The volume of the liquid in the conical flask is 980 π cm³
What is a Cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Given data ,
Let the two cones be A and B
Now , the smaller cone be A
The larger cone be B
The radius of the smaller cone is r = 8 cm
The height of the smaller cone is h = 20 cm
Now , the volume of the smaller cone V = ( 1/3 ) πr²h
Substituting the values in the equation , we get
Volume of cone A = ( 1/3 ) πr²h
Volume of cone A = ( 1/3 ) π x 8 x 8 x 20
Volume of cone A = 426.67 π cm³
Now ,
The larger flask is filled with height H = 20 cm
The radius of the larger cone is R = 14 cm
The height of the larger cone is H = 15 cm
Now , the volume of the smaller cone V = ( 1/3 ) πR²H
Substituting the values in the equation , we get
Volume of cone B = ( 1/3 ) πR²H
Volume of cone B = ( 1/3 ) π x 14 x 14 x 15
Volume of cone B = 980 π cm³
Therefore , the volume of the larger cone B is 980 π cm³
Hence , The volume of the liquid in the conical flask is 980 π cm³
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The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14+9(x-1)=y
Step-by-step explanation:
If x is the number of pizza's being delivered and the first pizza costs $14 then that pizza is already accounted for by the 14 in the equation, so you subtract x by 1 before multiplying it by 9, then add the 14 to the product you then get the total cost: y
There are 152 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 31 fans?
Answer:
182
Step-by-step explanation:
152
+31
---------
182
write an equation of a line perpendicular to the givin equation using the given point givne (8,2); x = -4
y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
In the perpendicular lines the product of slopes will be -1
m1m2=-1
y=x+4 is the given line, it has slope of 1, so the perpendicular line will have slope -1.
The line is passing through (8,2)
2=-1(8)+b
2=-8+b
2+8=b
10=b
Hence, y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4
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3 The Chemistry teacher requests a report on the topic: Sustainable energy. Chapter 5 of the textbook must be used and the delivery date is in three days. What kind of resources were provided for this investigation?
material and administrative
economic and didactic
institutional and methodological
time and source
Knowing that the teacher indicates the chapter of the book to use and the delivery date, the resources that were provided for the research on sustainable energy are:
WeatherFont¿What are the resources for conducting research?They are elements that must be taken into account and that are usable to develop the investigation.
Some examples of these resources are:
Time: it indicates the time that the investigation will take.Source: represents these bibliographic elements from which information is extracted to develop the investigation.¡Hope this helped!
....
......
......
.....
.....
...........
......
...
...
.....
...........
Answer:
Step-by-step explanation:
........................................................
What is the slope of line m?
Answer:-1/2
Step-by-step explanation:
Which uses the GCF to generate an expression equivalent to 24v-84?
O3(8V-28)
O 6(4v-14)
O 12(2v-7)
O 24(V-60)
Answer:
(c) 12(2v-7)
Step-by-step explanation:
You want the expression resulting from factoring out the greatest common factor from the sum 24v -84.
GCFThe greatest common factor here is the GCF of 24 and 84. We note that ...
24 = 12·2
84 = 12·7
and 2 and 7 have no common factors. Then the GCF of 24 and 84 is 12.
The factored expression is ...
24v -84 = 12(2v -7)
__
Additional comment
The GCF can also be found by considering the remainder from dividing 84 by 24. That remainder is 12, which divides both numbers with a remainder of 0. Hence 12 is the GCF.
If the remainder did not divide both numbers with a remainder of 0, then the process is repeated to find the GCF of the smaller number (24) and the remainder. (This is a description of Euclid's algorithm for finding the GCF.)
He region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 and within the cone z=x2+y2−−−−−−√ with z≥0; its boundary is the closed surface, S, oriented outward. Find the flux of F⃗ =x3i⃗ +y3j⃗ +z3k⃗ out of S
The flux of out of S is [tex]14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)[/tex].
What is Flux of the Vector Field?
Solving the flux of the vector field using the divergence theorem which has the following formula [tex]$\iint_S F \cdot d S=\iiint_E div} F(x, y, z) d V$[/tex] where F is the vector field [tex]$F=P i+Q j+R k$[/tex] and div F means the divergence of F which has the formula [tex]$F=\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}$[/tex]
Here, we let the vector field to be [tex]$\vec{F}=x i+y j+z k$[/tex]
[tex]$\vec{F}=x i+y j+z k$[/tex]
Now solving for [tex]${div} F$[/tex]
[tex]$$\begin{aligned}& {div} F=\frac{\partial x}{\partial x}+\frac{\partial y}{\partial y}+\frac{\partial z}{\partial z} \\& {div} F=1+1+1=3\end{aligned}$$[/tex]
Thus,
[tex]\iint_S F \cdot d S=\iiint 3 d V[/tex]
From the given region the limits of integrations in spherical coordinates are,
[tex]0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \frac{\pi}{4}, 1 \leq \rho \leq 2[/tex]
Thus,
[tex]\iint_S F \cdot d S=\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} \int_1^2 3 \rho^2 \sin \phi d \rho d \phi d \theta[/tex]
Integrate with respect to [tex]$\rho$[/tex]
[tex]\begin{aligned}& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 3\left[\frac{1}{3} \rho^3\right]_1^2 \sin \phi d \phi d \theta \\& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 7 \sin \phi d \phi d \theta\end{aligned}[/tex]
Integrate with respect to [tex]$\phi$[/tex]
[tex]\begin{aligned}& =\int_0^{2 \pi} 7[-\cos \phi]_0^{\frac{\pi}{4}} d \theta \\& =\int_0^{2 \pi} 7\left(-\frac{\sqrt{2}}{2}+1\right) d \theta\end{aligned}[/tex]
Integrate with respect to [tex]$\theta$[/tex]
[tex]\begin{aligned}& =7\left(-\frac{\sqrt{2}}{2}+1\right)[\theta]_0^{2 \pi} \\& =14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)\end{aligned}[/tex]
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Help me how do I do this (221x3 + 154x2 + 228x + 41) / (17x + 4)-4
The value of x from the equation (221x3 + 154x2 + 228x + 41) / (17x + 4)-4 is 992
How to find the value of x?In general, the algebraic expression should take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left side and all the remaining values to the right side to find the value of x. To find the answer, simplify the values. In algebra, the letter "x" is frequently used to represent an unknown value. It is referred to as a "variable" or "unknown" at times.
(221x3 + 154x2 + 228x + 41) / (17x + 4)-4
Multiplying 221*3 and 154*2 =663,308
( 663+308 + 228x + 41) / (17x + 4)-4
( 971+ 228x + 41) / (17x + 4)-4
=( 971+ 228x +41)
(17x + 4)
=1012+228x
(17x + 4)
-x=-992
x=992
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During the two-day drive to her sister's house, Audrey drove 320 miles the first day and 280 the second day. She stopped for gas twice, paying $24 and $31. She used 27 gallons of gas.
Which of the following cannot be determined using the information given?
A. cost of gas
B. how many gallons the gas tank holds
C. miles driven
D. miles per gallon of gas
The value not predicted for the given information is "how many gallons the gas tank holds".
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.
Here,
How many gallons the gas tank holds is the value that could not be predicted based on the information provided.
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Rewrite the following equation in slope-intercept form (y = mx + b), then identify the slope (m =) and y-intercept (b =) of the equation.
-3y – 5 = -2(x + 11) + 2
Answer: y = [tex]-\frac{2}{3} x[/tex] -5
Step-by-step explanation:
Distribute:
-3y-5=-2x(x+11)+2
Rewrite:
-3y-5=-2x-22+2
Combind alike terms:
-2x-20
Rewrite again:
-3y-5=-2x-20
Add 5 to both sides and rewrite:
-3y=-2x-15
Divide by -3:
y=[tex]-\frac{2}{3} x[/tex] - 5
(Sorry if it's incorrect im barely paying attention lol)
If 30200 dollars is invested at an interest rate of 6 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$30200\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=30200\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=30200(1.06)^5\implies A \approx 40414.41[/tex]
What is the solution to this system of equations? 3x+y+2z=6 6x−2y=2 3x+y−2z=0
The value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
What is a linear equation?It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a plane.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The linear equations are:
3x+y+2z=6
6x−2y=2
3x+y−2z=0
From equation (I) and (III)
6x + 2y = 6
From the above equation and equation (II)
12x = 8
x = 8/12 = 2/3
y = 1
z = 3/2
Thus, the value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3x+y+2z=6 6x−2y=2 3x+y−2z=0
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
Answer: 95 percent confidence interval
Step-by-step explanation: "you have a 5 percent chance of being wrong. with a 90 percent confidence interval, you have a 10 percent chance of being wrong a 99 percent confidence interval would be wider than a 95 percent confidence interval for example plus or minus 4.5 percent instead of 3.5 percent"
3. Find the volume of a sphere with a radius of 4 ft. (1 point)
Answer: =268.19047cm^3 or 268.08 rounded
Step-by-step explanation: using [tex]\frac{4}{3} *\pi *r^{3}[/tex] to get my answer.
Hope this helps :)
please help me with find x in the diagram below
Answer:
x = 125
Step-by-step explanation:
Given a heptagon with 60° and 90° angles marked, one marked 2x°, and the remaining angles marked x°, you want o know the value of x.
