The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone.
The surface area of the cylinder is 2πr(r+h), where r is the radius of the cylinder and h is its height.
The surface area of the cone is πr(l+r), where r is the radius of the cone and l is its slant height.
Since the cylinder and the cone have the same radius, we can call this radius r.
The total surface area of the solid object is therefore 2πr(r+h) + πr(l+r).
We are told that this total surface area is equal to 6336/210 = 30 sq. cm.
Thus, we can set up the equation: 2πr(r+h) + πr(l+r) = 30.
We are trying to find the value of l, which is the slant height of the cone. We are given the value of h, which is the height of the cylinder. We can substitute this value into the equation to get:
2πr(r+30) + πr(l+r) = 30.
This equation can be rearranged and solved for l to find the slant height of the cone.
l = sqrt(900 - 60r).
Since we are given that the slant height of the cone is 26 cm, we can substitute this value into the equation to solve for the radius of the cone:
26 = sqrt(900 - 60r)
Solving for r, we find that the radius of the cone is 15 cm.
Substituting this value back into the equation for the slant height of the cone, we find that the height of the cone is:
l = sqrt(900 - 60(15)) = sqrt(300) = 17.67 cm.
Thus, the height of the cone is approximately 17.67 cm.
PLEASE ANSWER ASAP!!
It's two sections and my answers are included but please correct them if I'm wrong
Some answers are correct, but not all. These are ones that need fixing.
2a.
[tex]\lim_{x\rightarrow-2^-}f(x) = 0[/tex] because as you come towards x = –2 from the left, your y-values are getting closer to 0.
2b.
[tex]\lim_{x\rightarrow-2^+}f(x) = 1[/tex] because as you come towards x = –2 from the right, your y-values are getting closer to 1.
2e.
[tex]\lim_{x\rightarrow5}f(x) = -1[/tex] because as you come towards x = 5 from both sides, your y-values are getting closer to -1.
3a.
[tex]\lim_{x\rightarrow3^-}f(x) = -1[/tex] because as you come towards x = 3 from the left, your y-values are -1.
[tex]\lim_{x\rightarrow3^+}f(x) = 1[/tex] because as you come towards x = 3 from the right, your y-values are 1.
[tex]\lim_{x\rightarrow3}f(x)[/tex] does not exist, since those two one-sided limits aren't don't agree.
3b.
[tex]\lim_{x\rightarrow0^-}f(x) = -\infty[/tex] because as you come towards x = 0 from the left, your y-values are getting huge in a negative way.
[tex]\lim_{x\rightarrow0^+}f(x) = \infty[/tex] because as you come towards x = 0 from the right, your y-values are getting huge in a positive way.
Taylor earns $10.35 per hour and is paid double-time for each hour that she works over 40 hours in a week. Determine Taylor's gross pay if she worked 48 hours last week.
$248.40
$579.60
$596.80
$414.00
Let A={9,8,3,0,5} and B={8,4,7,5,0}. Select from the following choices the one that represents the intersection of A and B?
The required intersection of the two sets A and B is given as A∩B = [8, 5, 0].
Given that,
Let A={9,8,3,0,5} and B={8,4,7,5,0}. The intersection of A and B is to be determined.
Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.
here,
P[PUB] = {9,8,3,4,0,5,7} = 7
P[A∩B] = P[A] + p[B] - P[AUB]
P[A∩B] = 5 + 5 - 10
= 3
From accumulating the common elements between the sets,
A∩B = [8, 5, 0]
Thus, the required intersection of the two sets A and B is given as A∩B = [8, 5, 0].
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Kayla is marking down slippers so that they sell. She advertises that they are now $37, down from $74. What percentage of discount is that
Consider the following solid s. The base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares. Set up an integral that can be used to determine the volume V of the solid. V = dx LIO 26TO = 2 dx Find the volume V of the solid. V=
The volume of the described solid is V = 16r³/3
Given,
A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)
Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = [tex]\int\limits^b_a {A(x)} \, dx[/tex]
The equation of circle x² + y² = r² where r is the radius of the circle.
