Answers
Part 1
\(x = g(y), \ c \le y \le d\\\\\\x = 3+4y^2, \ 1 \le y \le 2\\\\\\\frac{dx}{dy} = 8y, \ 1 \le y \le 2\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+[g'(y)]^2}dy\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+\left[\frac{dx}{dy}\right]^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+(8y)^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+64y^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}\sqrt{1+64y^2}*ydy\\\\\\\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\)
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
\(\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\displaystyle A = 2\pi*\frac{1}{128}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\left(\frac{2}{3}u^{3/2}+C\right)\Bigg]_{65}^{257}\\\\\\\displaystyle A = \frac{\pi}{64}\left(\left(\frac{2}{3}(257)^{3/2}+C\right)-\left(\frac{2}{3}(65)^{3/2}+C\right)\right)\\\\\\\displaystyle A = \frac{\pi}{64}*\frac{2}{3}\left((257)^{3/2}-(65)^{3/2}\right)\\\\\\\)
----------------------------
Part 3
\(\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^3}-\sqrt{65^3}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2*257}-\sqrt{65^2*65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2}*\sqrt{257}-\sqrt{65^2}*\sqrt{65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(257\sqrt{257}-65\sqrt{65}\right)\\\\\\\)
\(\displaystyle A = \frac{\pi}{96}*257\sqrt{257}-\frac{\pi}{96}*65\sqrt{65}\\\\\\\displaystyle A = \frac{257\pi\sqrt{257}}{96}-\frac{65\pi\sqrt{65}}{96}\\\\\\\displaystyle A = \frac{-65\sqrt{65}\pi}{96}+\frac{257\sqrt{257}\pi}{96}\\\\\\\)
Related Questions
Mme potatana ask the children to count as a whole class from 1 to 20 Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count. in your view support the method that you find important to enhance the strong number sense. Provide appropriate examples for your chosen method.
Answers
The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.
In order to enhance strong number sense in children, there are various methods that can be used.
In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.
Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.
The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.
This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.
Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:
1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.
2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.
3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.
Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.
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Sort the angles as acute, right, obtuse, or straight.
Answers
The top angle is right (90 degrees, kinda looks like a bent elbow).
The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).
The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).
4th is acute.
5th is straight because it's a straight line.
6th is also obtuse.
Have a good day :)
Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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(pls pls help!!) Calculate each value for ⊙P.
=
Area of shaded factor = (fraction) ft
Area of unshaded factor = (fraction) ft
Answers
The area of the shaded sector is 575π/9 square units.
The area of the unshaded sector is 325π/9 square units
What is the area of the sectors?
The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.
To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (230/360) x π(10)²
= (23/36) x 100π
= 575π/9 square units
To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (130/360) x π(10)^2
= (13/36) x 100π
= 325π/9 square units
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The weights X of an animal are distributed according to the
probability distribution shown.
What is the probability that the animal's weight will be less than
151 pounds?
O 0.25
O 0.50
O 0.60
O 0.75
Answers
The probability that the animal's weight will be less than 151 pounds is 0.50.
The correct option is B.
What is the probability that the animal's weight will be less than 151 pounds?Since the given probability distribution ranges from 148 to 152, and we need to find the probability that the animal's weight will be less than 151 pounds, we can add the probabilities corresponding to the weights less than 151.
From the distribution, we see that the probability of the animal's weight being less than 151 pounds is 0.2 + 0.3 = 0.5.
Therefore, the answer is O 0.50.
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Please break down how to do these pls
Answers
The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\) 2. 2\(x^{0}\)\(y^{-2}\)
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
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You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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Help please 111119228282
Answers
Here we have a dilation of scale factor 2.
How to describe the enlargement?We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.
To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:
L' = K*L
Here if we use the left sides, we will get:
for figure A; L= 2
for figure B: L = 4
4 = K*2
4/2 = K
2 = K
So this is a dilation of scale factor k = 2.
