The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.
The equation of the circle can be given as,
[tex]x^2+y^2=r^2[/tex]
Here, (r) is the radius of the circle.
Rewrite this equation as,
[tex]y^2=r^2-x^2\\y=\sqrt{r^2-x^2}[/tex]
This will give you the half the length of the side. Thus, the length of the side of the square is,
[tex]s=2y=2\sqrt{r^2-x^2}[/tex]
The area of the square it square of its side. Thus, the area of the square is,
[tex]A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})[/tex]
The volume of the solid can be got by integrating the area of the cross-section.
[tex]V=\int\limits {A(x)} \, dx[/tex]
Here, A(x), provides the area of the square at the point x. Thus,
[tex]V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}[/tex]
Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
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what is the value of the expression -8x3.2
Answer:
-25.6
Step-by-step explanation:
Hope this helped :>>>
Which of the following is irrational?
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the other 3 are perfect squares and have rational answers.
[tex]\sqrt{1.44} =1.2\\\sqrt{1}= 1\\\sqrt{4} =2[/tex]
[tex]\sqrt{2}[/tex]
A square root of any number that won't result in a whole number is irrational.
In this case, [tex]\sqrt{2}[/tex] is irrational.
An amphitheatre has 17 seats in the first row, 19 in the second, 21 in the third, and so on, for 32 rows. How many seats are in the amphitheatre?
Answer:
I believe your answer would be 2450 seats
Step-by-step explanation:
solve please!!!!!!!!
Answer:
m<ABC=42
Step-by-step explanation:
This image shows the majority of the math and all you do to get to that point is add 5x+13 and 3x+33 so you can find x which you will need to complete the equation for m<ABC, and you know they equal 70, which means all you have to do is take 8x+46=70 and work it out giving you x=3. then you can find m<ABC by pluging in 3 to the equation 3x+33, so 3*3=9, and 9+33=42, so your answer is m<ABC=42
What is the value of x?
Answer: 5
Step-by-step explanation:
1) Carolina walked to school on 12 of the 20 school days in March. Which value is NOT equivalent to the fraction of the school days in March that Carolina walked to school?
A) 60%
B) 0.06
C) 3/5
D) 0.60
The value that is not equivalent to the number of days Carolina walked to school during March is 0.06.
What is a fraction?A fraction represents the proportion or part in a whole, in this case, the number of days Carolina walked to school out of the total days in March.
This relationship can be expressed as:
A fraction:
12/20A simplfied fraction:
3/5 by dividing it into 4A number:
12/20 = 0.60 by dividing 12 by 20A percentage:
60% by multiplying the number by 100Learn more about fractions in: https://brainly.com/question/10354322
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Triangle MNO is rotated 180degree using the origin as the center of rotation.
On a coordinate plane, triangle M N O has points (negative 3, 2), (negative 3, 3), (negative 5, 2). Triangle M prime N prime O prime has points (3, negative 2), (3, negative 3), (5, negative 2).
Which sequences of transformations will produce the same results? Check all that apply.
a reflection over the x-axis and then a reflection over the y-axis
a reflection over the y-axis and then a reflection over the x-axis
a 90degree clockwise rotation about the origin and then a 90degree counterclockwise rotation about the origin
a translation 6 units right and then a reflection over the x-axis
a translation 4 units down and then a reflection over the y-axis
Answer:
A. a reflection over the x-axis and then a reflection over the y-axis
B. a reflection over the y-axis and then a reflection over the x-axis
So, When there is the reflection over to the x axis so it can be the reflection for the y-axis. and, the same is applied for y-axis as well.
Find the tive-number summary for the data set.
6, 8, 13, 15, 21, 23, 31
A. Minimum = 6
First quartile 31
Median
22
Third quartile = 8
Maximum = 23
B. Minimum = 6
First quartile = 8
Median
15
Third quartile = 23
Maximum = 31
C. Minimum = 31
First quartile = 13
Median = 22
Third quartile : 23
Maximum = 6
D. Minimum = 31
First quartile = 6
Median = 31
Third quartile = 15
Maximum = 8
Answer:
B
Step-by-step explanation:
HELP ASAP PLEASE
The table below shows the weights of Liam's pumpkin, l(w), and
Patricia's pumpkin, p(w), over a four-week period wherew represents
the number of weeks. Liam's pumpkin grows at a constant rate.
Patricia's pumpkin grows at a weekly rate of approximately 52%.
Assume the pumpkins continue to grow at these rates through week 13.
When comparing the weights of both Liam's and Patricia's pumpkins
in week 10 and week 13, which statement is true?
(1) Liam's pumpkin will weigh more in week 10 and week 13.
3) Patricia's pumpkin will weigh more in week 10 and week 13.
(3) Liam's pumpkin will weigh more in week 10, and Patricia's
pumpkin will weigh more in week 13.
4) Patricia's pumpkin will weigh more in week 10, and Liam's
pumpkin will weigh more in week 13.
Liam's pumpkin will weigh more in week 10, and Patricia's pumpkin will weigh more in week 13. Then the correct option is C.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The table below shows the weights of Liam's pumpkin, l(w), and Patricia's pumpkin, p(w), over a four-week period which represents the number of weeks.
Liam's pumpkin grows at a constant rate.
Patricia's pumpkin grows at a weekly rate of approximately 52%.
Let x be the number of the week and y be the weight in pounds.
The equation of Liam's pumpkin will be
[tex]\rm y - 2.4 = \dfrac{5.5-2.4}{7-6} (x- 6)\\\\y - 2.4 = 3.1(x- 6)\\\\y = 3.1x - 16.2[/tex]
Then the weight of Liam's pumpkin after 10 weeks will be
y = 3.1 × 10 - 16.2
y = 31 - 16.2
y = 14.8
Then the weight of Liam's pumpkin after 10 weeks will be
y = 3.1 × 13 - 16.2
y = 40.3 - 16.2
y = 24.1
The equation of Patricia's pumpkin will be
[tex]\rm y = a\times (1.52)^{x}[/tex]
For x = 6 and y = 2.5
Then
[tex]\rm 2.5 = a \times 1.52^6\\\\a \ \ = 0.203[/tex]
We have
[tex]\rm y = 0.203 \times (1.52)^{x}[/tex]
Then the weight of Patricia's pumpkin after 10 weeks will be
[tex]\rm y = 0.203 \times (1.52)^{10}\\\\y = 13.36[/tex]
Then the weight of Patricia's pumpkin after 13 weeks will be
[tex]\rm y = 0.203 \times (1.52)^{13}\\\\y = 46.93[/tex]
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.
Which of the following is the reciprocal 1/5 of ?How do I know if my answer is correct ? Please help me to solve this ! I really need help! Please heeeeelllllllpppppppp!
Answer:
5
Step-by-step explanation:
Repreical means opposite, so, 1/5 x 5 would equal one, thats a reciproal
Answer:
5
Step-by-step explanation:
The reciprocal of 1/5 would be 5. To find the reciprocal of a number, swap the numerator and the denominator.
Pls help! I don’t understand bc I’m not smart-
Answer:
78.5 m²
Step-by-step explanation:
The formula to find the area of a quarter of a circle: [tex]\frac{1}{4} * \pi * r^{2}[/tex], where [tex]r[/tex] is the radius (diameter ÷ 2) and the [tex]\pi[/tex] is alterable.
1) Substitute the given values into the formula.
= [tex]\frac{1}{4} * 3.14 * 10^{2}[/tex]
2) Solve it.
= [tex]\frac{1}{4} * 314[/tex]
= 78.5
3) Round it off to the nearest tenth. In this case, it has already been rounded off.
Create an equation that describes the greatest horizontal length, H, in terms of greatest vertical length v
The question illustrates a linear equation, and the equation that represents the greatest horizontal height is H = 2V + 3
How to determine the equation?From the complete question, we have the following highlights:
The greatest horizontal height is three more than twice the greatest vertical length.
This means that:
H = 2 * V + 3
Evaluate the product
H = 2V + 3
Hence, the equation that represents the greatest horizontal height is H = 2V + 3
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76250*18 maths problem
Step-by-step explanation:
1,372,500 ............
Answer:
1,372,500
Step-by-step explanaition
7 6 2 5 0
× 1 8
+ 6 1 0 0 0 0
+ 7 6 2 5 0
= 1 3 7 2 5 0 0
Therefore:
76250 × 18 = 1,372,500
James is constructing a circle circumscribed about a triangle. He has partially completed the construction, as shown below. What should be his next step in the construction?.
Answer:
The correct answer is A.
Connect the arc markings to complete the perpendicular bisector.
Step-by-step explanation:
X + 3/2= 2 1/4 whats the answer
Move all terms not containing x to the right side of the equation.
Exact Form:
x=15/4
Decimal Form:
x=3.75
Mixed Number Form:
x=3 3/4
hope this helps
Which system of equations is satisfied by the solution shown in the graph?
9
2 3 4 5 X
-5
-4
3
8
N
6
51
3.
Answer:
y = x + 10y = -x + 6Step-by-step explanation:
Equation of Red Line
Slope (m) = rise/runSlope (m) = 1/1 = 1y-intercept (c) = (0, 10)⇒ y = mx + c⇒ y = x + 10Equation of Blue Line
Slope (m) = rise/runSlope (m) = -1/1 = -1y-intercept (c) = (0, 6)⇒ y = mx + c⇒ y = -x + 6A surfer paddles out past breaking waves, rides a wave, paddles back out past the breaking waves, rides another wave back to the beach. Draw a sketch of a graph (with labels) that shows the surfer's possible distance from the beach over time. Show work
Answer:
Past the waves to the beach
Step-by-step explanation:
They never went past the breaking waves that much and started at the beach
Maria is tracking weight progress.She weighed 125 pounds in March and now she is 115 pounds. What is the percent change of her weight?
Answer:
10%
Step-by-step explanation:
if she weight 125 and is 115 pounds now then the percentage would = 10% because 125 - 115 = 10%
The captain of a riverboat cruise charges $36 per person. The cruise averages 300 customers a day. The captain is considering increasing the price. A survey indicates that for every $2 increase in price, there would be 10 fewer customers. What price would maximize revenue?
hi people! so, i have a math dyslexia, this means i have a really hard time not only understanding math, but keeping up with all the problems and new stuff, could someone just give me an explanation of what algebra is in a way that you would describe it to a 5 year old?
Answer:
Math with letters
Step-by-step explanation:
Algebra is just like normal math but instead of you knowing all the numbers there are some numbers you dont know and those are replaced with letters. letters are there to you can replace them with any number, or if given the right problem you might have to find out what number replaces the letter to give you the right answer. for example take 1+x=2 here x would be replaced with 1 to make this true. or take y=2-x+3 if you replace x with any number you want that changes the (y) value to give you anything you want. Also the letters can be any letter you want they dont mean anything just there as place holders for numbers.
A salad dressing is made by mixing oil and vinegar in the ratio 7:2. Joshua makes 900ml of salad dressing. How much oil does he use?
Give your answer in millilitres (ml)
The answer to this question is 700 ML
Write
22
48
in lowest terms.
Answer:
11 and 24
Step-by-step explanation:
I really need help with this question.. I've been stuck on it for a while
Answer:
that forms a triangle .
.....
Please help!! Will mark brainlyest.
Answer:
what's your question
Step-by-step explanation:
ello
A state offers specialty license plates that contain 2 letters followed by 3 numbers. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system
I am pretty positive the answer is 17,576
LLNNN, we contain 676000 combinations available for license plates.
How to estimate the number of possible license plates?The number on license plates exists in the form LLNNN, where L denotes a letter and N denotes a number.
As L can be anything from A to Z, there exist 26 combinations for that and as repetition stands allowed, for second and third letters, we also contain 26 combinations available, and therefore 26 × 26 = 676 combinations for letters.
But numbers exist from 0 to 9 i.e. 10 combinations for each place and a total of 10 × 10 × 10 = 1000 combinations.
Therefore, LLNNN, we contain 676000 combinations available for license plates.
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PLEASE HELP! 5TH GRADE MATH, PLEASE GIVE BRAINLIEST!
Answer: 1 divided by 7
Step-by-step explanation: fraction bar is equal to division
Answer:
C or D but mostly D because the fraction is 1 into 7 and D is dividing 1 into 7 so if correct please consider brainliest
<3
Step-by-step explanation:
Which construction uses the compass for only one step in addition to drawing the circle itself? an equilateral triangle inscribed in a circle a square inscribed in a circle a regular hexagon inscribed in a circle a diameter of a circle
The construction that uses the compass for only one step in addition to drawing the circle itself is A. an equilateral triangle inscribed in a circle.
What is a compass?It should be noted that a compass simply means a device that's used to show cardinal directions. It's also used in mathematics to draw shapes.
In this case, the construction that uses the compass for only one step in addition to drawing the circle itself is an equilateral triangle inscribed in a circle.
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Can someone help me find the answer?
Answer: 16.2
Step-by-step explanation:
3x+11+ 8x+2=90
then subtract 3 on both sides (8-3) to equal 5x
then subtract 2 from 11
so you should have 9+5x= 90
subtract 9 from 90
so 5x=81 and then divide to get 16.2
Answer:
(3x+11) = 32 degrees
(8x+2) = 58 degrees
Step-by-step explanation:
The two expressions equal 90 degrees when added together, so we use this equation to find out their values:
(3x+11) + (8x+2) = 90
11x+13 = 90
11x+13-13 = 90-13
11x = 77
11x/11 = 77/11
x = 7
Now that we know x equals 7, we can factor it in both of the expressions to find their true values:
3x+11
3(7)+11
21+11
= 32 degrees
8x+2
8(7)+2
56+2
= 58 degrees
We know this is correct because both values equal to 90 degrees:
32 + 58 = 90
If an investor has a $5,000 pretax return, the state tax rate is 4.5%, and the federal tax rate is 22.0%, what is the real investment value? $1,325 $3,675 $3,900 $4,775
Based on the given parameters, the real value of the investment is $3675
How to determine the value of the investment?From the question, the given parameters about the investment are:
Pretax return = $5,000
State tax rate = 4.5%
Federal tax rate = 22.0%
The real value of the investment is calculated using the following formula
Real investment value = Pretax return - [(Pretax return * State tax rate) * Pretax return * Federal tax rate)]
Substitute the given values in the above equation.
Real investment value = 5000 - [(5000 * 4.5%) + (5000 * 22.0%)]
Evaluate the products
Real investment value = 5000 - [225 + 1100]
Evaluate the sum in the above equation
Real investment value = 5000 - 1325
Evaluate the difference in the above equation
Real investment value = 3675
Hence, the real value of the investment is $3675
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Answer:3675
Step-by-step explanation:
PLS HELP FAST!! What does (87)4 equal?
Write your answer as a fraction, using the / symbol, like this: 42/53
Answer:
348
Step-by-step explanation:
(87)4
87×4
348
it's simple brackets mean multiplication