Equation of upper semicircle yu= √(r²-x²) and
Equation of lower semicircle yl = -√(r²-x²)
Area of cross-section A(x) = (yu² - yl²)
Substitute yu and yl values
A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²) (1)
The limit for volume v varies from -r to r
Thus Volume v = ₋[tex]\int\limits^r_r {A(x)} \, dx[/tex]
Substitute A(x) from (1)
V = ₋[tex]\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx[/tex]
⇒V = 4[r²x - x³/3 ]
⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3
The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3
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20 point question! Please help!
Find the requested value.
f(4) for f(x) =
(7x+7, if x ≤0
2-3x, if 0
X, if x ≥ 3
A)4
B)3
C)35
D)-10
The requested value of f(4) is -10.
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Here, we have
Given: f(x) =(7x+7, if x ≤ 0
2-3x, if 0 =X, if x ≥ 3
f(4) means the value of f(x) when x = 4.
Which expression on the right applies when x = 4?
The first one because it applies only when x ≤ 0 and
The last one because it applies when x ≥ 3 and 4 is greater than 3. The answer is the last expression.
since 4 lies between 0 and greater than
f(4) = 2 - 3(4)
f(4) = -10
Hence, the requested value of f(4) is -10.
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The student body at Springfield Middle School was surveyed about their preference between math and reading. The data below shows the results of the survey organized by gender. Use this two- way frequency table to answer the questions below.
Answer: 2
Step-by-step explanation:
You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants. Write an equation that can be used to find the price of the shirts and pants. Directions: Write the equation in both slope-intercept and standard form for each of the scenarios below. a. Standard Form: b. Slope-Intercept Form: c. If the shirts cost $20 each how much were each of the pants? d. Using the Standard Form, identify the x-intercept of the graph and explain how the x-intercept relates to the price of the pants and shirts. e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the price of the pants and shirts
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> the price of the shirt
y ---> he price of the pants
we have that
The price of three shirts plus the price of two paints must be equal to $300
so
This is the equation of the line in standard form
Convert to slope intercept form
Isolate the variable y
subtract 3x both sides
Divide by 2 both sides
----> equation of the line in slope intercept form
Find out the x-intercept
Remember that the x-intercept is the value of x when the value of y is equal to zero
In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero
Using the Standard Form, identify the x-intercept of the graph
The standard form is
The x-intercept is C/A
we have
so
The x-intercept is the point (100,0)
That means---> The price of the shirt is $100 when the price of the paints is equal to $0
Alternative method to find out the x-intercept (equation in slope intercept form)
For y=0
solve for x
The x-intercept is the point (100,0)
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Parallel lines are cut by the transversal shown. Determine the measures of the requested angles.
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
y = x5, y =
square root of x
; about the x-axis
Rotating the area bounded by the given curves around the designated line yields the solid's volume as [tex]V = \frac{9}{22}\pi[/tex]
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.
The amount
of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,
[tex]`y = f(x) = \sqrt{x}``y = g(x) = x^5`[/tex]
By rotating the area around the x-axis, the solid's volume is given by (using washer method)
[tex]V = \pi int_a^b [f^2(x)-g^2(x)]dx[/tex]
evaluate the integral, limit the plugins, and
[tex]V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi[/tex]
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The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
The population of the city in 2000 = 23.1 million
In 2006 the population will be equal to 28.3 million
Applications of Compound interest:Compound interest may be used in a variety of situations, including increasing or decreasing population, Increasing the count of bacteria increasing an item's value, and a decrease in an item's worth.
The formula for Compound interest is given by
A = Pe^rtWhere P = Principal amount or Initial value
r = rate of interest or increase
t = time period
Here we have
The formula [tex]A = 23.1 e^{(0.0152t)}[/tex] represents the population of a US state, A, in millions, 't' years after 2000.
Here we need to solve the following questions
a. What was the population of the state in 2000
Compare the given formula with A = Pe^rt
=> [tex]23.1 e^{0.0152t} = Pe^{rt}[/tex]
=> Initial value or initial population, P = 23.1 and
rate of increase r = 0.0152
Therefore,
The population of the city in 2000 = 23.1 million
b. When will the population of the state reach 28.3 million?
As we know in 2002 the population = 23.1 million
Let's assume that after 'n' year the population will become 28.3 million
As we know Rate of increase = 0.0152
From the given formula
Population of the city after n, A = 23.1 e^(0.0152n)
As we assumed the population after n years = 28.3
=> 23.1 e^(0.0152n) = 28.3
=> e^(0.0152n) = 28.3/23.1
=> e^(0.0152n) = 1.225
Apply log on both sides
=> log e^(0.0152n) = log 1.225
=> 0.0152n log e = log 1.225
=> 0.0152n (1) = 0.0881
=> n = 0.0881/0.0152
=> n = 5.8 ≅ 6
After 6 years the population will be 28.3 million
After 6 years i.e 2000 + 6 = 2006
Therefore,
In 2006 the population will be equal to 28.3 million
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Lena sold 4,832 copies of her book. Elias sold 4,832 times one-fourth copies of his book. Which statement compares the number of books sold?
Elias sold four times the number of books Lena sold.
Elias sold one-fourth the number of books Lena sold.
Lena sold twice the number of books Elias sold.
Lena sold one-fourth the number of books Elias sold.
Answer:
B) Elias sold one-fourth the number of books Lena sold.
Step-by-step explanation:
How is this the answer? Well after I looked at the problem again, I realized what I needed to do. I needed to do 4,832*1/4 which is 1208.
I got this from the line that says "Elias sold 4,832 times one-fourth copies"
I hope this helps!!!!
help meeeeeeeeeee pleaseee
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations. An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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Suppose that the functions f and g are defined for all real numbers x as follows.
f(x)=4 x
g(x)=2 x-5
By using the concept of function, it can be calculated that-
(g.f)(x) = 8x - 5
(g - f)(x) = -2x - 5
(g + f)(3) = 13
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
f(x) = 4x
g(x)= 2x - 5
(g.f)(x) = g(f(x)) = 2(4x) - 5 = 8x - 5
(g - f)(x) = g(x) - f(x) = 2x - 5 - 4x = -2x - 5
(g + f)(x) = g(x) + f(x) = 2x - 5 + 4x = 6x - 5
(g + f)(3) = 6 [tex]\times[/tex] 3 - 5 = 13
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Mrs. Perky bought 2 3/4 gallons of blue paint. Each gallon of blue paint cost $19.50. Mrs. Perky also bought 1 1/3 gallons of orange paint. Each gallon of orange paint cost $16
Answer:
$74.96 if rounding to hundredths place.
Step-by-step explanation:
If you are looking for the total amount spent, first we will convert 2 3/4 into a decimal, which is 2.75. 2.75 X 19.50 = 53.625. She bought 53.525 dollars worth of blue paint, now we solve for orange. 1 1/3 X 16 = 64/3, which is simplified to 21 1/3. If we add the two togetherwe get 74.9583, but the 3 is repeated. If you are asked to rount to the 100th place, the asnwer is $74.96. If you are rounding to nearest dollar, it is about $75.
Hope this helped :)
In 52.38, which is in the tens place
Answer:5
Step-by-step explanation:
5 2 . 3 8
5= tens
2= ones
3= tenths
8= hundreths
The formula A=18.5 e⁰.¹⁷⁰⁸⁺ models the population of a US state, A, in millions,
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 26.6 million?
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The equation is given below.
[tex]\rm A = 18.5 \times e^{0.1708\times t}[/tex]
The population of the state in 2,000 is calculated as,
[tex]\rm A = 18.5 \times e^{0.1708\times 0}[/tex]
A = 18.5 × e⁰
A = 18.5 Million
The time at which the population of the state reaches 26.6 million will be given as,
[tex]\rm 26.6 = 18.5 \times e^{0.1708\times t}\\\\1.4378 = e^{0.1708\times t}[/tex]
Take natural log on both sides, then we have
0.1708 × t = ln 1.4378
t = 2.126 years
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
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help simplify this 3^1-1
Answer: 2 or 1?
Step-by-step explanation:
3^1 = 3 then 3 - 1 = 2
or 3^(1 - 1) then 3^0 = 1
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 50 POINTS
Answer:
Step-by-step explanation:
Its A
Answer:A
Step-by-step explanation:A cylinder with 8 units.
Mrs tucker writes the fraction 11/4
Answer: 4 2/3
Step-by-step explanation:
Find the value of Za:
Z 0.47=
Round to 2 decimals
The value of za is 80.47.
