxes.
Answer:
30:1 (30 words to 1 minute)
1:2 (1 word to 2 secs)
30:60 (30 words to 60 seconds)
Step-by-step explanation:
Can i get brainliest?
54.55÷5 people what is a good estimate for quotient
See attachment for math work and answer.
please help me guys find the slope
Answer:
[tex]m=4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Pick any 2 points from the chart.
Point (-5, -7)
Point (-4, -4)
Step 2: Find slope m
Substitute: [tex]m=\frac{-4+7}{-4+5}[/tex]Add: [tex]m=\frac{4}{1}[/tex]Divide: [tex]m=4[/tex]Write
7
as a decimal.
25
0
Answer:
0.07
Step-by-step explanation:
Anna got 45 answers correctly out of an unknown number of questions
which was 90% correct. How many questions were there?*
5 or
55 or
60
Answer:
The answer for this problem would be 50.
Step-by-step explanation:
If you calculate 90% of 50, you should get 45 so, the answer is 50.
A runner runs 400m west then changes direction and runs 600m south, If the entire trip takes 35s, what is the average speed? Give your answer in to two decimal places.
Average Speed = Total Distance / Total Time
Total Distance = 400m + 600m = 1,000m
Total Time = 35s
Average Speed = 1,000/35 = 28.57 m/s (approx.)
Answer:Average Speed in two decimal places is 28.57 m/s (approx.)
Is the number 2 composite or prime
Answer:
prime Number
Step-by-step explanation:
because 2 can be only divided by itself and one
Answer:
the number 2 is the only even prime number
is it better to buy 3 gifts and get one free or use a coupon for 20% off of three. which is cheaper i’m too lazy to do it :~|
Answer:
Coupon
Step-by-step explanation:
C O U P O N
Answer:
coupon
Step-by-step explanation:
You are making a poster to support your friend for homecoming. Your original photo is 4 inches by 6 inches. You want the photo on the poster to be 5 feet by 7.5 feet. What is the scale factor of this dilation? PLEASE HELP!!!!
The answer is 9.
We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.
First of all we will convert dimensions of poster from feet to inches.
Now, let us compare sides of our original photo with corresponding sides of poster.
Now, let us compare the second pair of corresponding sides.
We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.
madison and jacob are training for a 5k. Below shows a week of their running log complete the tables
Answer:
asxas
Step-by-step explanation: