Find the volume of the solid whose base is the circle x^2+y^2=81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.
Find the area of the vertical cross section A at the level x=6.
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The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The equation of the base circle is given below.
x² + y² = 81
x² + y² = 9²
Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.
h = 2r
h = 2 x 9 = 18
The volume of the cone will be
V = (1/3)πr²h
V = (1/3) × π × 9² × 18
V = 1526.8 cubic units
The area of the vertical cross-section A at the level x = 6 will be
A = (1/2) x (18 - 6) x (18 - 6)
A = (1/2) x 12²
A = (1/2) x 144
A = 72 square units
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Related Questions
Write an equation in point-slope form of the line through point p(9, -1) with slope -5.
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long division 573÷15=
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15 goes int 57 3 times: 45
57-45=12, bring down the 3
15 goes into 123 8 times
123-120=3
573/15= 38 with a remainder of 3
38R3 is the answer
When twotwo basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. what is the probability that they shoot free throws in alphabetical order? assume each player has a different name?
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Since, the are going to throw alphabetically, there is 1 way for the names to be arranged alphabetically.
Therefore, the probability that they shoot free throws in alphabetical order is [tex] \frac{1}{2} = 0.5[/tex]
Final answer:
The probability of shooting free throws in alphabetical order is 0.5.
Explanation:
Probability of shooting free throws in alphabetical order:
Determine the total number of ways the players can shoot. There are 2 players, so 2! (2 factorial) = 2 ways.
Calculate the number of ways they can shoot in alphabetical order. As they have different names, only 1 way exists.
Probability = (Number of ways shooting in alphabetical order) / (Total number of ways to shoot) = 1/2 = 0.5.
I Need to identify the property that justifies each step to simplify the expression
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1) equality of addition , subtraction , multiplication, and division
A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria. Find each population density, to the nearest hundredth. Which statement is true? Dish A has the lowest population density. Dish C has the greatest population density. Dish A and Dish B have approximately the same population density. Dish C and Dish D have approximately the same population density.
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The statement that is True is Option D which says:
"Dish C and Dish D have approximately the same population density."
What is Population Density?The population density of an area is the Number of Entities in that space/Total Area occupied by the population.
It can also be written as Dp = N/A.
Because the Dp of Dish C and Dish D is approximately 0.68, we can say that they have approximately the same Dp.
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Where are the asymptotes of f(x) = tan(4x − π) from x = 0 to x = pi over 2 ?
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The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
It is where cos(4x-π) = 0
cos(4x-π) = 0 when the inside is -π/2 , π/2 , 3π/2
4x - π = π/2
4x = π/2 + π
4x = 3π/2
x = 3π/8
4x - π = 3π/2
4x = 3π/2 + π
4x = 5π/2
x = 5π/8
This ones outside the interval (5π/8 > π/2) , try -π/2
4x - π = -π/2
4x = -π/2 + π
4x = π/2
x = π/8
Asymptotes are π/8 and 3π/8
Answer:
D 3pi/8 , 5pi/8
Step-by-step explanation:
If an amount of money, called principle, p, is deposited into an account that earns interest at a rate r, compound annually, then in two years that investment will grow to an amount A, given by the formula A=P(1+r)^2. If a principle amount of $5000 grows to $5940.50 in two years, what is the interest rate?
Answers
A = P(1+r)^t
A = $5940.50
P = $5000
r = ?
t = 2yrs
$5940.50 = $5000(1+r)^t
-------------- --------------------
$5000 $5000
1.1881 = (1+r)^2
sqrt(1.1881) = 1+r
1.09 = 1+r
-1 -1
------- ----
0.09 = r
r = 0.09
Final answer:
By using the compound interest formula A=P(1+r)² and the given values, we find the interest rate to be approximately 0.09, or 9% annually.
Explanation:
To find the interest rate r that grew the principal P from $5000 to $5940.50 over two years with compound interest, we use the formula A=P(1+r)². Here, A is the amount of money accumulated after n years, including interest. We are given that A is $5940.50 and P is $5000.
