Let V be the volume of a right circular cone of height h=14 whose base is a circle of radius R=2. An illustration a right circular cone with horizontal cross sections. The right circular cone has a line segment from the center of the base to a point on the circle of the base is labeled capital R, and the horizontal line from the vertex is labeled h.
Required:
Use similar triangles to find the area of a horizontal cross section at a height y.
Answer:
The area of a horizontal cross section at a height is [tex]\pi\times(2-\dfrac{y}{7})^2[/tex]
Step-by-step explanation:
Given that,
Height = 14 m
Radius = 2 m
Let V be the volume of a right circular cone
We need to calculate the value of R
Using given data
[tex]\dfrac{h}{r}=\dfrac{h-y}{R}[/tex]
Put the value into the formula
[tex]\dfrac{14}{2}=\dfrac{14-y}{R}[/tex]
[tex]7R=14-y[/tex]
[tex]R=2-\dfrac{y}{7}[/tex]
We need to calculate the area of a horizontal cross section at a height y
Using formula of area
[tex]A=\pi R^2[/tex]
Put the value into the formula
[tex]A=\pi\times(2-\dfrac{y}{7})^2[/tex]
Hence, The area of a horizontal cross section at a height is [tex]\pi\times(2-\dfrac{y}{7})^2[/tex]
The area of the circular cone at height y can be derived as a function, A,
having y as the input variable.
Correct response:
[tex]Area \ of \ horizontal \ cross \ section \ at \ height \ y \ is \ \underline{ A = \pi \times \dfrac{\left(14 - y\right)^2}{7} }[/tex]
Method used for deriving the areaThe given parameters are;
Shape of figure = Right circular cone
Height of the cone, h = 14
Base radius, R = 2
Required:
The area of a cross section at a height y using similar triangles
Solution:
We have using similar triangles;
[tex]\mathbf{\dfrac{h}{h - y} }= \dfrac{R}{r} [/tex]
Which gives;
[tex]\mathbf{\dfrac{14}{14 - y}} = \dfrac{2}{r} [/tex]
Therefore;
2·(14 - y) = 14·r
28 - 2·y = 14·r
[tex]r = \dfrac{28 - 2 \cdot y}{14} = 2 - \dfrac{y}{7} [/tex]
The horizontal cross sectional area, A = π × r²
Therefore;
[tex]Area \ of \ the \ cross \ sectional \ area,\ A = \pi \times \left(2 - \dfrac{y}{7} \right) = \underline{ \pi \times \dfrac{\left(14 - y \right)^2}{7} }[/tex]
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The sum of two numbers is 33. One number is 2 times as large as the other
Answer:
11 and 22
Step-by-step explanation:
x + y = 33
y = 2x
x + 2x = 33
3x = 33
x = 11
Simplify x - 1 / 5(x - 1)^2
Answer:
1/5(x-1)
Step-by-step explanation:
cancel x-1
then we get
1/5(x-1)
If not understand comment below.
pls help me with number 12 I don’t know the answer I have been trying for a long time pls help
Answer:
m=1/1 or just 1, b=(0,3.5) equation:y=x+3.5
Step-by-step explanation:
The pattern is as x increases by 1, so does y by the same amount, 1. This means the line is at a 45 degree angle increasing vertically and horizontally at the same pace. However, it is moved up 3.5 units in the y direction because when x=0, y=3.5
21. A store display will have 6 rows, with 12 containers in each row.
If 39 containers has been set up so far, explain how to find the
number of containers that still need to be set up. Then solve the
problem.
what is the distance between points (4,0) and (8,-5)
Answer:
(4,5)
Step-by-step explanation:
answer quick! ......................
Answer:
10 units up
Step-by-step explanation:
An example of this is where the graph changes from (0,0) to (0,10)
Have an amazing day!
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Given the following functions, find the indicated values.
f(x) = 6 - 2x
(a) f(-3)
(b) f(0)
(c) f(4)
(a) f(-3)=blank
plz help
Answer:
f(-3)=6-2x is f(-3)=6-2(-3) this equals f(-3)=12
B f(0)=6
C f(4)= -2
Step-by-step explanation:
Bacisly you would just have to sub in the x portion of your problem. Then you can solve like normal
A function is a relationship between inputs where each input is related to exactly one output.
The value of f(-3) is 12
The value of f(0) is 6
The value of f(4) is -2
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 6 - 2x
Substitute x = -3, 0, and 4 on f(x).
f(-3) = 6 - 2 x (-3) = 6 + 6 = 12
f(0) = 6 - 2 x 0 = 6 - 0 = 6
f(4) = 6 - 2 x 4 = 6 - 8 = -2
The inputs are -3, 0, and 4.
The outputs are 12, 6, and -2.
Thus,
The value of f(-3) is 12
The value of f(0) is 6
The value of f(4) is -2
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x <-8
Graph the inequality
Answer:
<--------
<----|---|---|---|---|---|---|----------
-9 -8 -7 -6 -5 -4 -3
Step-by-step explanation:
Six chicken sandwiches and four drinks cost $16.00. Six chicken sandwiches
and two drinks cost $14.00. How much is a chicken sandwich?
Answer:
$2.67
Step-by-step explanation:
16 ÷ 6 = 2.66666666667
2.67 x 6 = 16.2
(well, it was close.)
Sorry if it's wrong.
Bye, have a great day.
Choose bank, credit union, or both for each statement below:
Must be part of a specific member group to join
Profits are given to shareholders
Offer checking and savings accounts, CDs, loans
Deposits are insured up to $250,000
Fees tend to be higher
Interest customers earn on deposits tends to be higher
Answer:
Must be part of a specific member group to join . - CREDIT UNION.
Credit Unions require that you are a member of a member group to join as well as other entry requirements unlike a bank where the qualification rules are less stringent.
Profits are given to shareholders . - BANK.
A Bank is owned by its investors and shareholders so they will have to distribute profits to them unlike a Credit Union that is owned by its members.
Offer checking and savings accounts, CDs, loans . BOTH.
Both Credit Unions offer these financial products and accounts.
Deposits are insured up to $250,000 - BOTH.
Both of these types of Institutions are insured up to $250,000 by the United States Governments. Credit Unions are insured by the National Credit Union Share Insurance Fund (NCUSIF) and banks are insured by the FDIC (Federal Deposit Insurance Corporation).
Fees tend to be higher . BANKS.
Banks are for profit institutions so they will charge higher fees to make more profit for their investors.
Interest customers earn on deposits tends to be higher. - CREDIT UNIONS.
Credit Unions earn higher deposit interest for customers because they are not-for-profit so do not have to offer less rates to keep more money for their investors.
Bank, credit union, or both have been for each of the statements below:
Credit Union: Must be part of a specific member group to join. Banks: Profits are given to shareholders. Both: Offer checking and savings accounts, CDs, loans. Both: Deposits are insured up to $250,000. Banks: Fees tend to be higher. Credit Unions: Interest customers earn on deposits tends to be higher.Meaning of Banks and Credit UnionBanks are financial institutions that have licenses to accept deposits from customers and provide loans when the conditions are met.
Credit Unions, on the other hand, are not operated for the purpose of making profits. They are formed by members who hold an agreement and their methods of operation are similar to the commercial banks.
In the given points above the similarities and differences between these two financial institutions are shown.