Sum of anglesThe sum of the interior angles of a heptagon is ...
180° × (7 -2) = 900°
Using the given values, this tells us ...
90° +x° +x° +x° +x° +60° +2x° = 900°
6x = 750 . . . . . . . divide by °, subtract 150
x = 125 . . . . . . divide by 6
The value of x is 125.
__
Additional comment
The attached figure is drawn with correct angles.
The sum of interior angles of an n-gon is 180°×(n -2).
The arenas pay for two cars every month they pay $250 for Miss Herrera's car and 375 for Mr. editor struck what kind of expense is a car payment made each month
In the continuous Efm=300+20m. series, if mean (x)=15+m and Find the number of terms N.
Answer:
the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
Step-by-step explanation:
The mean of a series is calculated by taking the sum of all the terms in the series and dividing it by the number of terms. In this case, the mean of the continuous series Efm=300+20m is given as x=15+m.
To find the number of terms N in the series, we can use the formula for the mean to solve for N. The formula for the mean is:
mean = sum of terms / number of terms
Substituting the given values, we get:
15+m = (300+20m) / N
We can then multiply both sides of the equation by N to isolate the sum of terms:
(15+m) * N = 300+20m
This simplifies to:
15N + mN = 300 + 20m
We can then combine like terms to get:
(15+20)N = 300
35N = 300
Dividing both sides by 35, we get:
N = 300/35
N = 8.57
Since the number of terms must be a whole number, the number of terms N in the series is approximately 8.57, which is approximately equal to 9.
Please help
What inequality does the number line show?
Write your answer starting with
x (example: x < 3)
Answer:
x ≥ -7
Hope this helps : )
Step-by-step explanation:
The number line is showing a closed dot which means that the number the dot is on is a solution to the equation too. Since the arrow is pointing to the right (positive/greater numbers), then the sign is greater than and equal to.
Sharon started with $42 in her bank account and
added $16 per week. Neil started out $70 in debt and deposited $30 per week. Determine how many weeks it will take them to have saved the same amount of money.
The number of weeks it will take them to have saved thesame amount is 8 weeks
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.
if x represents the the number of weeks for saving and y represents the equal saved amount, then
42+16x = y equation 1
-70+ 30x = y equation 2
subtract equation 1 from 2
-70-42+16x- 30x= 0
-112+14x= 0
collect like terms
-112=-14x
divide both sides by 14
x= -112/-14
x= 8weeks
therefore it will take them 8 weeks to have equal savings
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Determine the equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x.
Option:
The equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x is [tex]$\frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1$[/tex]
The answer provided below has been developed in a clear step by step manner.
Given asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex] and
vertices (1,6) and (1,-12)
What is hyperbola ?
Standard hyperbola through origin when values of x for the vertices are equal. [tex]$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$[/tex]
Now solve the asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex]
After solving we get [tex]$\mathrm{x}=1 \quad$[/tex]and [tex]$\quad \mathrm{y}=-3$[/tex]centre =(1,-3)
translation in form of [tex]$\mathrm{x}_1$[/tex] and [tex]$\mathrm{y}_1$[/tex]
[tex]$\mathrm{x}_1=\mathrm{x}-1 \quad$[/tex] and [tex]$\quad \mathrm{y}_1=\mathrm{y}+3$[/tex]
Distance from vertices (1,6) and (1,-12) to centre (1,-3) is [tex]$9=\mathrm{a}$[/tex]vertical symmetry the asymptotes have a slope [tex]$=\pm 3=a / b$[/tex] so [tex]$\mathrm{b}=\frac{9}{3} \Rightarrow \mathrm{b}^2=9$[/tex]
Put all the values of a and b into original equation
[tex]$$\begin{aligned}& x_1=x-1 \quad \text { and } \quad y_1=y+3 \\& \Rightarrow \frac{(y+3)^2}{3^2}-\frac{(x-1)^2}{9^2}=1 \\& \Rightarrow \frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1\end{aligned}$$[/tex]
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Examine the table, which represents a linear function.
Input (x) Output (y)
−3 14
0 7
3 0
6 −7
What is the initial value of the function?
A: 3
B: -3
C: 0
D: 7
Answer: 7
Step-by-step explanation:
The initial value of the function is the value of [tex]y[/tex] when [tex]x=0[/tex].
Alice's savings account earns 3.75% interest per year. If she put $9,500 into the savings account, how much interest would be earned in a year?
Hello,
I hope you and your family are doing well!