Let's plug in the values and solve for r:
5940.50 = 5000(1+r)²
1.1881 = (1+r)²
To find r, we take the square root of 1.1881:
Subtracting 1 from both sides to isolate r, we get:
r = 1.09 - 1
r = 0.09
The approximate interest rate is 0.09, which means the annual interest rate is 9%.
43 ones x 3 tens= Tens
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Place value is the value of each digit in a number.
The value of 43 ones x 3 tens is 129 tens
43 ones x 3 tens = 129 tens.
What is a place value?
Place value is the value of each digit in a number.
Example: 2345.67
2 – thousands place value
3 – hundreds place value
4 – tens place value
5 – ones place value
6 – tenths place value
7 – hundredths place value
We have,
43 ones x 3 tens
43 ones can be written as 43
3 tens can be written as 30
So,
43 ones x 3 tens = 43 x 30
43 x 30 = 1290
This means,
1290 = 129 tens
43 ones x 3 tens = 129 tens
Thus,
The value of 43 ones x 3 tens is 129 tens
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kim and brittany are selling chocolate chip cookies and red velvet cupcakes. kim made $81 selling 18 chocolate chip cookies and 12 red velvet cupcakes .brittany made $77 by selling 2 chocolate chip cupcakes and 24 red velvet cupcakes . what was the price of each type of cupcake ?
Answers
The science club raised money to clean the beach. They spent $29 on trash bags and $74 on waterproof boots. They still have $47 left. How much did they raise?
Answers
Answer:
They raised $150
Step-by-step explanation:
In order to solve this you just need to reverse the actions that they took in order to get to 47 dollars left, so the total amount they raised will be represented by letter X, so 47 is what is left after spending 29 on trash bags and 74 on waterproof boots, that means that from the total we are withdrawing those amounts and the result will be 47:
Total-Money spent=47
X-29 - 74= 47
x=47+74+29
x=150
So now we know that they originally had 150 dollars and that would be what they raised.
Two pools are being filled with water. To start, the first pool contains 890 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 20.5 liters per minute. Water is being added to the second pool at a rate of 42.75 liters per minute.
Answers
First pipe empties at the rate of 540,000/150=3600 liters/min
Second pipe empties at the rate of 540,000/225=2400 liters/min
Together, both pipes empties at the rate of 3600+2400=6000 liters/min, so our equation to solve is:
6000*x=540000
find the missing values in the ratio table .then write the equivalent ratios .
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9 shoes to 12 socks
18 shoes to 24 socks
The missing values are 12 and 18.
The ratios are [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].
The given table is:
[tex]\begin{center}\begin{tabular}{ c c c c } shoes & 36 & 9 & y \\ socks & 48 & x & 24 \\\end{tabular}\end{center}[/tex]
Since all the columns are pertaining same ratio; thus we have:
[tex]\dfrac{36}{24} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\dfrac{3}{4} = \dfrac{9}{x} = \dfrac{y}{24}\\\\\\or\\\\\dfrac{3}{4} = \dfrac{9}{x}\\\\x = 12\\\\and \\\\\dfrac{3}{4} = \dfrac{y}{24}\\\\y = 18[/tex]
Thus, the missing values x and y are 12 and 18 respectively.
And the are ratios [tex]\dfrac{9}{12}[/tex] and [tex]\dfrac{18}{24}[/tex].
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To paint a sunset, you make a shade of orange paint using 55 drops of red paint for every 88 drops of yellow paint. If you use 1515 drops of red paint, how many drops of yellow paint would you need?]