What is value?Value is the regard that something is held to deserve,the important, worth or usefullness of something.
let us find the value of zero Alpha, Given that alpha is .32. So the value of Z the it is 0.32. Well, we need to begin to considering that we need to the find actually the differentiate one minus alpha. Thus it is going to be in this case one of the (-) 10.32. This is going to be the 0.68. So actually Z of .32, we're going to need to find 0.68 inside the Z table. So let's look at it at it. Look at that at 0.68 oh eight.Let give us the Z score of 80.47. So we can tell that the Z score of zero of alpha, given that the Alpha is 00.32 is going to be 0.47.
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The graph shows the proportional relationship between the number of gems collected and the number of levels that h been completed in a video game.
Determine the constant of proportionality for the relationship.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The constant of proportionality for the relationship is 70.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
We have,
The number of gems collected at different levels is:
At 2 levels, 140 gems are collected.
At 4 levels, 280 gems are collected.
At 6 levels, 420 gems are collected.
This means.
y ∝ x
y is the number of gems collected.
x is the level.
Now,
y = kx
140 = k x 2
k = 140/2
k = 70
Thus,
The constant of proportionality for the relationship is 70.
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Consider the algebraic expression
32pq2−4p2q+12pq−7
Find terms that are not constants.
a) 32p2q,−4p2q,12pq, 7
b) 32, -4, 12, 7
c) 32pq2,4pq2,12pq
d) 32pq2, −4p2q, 12pq
The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
⇒ 32pq² - 4p²q + 12pq - 7
Now,
We know that;
In the algebraic expression the constant term has no variables.
Thus, The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
Therefore, The term which are not constant are;
⇒ 32pq², - 4p²q, 12 pq
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I need help guys can someone help me out?
Answer:
Below
Step-by-step explanation:
$ 5 for the first one <=== a fixed constant ....admission charge
.25 per minute <===== charges dependent on the number of minutes
Answer:
pls rate brainliest
Step-by-step explanation:
the entrance fee to the skating rink=$5
each minute the skater uses the rink costs=$0.25
HOPE IT HELPED YOU
The width and length of a rectangle are 12 units and 16 units. What is the length of the diagonal of the rectangle
The diagonal of a rectangle with a width of 12 units and a length of 16 units is 20 units
Calculating the diagonal of a rectangleFrom the question, we are to determine the length of the diagonal of the rectangle
From the given information,
The width of the rectangle is 12 units
and
The length of the rectangle is 16 units,
The diagonal, D, of a rectangle is given by
D = √(l² + w²)
Where l is the length of the rectangle
and w is the width of the rectangle
l = 16
w = 12
Thus,
The diagonal of the rectangle is
D = √(16² + 12²)
D = √(256 + 144)
D = √400
D = 20
Hence, the diagonal is 20 units
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What’s the answer please thank u
Answer: 1/2
Step-by-step explanation:
slope is rise over run (up and down over left to right)
the perimeter of the rectangle is 26inches and the length is 8 inches what is the width?
Answer:
5 inches
Step-by-step explanation:
P=2(l+w)
Solving for w
w = p / 2 - l = 26 /2 - 8 = 5
Simplify the Linear Expression 6(y + 2) + 9 Responses
The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear expression is given as,
⇒ 6(y + 2) + 9
Simplify the expression, then we have
⇒ 6(y + 2) + 9
⇒ 6y + 18 + 9
⇒ 6y + 27
The linear expression 6(y + 2) + 9 in the simplified form will be 6y + 27.
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Suppose that balloon owners get to pay lower costs for insurance next year. How would this affect the demand curve for balloon rides? How would this affect the supply curve for balloon rides?
A balloon payment is a one-time, large-scale principal payment made near the end of the loan term.
What impact would this have on the demand curve for hot air balloon rides?Total revenue is the amount of money made from the sale of a specific number of items at a specific price.A demand curve is a graph that shows the amounts of stores consumers want at different prices and contains the demand for that product on the y-axis and the price on the x-axis.If a product's price decreases, consumers are more likely to choose it over alternatives that are suddenly more expensive or to simply purchase more quantities of the product, which raises demand from customers.In a similar vein, demand will decline if price rises, all else being equal.To learn more about demand curve demonstrate refer to:
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