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A mountain lodge charges a weekly cabin rental fee of $450 for a single guest, plus $125
for each additional guest.
Which of these equations models the relationship between the number of guests, x, and
the total charge, y?
A. y = 450 + 125x
B. y = 450+ 125(x - 1)
C. y = 450+ (125 - 1)x
D. y = (450-x) + 125
Answers
The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.
TRUE/FALSE. The set of positive integers and the set of negative integers a partition of the set of integers
Answers
The given statement "a divide of the collection of integers is the positive integer set and the negative integer set" is FALSE.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.
The inverse additives of the equivalent positive numbers are the negative numbers.
The Z symbol is a common way for mathematicians to refer to an integer set.
The set of integers is not divided into the set of positive integers and the set of negative integers.
The lowest group and ring of the natural numbers are formed by the integers.
To distinguish them from the more generic algebraic integers, the integers in algebraic number theory are occasionally designated as rational integers.
In actuality, (rational) integers are rational numbers that are also algebraic integers.
Therefore, the given statement "a divide of the collection of integers is the positive integer set and the negative integer set" is FALSE.
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Manuel rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 92 cents for each mile driven. Manuel had to pay $141.11 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
8
Step-by-step explanation:
Help. No links. You need to find volume. Ty :3
Answers
Answer:
I can't see the image but to help the formula is volume=LENGTH x Width x Height :)
Step-by-step explanation:
for the left half of the figure, you can find the volume by doing 8x4x13, which is 416. the right half volume can be found by doing 7x3x13 which is 273. 416 + 273 is 689.
HELP ME QUICK! ASAP! A stock clerk is arranging a case of 24 bottles of shampoo on a shelf. Each bottle contains 375 milliliters of shampoo. How many liters of shampoo do all bottles contain? Show your work.
PLEASE SHOW UR WORK LIKE HOW U GOT IT
Answers
The faculty of a certain four-year college consists of 179 teachers. There are 663 first-year students. The student-to-faculty ratio for the entire college is 15 to 1. What is the total number of second-, third-, and fourth-year students?
A 1,989
B 2,022
C 2,652
D 2,685
Answers
Fill in the missing values below one at a time to find the quotient when x^3 - x^2 - 3x + 2 is divided by x - 2.
Answers
Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.
To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:
Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²
Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.
Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.
Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.
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Keilantra's math teacher plots student grades on their weekly quizzes against the
number of hours they say they study on the pair of coordinate axes and then draws
the line of best fit. What does the slope of the line represent?
Answers
The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.
In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.
For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.
On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.
Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
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Which of the following could be the first step in solving the equation below?4x = 17O A. log 4* = log 17OB...4-2.17C. log 4* = 17D. 44* = 477
Answers
In the given equation the vraible x is in exponent with 4 at base. So to solve this equation we takr log on both side of equation, as
\(\log (4^x)=\log 17\)Further we simplify the expression y using logarthimic property.
Thus first step for solving the equation is taking log on both side. So answer is,
\(\log 4^x=\log 17\)Option A is correct.
3
How many full 4 3/4in. sheets can be cut from 22 1/8in. stock?
3
The 22 1/8in stock can be cut into full sheets of length 4 3/4in.
Answers
The number of sheets that can be cut from 22 1/8 inches would be 4 25/38
How to solve for the divisionTo solve this, I would first have to convert the values to decimals
4 3/4in = 4.75 inches
22 1/8 = 22.125
To get the full length that can be cut from the 22.125, we would have to divide. That is;
22.125 / 4.75
= 4.657
4 25/38
The number of full sheet that can be cut from this would be 4 25/38
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If PQ=11 and QR=12, what is PR
Answers
Answer:
PR = 23
Step-by-step explanation:
Step 1:
PQ + QR = PR
Step 2:
11 + 12 = 23
Answer:
PR = 23
Hope This Helps :)
mega movies hotel a fil premiere on Friday night. they charged $7 for adults and $5 for children. One hundred twenty-three adults and children attended, and $829 was made in ticket sales. How many children and how many adults went to the film premiere?