To calculate the amount of interest earned on a savings account, you can use the following formula:
interest = principal * rate * time
In this case, the principal is $9,500, the rate is 3.75%, and the time is 1 year. Plugging these values into the formula, we get:
interest = $9,500 * 3.75% * 1 year = $356.25
So, in a year, Alice would earn $356.25 in interest on her savings account.
-----
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Happy Holidays!
The wavelength of green light in a spectrum is about 0.000003 feet. Which
number best approximates this length as a power of 10?
The scientific notation of the wavelength of green light in a spectrum
is 3×10⁻⁶ feet.
What is scientific notation?In scientific notations numbers are written in the form of a base that is
0 ≤ b < 10 and multiplied by 10ⁿ where n represents integers.
We write large standard numbers in scientific form in a compact manner.
Given, The wavelength of green light in a spectrum is about 0.000003 feet.
Now, the decimal is 6 places before so we have to move the decimal 6 places to the right, and to maintain the actual value we'll raise it to 10⁻⁶.
Therefore, 0.000003 feet,
= 3×10⁻⁶ feet.
So, the wavelength of green light is 3×10⁻⁶ feet.
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What would you use to graph the inequality y ≥ 4 ?
The coordinate plane
A number line
The origin
This inequality cannot be graphed.
A number line use to graph the inequality y ≥ 4.
How do you graph an inequality?Treat the,, >, or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.Pick a point that is not on the line next. Verify if the inequality is satisfied by this point. The area containing that point should be shaded if it satisfies the inequality. Shade the area that does not contain that point if it does not satisfy the inequality. Every point in the shady area satisfies the inequality.Explanation :
y = − 4 is a horizontal line at -4, since
y ≥ − 4, the area above -4 will be shaded and the line will be solid since it is greater than AND equal to:
graph{y>=-4 [-10, 10, -5, 5]}
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Need help on this question ASAP PLEASE AND THANK YOU
Answer:
which class question is this
HELP ASAP!! graph the system of equations below by graphing both equations below on a piece of paper. what is the solution?
y=x-1
y=3x+1
A. 1, -2
B. -1, -2
C. 2, 1
D. -1, -1
Answer: Our answer set is( -1,-2 )
Step-by-step explanation:
y = x - 1
y = 3x + 1
We can use the combine method here.
==> - 1y + 1x = 1 (y = x - 1)
==> -1y +3x = -1 (y = 3x + 1)
- 1y + 1x = 1
-1y +3x = -1
To single out any of the two variables, we need them to cancel out. Let us choose to cancel out y. We therefore multiply by negative 1 in the first re-arranged equation.
==> -1* (- 1y + 1x )= (1 ) * -1
Now we add the equations
==> 1y -1x = -1
==>-1y +3x = -1
______________
2x = -2
Divide.
==> x = -1
Now we insert x into any of the two original equations;
y = (-1) - 1
==> y = -2
Our answer set is( -1,-2 )
In the coordinate plane, line q has slope 6 and y-intercept (0, 8). Line p is the result of dilating line q by a factor of 4 with center (0, 4). What is the y-intercept and slope of line p?.
The line r has slope 6 and coordinates in the specified coordinate plane, based on the given dilation (0, 12)
Dilation:
Dilation is the scaling factor multiplied by the supplied line to line ratio.
Given
Line p in the coordinate plane has a y-intercept and a slope of 6. (0, 8). Line p is dilated by a factor of 4 with center to produce line r. (0, 4).
Here, we need to determine line r's slope and y-intercept.
Here, the scaling factor is known to be 4.
Consider the line r's slope, which won't change, and its intercept, which will be their ordinate added.
So, it can be written as,
=> Intercept = 8 + 4
=> Intercept = 12
Therefore, the line r has slope 6 and coordinate (0, 12).
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Landon and Colin bought 1/2 pound of trawberrie. They are haring the trawberrie equally. How many trawberrie will each peron receive?
Using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The four basic mathematical operations, according to the majority of people, are addition, subtraction, multiplication, and division.
So, the strawberries both Landon and Colin will get are:
We know that Landon and Colin brought 1/2 strawberries.
They share is equally that is:
1/2 ÷ 2
Now, solve as follows:
1/2 ÷ 2
1/2 ÷ 2/1
1/2 * 1/2
1/4
Therefore, using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.
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y=-12-3x what is the answer and how do you do this
Answer:
You draw the line of the graph and every point on the line is a solution
Step-by-step explanation:
y = mx + b You graph the b which is the y intercept. This is where the graph crosses the x axis. In this case it is -12. From that point (0,-12) You follow a pattern which is the slope. In this case the slope is -3. That mans that you move three units down and then 1 unit right.
I highlighted a few points on the line. Every point on the line is a solution.