Learn more about Banks here:
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1 Solve the expression 8 x 5 – 12 x + 5 using PEMDAS. 3
39
40
41
42
Answer:
39
Step-by-step explanation:
my h shopping bill come to fourteen pounds and eight-six peace how much change should i receive from 20 pounds note
Answer:
5 pounds 14 pence
50 -19= 31
Step-by-step explanation:
Factor 16a + 72 to find the equivalent expression
Answer:
[tex]=8\left(2a+9\right)[/tex]
Step-by-step explanation:
[tex]16a+72[/tex]
[tex]\mathrm{Rewrite\:}16\mathrm{\:as\:}8\cdot \:2[/tex]
[tex]\mathrm{Rewrite\:}72\mathrm{\:as\:}8\cdot \:9[/tex]
[tex]=8\cdot \:2a+8\cdot \:9[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}8[/tex]
[tex]=8\left(2a+9\right)[/tex]
Hence, the correct answer is [tex]=8\left(2a+9\right)[/tex]
Answer:
8(2a+9)
Step-by-step explanation:
Hope this helps
Suppose you were to collect data for each pair of variables listed below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) Cell phone data plans for a person who wants a large file size: file size, cost b) Lightning strikes by a person watching a lightning storm: distance from lightning, time delay of the thunder c) A streetlight that you are approaching: its apparent brightness, your distance from it d) Cars being catalogued at a dealership: weight of car, age of owner
Answer and explanation:
1. Cost is response variable while file size is explanatory variable. Cost is response variable here because it is the dependent variable and the other is the independently variable that affects the dependent variable cost. The scatter plot will show how much cost increase with each change in file size. Scatter plot is in positive direction and strong
2. Time of delay of thunder is response variable while distance from lightning is explanatory variable. Time of delay is dependent variable while the other is independent variable which affects it. Scatter plot shows how much delay of thunder changes with change in distance from lightning. Positive scatter plot and strong
3. Your distance from it is explanatory variable while apparent brightness is response variable. Distance from it is independently variable while the the other is dependent variable. Scatter plot shows change of brightness with each change of distance. Negative direction as distance increase results in brightness decrease. It is strong.
4. weight of car is response variable while age of owner is explanatory variable. Weight of car is dependent variable while the other is independent variable. Scatter plot shows change of weight of car with change of age of owner. Positive direction as one increases the other increases. Strong
Find the length of The side of a square with area 225square units
Answer:
Step-by-step explanation:
Let length of side = x
area = x²
so x² = 225 = 15²
then x = 15 units
Answer:
Formula for area of square;
A = a^2
where a represents the length of one side of the square, so;
A = a^2
given that the total area is 225,
225 = a^2
√225
= 15
PLEASE HELP WILL GIVE BRAINLIEST TY
You go to the doctor and he gives you 15 milligrams of radioactive dye. After 20 minutes, 7.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm.
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived?
Give your answer to the nearest minute.
How many minutes will you spend at the doctor's office?
Answer:
=34 minutes.
Step-by-step explanation:
Done according to my own understanding!
15mg - 7.25mg = 7.75mg
7.75mg / 20min = 0.3875mg per minute
7.25mg - 2mg = 5.25mg
5.25mg / 0.3875mg = 13.5483871 minutes
13.5483871 minutes + 20 minutes = 33.5483871 minutes
=34 minutes.
7. Which of the following is true about the set of all solutions for f(x) = 4x?
Select all that apply.
A. It is continuous,
B. It is linear
C. It is exponential
D. The point (1,4) falls on the graph,
E. The point (4,0) falls on the graph,
Answer:
B.It is linear 180=3x2+24x+36
Step-by-step explanation:
Find the solution set to the given equation. Answer only in numbers.
4x2 – 16x = 0
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{4x^2 - 16x = 0}\\\large\text{FACTOR the LEFT SIDE of the given equation.}\\\mathsf{\rightarrow 4x(x - 4) = 0}\\\large\text{After step 1 is complete, set the factors to equal to 0.}\\\mathsf{\rightarrow 4x = 0\ or\ x - 4 = 0}\\\larg\text{Lastly, you have to SIMPLIFY new equations you have now.}\\\mathsf{\rightarrow x = 0\ or\ x = 4}\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{x = 0\ or\ x = 4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]plus help me its really simple ill give you the brainiest
Answer:
Whole Numbers
Step-by-step explanation:
Whole numbers is the only set of numbers in the following choices that don't include negative numbers (only positive integers and zero). Therefore, since -7 is negative, it doesn't belong to whole numbers!
The tuition cost for part-time students taking C credits at Stonewall College is given by 300+300C dollars.
A-Find the tuition cost for 13 credits. Do not use dollar signs or commas in your answer.
B-If the tuition cost is $3300, how many credits are taken?