Answers
Answer:
107 adults 16 children
Step-by-step explanation:
can i get brainlest
Please help me please
Answers
Answer:
To be honest I don't know I just need some points 1+1=2
Step-by-step explanation:
find the length of a side of a square for the area given 100/9 square meters
Answers
Answer: A side of a square for the area given 100/9 square meters, then length = 3.33 meters .
Step-by-step explanation:
The area of a square is (100/9) cm.
So, find out the length of the square?
Then,
Define Square:
A square is closed, two-dimensional shape with 4 equal sides. A square is a quadrilateral. We can find the shape of a square in a game board or chess board, a wall clock and in a slice of bread, around us.
The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.
Define Area of Square:
Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units with the standard unit being square meters (m²).
The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.
Area of a Square = Side × Side
Therefore, the area of square = side² square units
A = s²
Means, A= area of square
You have the area so you need to find the side length that when multiplied by itself equals that area. If you don’t know what number squared is (100/9) you can plug and chug or use a calculator with square roots.
Replace with A=(100/9) values,
We can write,
A = s²
(100/9) = s²
Then we can solve it,
\(\sqrt{100/9}\) = s
\(\sqrt{\frac{(10^{2}) }{3^{2} } }\) = s
We can write, \(\sqrt{10^{2} }\) = 10 , and \(\sqrt{3^{2} }\) = 3
Then,
(10/3) = s
Therefore, s = (10/3)
s = 3.33 meters
So, length = 3.33 meters
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A(6, -5) and B(-1, 2) in the ratio of 2:5
Answers
Answer:
p(x,y)= (4,-3)
Step-by-step explanation:
all explainations are in the picture below.
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
!PLEASE ANSWER ASAP! THANK YOU IN ADVANCE!
mrs. piggiewinkle knows how to use texting, instant messenger, emailing, calling, and mailing letters to communicate with her students. she must select 2 methods of communication out of the 5 to send her students an important message. in how many ways can choose the communication methods?
Answers
Answer:
Step-by-step explanation:
She must write an email to the new employees explaining how to access documents that need editing and what to do with new versions of the documents.
Answer: 20 ways
Step-by-step explanation: I believe that you would need to use permutation, so:
5P2 = 20
Jill is going to buy a new toaster. The price of the toaster is $78. If sales tax is 7%, how much does Jill pay total for the toaster?
Answers
Answer:
$83.46
Step-by-step explanation:
hope it helps
A bag of 10 Marbles has the following composition:
Red – 3
Green – 4
Blue – 2
Yellow – 1
What is the Simple Probability of reaching in and extracting a Yellow marble?
Answers
Answer: So, the simple probability of reaching in and extracting a yellow marble from the bag is 0.1 or 10%.
Step-by-step explanation: To calculate the simple probability of reaching in and extracting a yellow marble from the bag, we need to divide the number of yellow marbles by the total number of marbles in the bag.
The bag contains a total of 10 marbles, and there is only 1 yellow marble. Therefore, the probability of extracting a yellow marble can be calculated as:
Probability = Number of Yellow Marbles / Total Number of Marbles
Probability = 1 / 10
Simplifying this fraction gives us:
Probability = 0.1 or 10%
Hope this helps!
5/6 + 3/4 + 2/3 pls
Answers
Answer:
2.25 i believe
Step-by-step explanation:
The insurance premium of a new bus is GH¢93.30 plus 15% of the insured value. What is the insurance premium of a bus whose insured value is GH¢250.00?
Answers
The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.
Let's first calculate 15% of¢250.00:
15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50
Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:
GH¢93.30 + GH¢37.50 = GH¢130.80
Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
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There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars
Answers
Answer:
4 different spots
Step-by-step explanation:
12 - 4 spaces in between = 8 spaces
8 spaces / 4 cars = 4 spots
4 spots and 4 cars = 4 different spots for each car
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