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In , is a right angle. find the remaining sides and angles. round your answers to the nearest tenth . show your work. a = 3, c = 1 9
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Find an equation of the tangent line to the bullet-nose curve y=|x|/sqrt(2−x^2) at the point (1,1) I think that square root is what is confusing me on this question
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[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{x\sqrt{2-x^2}}{\sqrt{x^2}}~~+~~\frac{x\sqrt{x^2}}{\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{x(2-x^2)~~+~~x(x^2)}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{2x\underline{-x^3+x^3}}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{2x}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}[/tex]
[tex]\bf \cfrac{dy}{dx}=\cfrac{2x}{\sqrt{x^2}\sqrt{2-x^2}(2-x^2)} \implies \boxed{\cfrac{dy}{dx}=\cfrac{2x}{|x|\sqrt{2-x^2}(2-x^2)}} \\\\\\ \left. \cfrac{dy}{dx} \right|_{1,1}\implies \cfrac{2(1)}{|1|\cdot \sqrt{2-1^2}(2-1^2)}\implies 2\\\\ -------------------------------\\\\ \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2(x-1)\implies y-1=2x-2 \\\\\\ y=2x-1[/tex]
What is 2/3 times 3/4
Answers
1/2 is your answer
hope this helps
[tex] \frac{2}{3} [/tex] × [tex] \frac{3}{4} [/tex]
First, you would cross simplify the equation... But, you don't have to do it now, you can do it at the end (I think this was is easiest).
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex]
Finally, you would answer the equation.
[tex] \frac{1}{1} [/tex] × [tex] \frac{1}{2} [/tex] = [tex] \frac{1}{2} [/tex]
Your answer would be [tex] \frac{1}{2} [/tex].
I hope this helps!
Number 49....I need help
Answers
now, also let's keep in mind that, when the car was driven for 200 miles, that's 200/25 or 8 25mile intervals, so the 25mile charge kicked in 8 times.
[tex]\bf \stackrel{cost}{y}=\stackrel{fixed~charge}{F}+\stackrel{25mile~intervals}{m}\quad \stackrel{25mile~charge}{x}\implies y=F+mx\\\\ -------------------------------\\\\ \begin{cases} 200=F+2x\implies 200-2x=\boxed{F}\\ 245=F+8x\\ ----------\\ 245=\boxed{200-2x}+8x \end{cases} \\\\\\ 45=6x\implies \cfrac{45}{6}=x\implies \cfrac{15}{2}=x\impliedby \begin{array}{llll} \textit{so the 25mile charge is}\\ \textit{7 bucks and 50cents} \end{array} \\\\\\ [/tex]
[tex]\bf 200=F+2\left( \frac{15}{2} \right)\implies 200=F+15\implies 185=F \\\\\\ \textit{and the \underline{fixed charge} is 185 bucks then, let's check for 450} \\\\\\ \boxed{y=185+\frac{15}{2}x}\qquad \begin{cases} 450~miles\\\\ \cfrac{450}{25}\implies 18~\textit{\underline{25mile intervals}}\\\\ x=18 \end{cases} \\\\\\ y=185+\cfrac{15}{2}\cdot 18\implies y=185+135\implies y=320[/tex]
The submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise 63 feet and then drop 84 feet. Write an expression that describes this situation
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What are the coordinates of the vertices of the triangle under the translation (x, y) mc011-2.jpg (x + 1, y - 4)?
(0, -3), (0, 0), (3, -3)
(-3, 0), (3, -3), (0, -3)
(0, -3), (-3, -3), (-3, 0)
(-3, 0), (0, 0), (-3, -3)
Answers
(-1,1) (-4,1) (-4, 4)
translation (x, y) to (x + 1, y - 4)
(0,-3) (-3,-3) (-3, 0)
answer
(0, -3), (-3, -3), (-3, 0)
it is c :
(0,-3), (-3,-3), (-3,0)
just take the X and Y of the coordinates of the original triangle and substitute it in the given equation (x + 1, y - 4)
try it out yourself it works :)
Dennis wrote down a three digit number, The digit in the tens place is 2 more than the digit in the hundreds place. The digit in the ones place is 6less than the digit in the tens place. The digit in the hundreds place is odd number. What is the three digit number?