Answer:
[tex]part \: a. \\ t = 300+300(13) = 300+300C = \\300 + 3,900 = 4,200 \\ t = 4,200[/tex]
[tex]part \: b. \\ 3300 = 300+300(c) \\ 3300 - 300 =300(c) \\ 3000 \div 300 = c = 10 \\ c = 10[/tex]
a.
The tuition cost for 13 credits is
= 300 + 300C
= 300 + 300 (13)
= 300 + 3900
= 4,200 dollars.
b.
And, the number of credits is
$3,300 = 300 + 300C
$3,300 - 300 = 300C
$3,000 = 300C
C = 10 credits
Therefore we can conclude that
The tuition cost for 13 credits is $4,200.And, the number of credits that are taken is 10.Learn more about the credit here: brainly.com/question/1475993
A restaurant has square tables. Only one person can sit on either end of the table.
Now
Write out the formula to show how you to work out the "number of people" from the number of tables.
Someone making the booking for 20 people. How many tables must be pushed together?
Answer:
10
Step-by-step explanation: Because 10x2=20
so in this case if they were to push the tables togther only 1 can sit at one square table if there pushed together
unless each table held 2 people like one on one side and one on the other it would be the same formula because 10 on one side of the tables and 10 on the other side would be 10x2
10+10=20 or 10x2=20
ethier one would be the same
hope this helps you!
What is the constant rate of change of the
function represented in the table?
Answer: it is -4 or c
Step-by-step explanation:
Consider the following equation. 4x + 2 = 8x - 5 Which equation and explanation could represent a step in finding the value of x? (4x) + 2 = * (8x) - 5 Use the multiplication property of equality to simplify the variable term on the left side of the equation. 4x + 2-5= 8x - 5 + 5 Use the addition property of equality to move the constants to one side of the equation. 11 / + 2 (4x + 2) = | (8x - 5) Use the multiplication property of equality to simplify the variable terms on both sides of the equation. O 4x + 2 - 4x = 8x - 5 - 4x Use the addition property of equality to move the variables to one side of the equation.
Answer:
Step-by-step explanation:
Given the expression 4x+2 = 8X-5. To find the value of x, we need to follow the steps;
Sep 1:
Add 5 to both using addition property to move 5 to both sides
4x+2+5= 8x-5+5
4x+7 = 8x
Step 2:
Collect like terms
4x-8x = -7
-4x = -7
Step3:
Divide both sides by -4
-4x-4 = -7/-4
x = 7/4
Rectangle A has a length of 2 and a width of 10. Rectangle B has a length of 4
and a width of 5. Rectangle A and Rectangle B (doing a test please answer fast)
Answer: dang bro i never do flvs that early in school. Sorry my guy i got no answer to that. Im quite dumb myself in math
Step-by-step explanation:
An aeroplane X whose average speed is 500°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 120° to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree
Answer:
72
Step-by-step explanation:
ch rectangle. Then write an equation and solve it.
and width of each rectangle.
- 4
A=64
*-4
loc- 4
*-4
Use the graph to determine iffis odd, even, or neither
O A. Even
A
OB
Neither
OC. Odd
Answer: it is neither
Can you please help me thank you
Solve for x:
3(x-4+1b)=8
Step-by-step explanation:
[tex]3\left(x-4+1\cdot \:b\right)=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3\left(x-4+1\cdot \:b\right)}{3}=\frac{8}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x-4+b=\frac{8}{3}[/tex]
[tex]\mathrm{Subtract\:}b\mathrm{\:from\:both\:sides}[/tex]
[tex]x-4+b-b=\frac{8}{3}-b[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x-4=\frac{8}{3}-b[/tex]
[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]
[tex]x-4+4=\frac{8}{3}-b+4[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=-b+\frac{20}{3}[/tex]
[tex]\\ \rm\Rrightarrow 3(x-4+b)=8[/tex]
[tex]\\ \rm\Rrightarrow 3x-12+3b=8[/tex]
[tex]\\ \rm\Rrightarrow 3x+3b=20[/tex]
[tex]\\ \rm\Rrightarrow x+b=20/3[/tex]
[tex]\\ \rm\Rrightarrow x=20/3-b[/tex]