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The problem is
2n>14
n=?
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n>14/2
n>7
=n>7
so, n can be any number which is greater than 7.
Walter takes 7/10 of an hour to mow 2/5 of an acre of lawn. At this rate, how many acres will he mow in an hour?
Answers
Answer:
4/7 acres per hour
Step-by-step explanation:
A train moving at a constant speed of 70.0 km/h moves east for 45.0 min, then in a direction 55.0° east of due north for 25.0 min, and then west for 55.0 min. what is the average velocity of the train during this run? (let the +x-axis point towards the east and the +y-axis point towards the north.)
Answers
The result will be your average velocity (a vector quantity).
Beverly made a deposit of $375 into her checking account. Then she withdrew $ 65. The next day, she wrote a check for $ 135. She had $475 before any of these transactions. How much money is in her account now?
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add 375(since made deposit)
475+375=850
850-65=785
785+135=$920
how many hours would someone who earns 9.75 per hour have to work to earn 351
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351/9.75 = 36
x = 36
Thus, 36 hours must be worked in order to get $351 if you have a salary of $9.75
a 3 pound pork loin can be cut into 10 pork chops of equal weight. how many ounces are in each pork chop? please show your work
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3 Pound Pork Loin-48 Ounces
48÷10=4.8
Answer= Each Pork chop weighs 4.8 ounces
Y=(2x-3)^5(2-x^4)^3 differentiate the function please
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Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?
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Y=360*(1+0.03)^x
Answer:
D
Step-by-step explanation:
Norma and Rene are serving cupcakes at a school party. If they arrange the cupcakes in groups of 2.3.4.5. or 6 they have exactly one cupcake left over. what is the smallest number of cupcakes they could have?
Answers
We are given that there are 5 groups which are:
group of 2
group of 3
group of 4
group of 5
group of 6
and 1 left over
So the smallest number of cupcakes would simply be the sum of all:
smallest number of cupcakes = 2 + 3 + 4 + 5 + 6 + 1
smallest number of cupcakes = 21
Write a rule for the linear function in the table.
x; f(x)
2 8
5 17
5 11
11 23
A; f(x) = x + 5
B;f(x) = x + 1
C;f(x) = 2x + 1
D;f(x) = –2x – 1
Answers
the correct answer is A. [tex]\( f(x) = 2x + 1 \).[/tex]
To find the rule for the linear function represented in the table, we can use the formula for a linear function, which is:
[tex]\[ f(x) = mx + b \][/tex]
Where:
- m is the slope of the line
- b is the y-intercept
Given the table:
[tex]\[ \x & : 2, 5, 8, 11 \\f(x) & : 5, 11, 17, 23\end{align}\][/tex]
We can start by finding the slope (m) using the formula:
[tex]\[ m = \frac{{f(x_2) - f(x_1)}}{{x_2 - x_1}} \][/tex]
Let's choose two points from the table, for example, (2, 5) and (5, 11):
[tex]\[ m = \frac{{11 - 5}}{{5 - 2}} \]\[ m = \frac{{6}}{{3}} \]\[ m = 2 \][/tex]
So, we have found that the slope m is 2.
Now, we can use the slope-intercept form of a line to find the y-intercept (b). We can pick any point from the table to do this. Let's use the point (2, 5):
f(x) = mx + b
5 = 2(2) + b
5 = 4 + b
b = 5 - 4
b = 1
So, we have found that the y-intercept b is 1.
Now, we can write the rule for the linear function:
[tex]\[ f(x) = 2x + 1 \][/tex]
Therefore, the correct answer is A. [tex]\( f(x) = 2x + 1 \).[/tex]
The complete question is:
Write a rule for the linear function in the table.
x = 2,5,8,11
f(x) = 5,11,17,23
A. f(x) = 2x + 1
B. f(x) = x + 5
C. f(x) = –2x – 1
D. f(x) = 1/2x+1