When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.
Explanation:The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.
Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.
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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]
Let's analyze the relationship between the volume of a cylinder and its dimensions.
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
[tex]\( r \)[/tex] is the radius of the cylinder,
[tex]\( h \)[/tex] is the height of the cylinder.
Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]
Now, let's compare the volumes before and after the increase in radius:
1. Original Volume [tex](\( V_{\text{original}} \))[/tex]
[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]
2. New Volume [tex](\( V_{\text{new}} \))[/tex]
After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].
[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]
Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]
[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]
❤️ Kinda fuzzy but can anyone help?
Answer:
thats to hard
Step-by-step explanation:
get a calculater
helpppppppppppppppppppppppp
A shoe store marks up it's merchandise by 8%. What was the selling price of a pair of shoes whose wholesale price is $24.50?
Answer: The selling price of a pair of shoes is $26.46.
Step-by-step explanation:
Given : The wholesale price of a pair of shoes = $24.50
i.e. C.P. = $24.50
Mark up percent = 8% = 0.08 ( To convert a percentage into decimal we divide it by 100)
Formula : S.P. = (Mark up percentage ( in decimal)) x (C.P.)+ (C.P.)
i.e.
[tex]S.P.=(0.08) \times (24.50)+24.50\\\\\Rightarrow\ S.P.=(0.08+1)(24.50)\\\\\Rightarrow\ S.P.=(1.08)(24.50)\\\\\Rightarrow\ S.P.=26.46[/tex]
Hence, the selling price of a pair of shoes is $26.46.
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
A. ∠J ≅ ∠M
B. ∠L ≅ ∠R
C. ∠K ≅ ∠N
D.∠R ≅ ∠K
Answer:
B. <L=<R
Step-by-step explanation:
^^^Just too test got 100%
Liam owns some rectangular plots of land. All of the plots are the same length, x, and the width of each plot is 5 yards less than the length. The total number of plots Liam owns is 20 more than the length of a plot. If the total area of all the plots Liam owns is 2,688 square yards, which statements about the length of each plot are true?
*The equation x3 − 15x2 − 100x − 2,688 = 0 can be used to find the length of each plot.
**The equation x3 + 25x2 + 100x − 2,688 = 0 can be used to find the length of each plot.
***The equation x3 + 15x2 − 100x – 2,688 = 0 can be used to find the length of each plot.
****The length of each plot is 12 yards.
*****The length of each plot is 8 yards.
Final answer:
The correct equation to find the length of each of Liam's rectangular plots is x³ + 15x² - 100x - 2,688=0. This cubic equation must be solved to determine the actual length of each plot.
Explanation:
To solve the problem involving Liam's rectangular plots of land, you need to find the length x of each plot. Since the width is 5 yards less than the length, the width is x - 5 yards. With the number of plots being 20 + x, and the total area given as 2,688 square yards, you can set up an equation using the area of a rectangle (length times width) multiplied by the number of plots equal to the total area
The correct equation to determine the length of each plot is as follows:
X (width) × X (length) × (number of plots) = total area
(x) (x - 5) (20 + x) = 2,688
x(x - 5)(x + 20) = 2,688
x³ + 15x² - 100x = 2,688
This simplifies to the equation x³ + 15x² - 100x - 2,688 = 0, which corresponds to option three. Upon solving this cubic equation, you would find the length of each plot. However, the last options are not supported by the given information and should be solved for using the derived equation.
A triangle has an area of 40 square units. Its height is 8 units. What is the length of its base?
The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain river normally flows at a speed of 2 miles per hour. What must its speed be in order to transport particles that are 15 times as massive as usual? Round your answer to the nearest hundredth.
The speed of the river must be about ____ miles per hour.
Please explain how to do it I have the answer but don't know how to get to it.
To transport particles that are 15 times as massive as usual in a river, the speed of the river would need to increase to about 4.14 miles per hour, calculated based on a proportionality relationship to the sixth power.
Explanation:Given the mass of the particles that a river can transport is proportional to the sixth power of the speed of the river, we can express this relationship as m ∝ v6, where m is the mass of the particles and v is the speed of the river. Then, m1/v16 = m2/v26 which is a statement of the proportionality. If a river, with a normal speed of 2 miles per hour (v1), can transport particles of a certain mass (m1), in order to transport particles that are 15 times as massive as usual (m2 = 15m1), we want to find the required speed (v2).
Substituting the known quantities into the proportionality, we get m1/26 = 15m1/v26. Simplifying this equation gives 1/26 = 15/v26.
To solve for v2, you can perform a sixth root operation on both sides of the equation, resulting in v2 = 6√(15*26). By calculating this, the required speed is nearly 4.14 miles per hour.
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hello please help me with this quick
The newspapers cover page is 3/8 text and photographs filled the rest if 2/5 of the text is an article about endangered species, what fraction of the cover page is the article about endangered species
The article about endangered species is ³/₂₀ of the cover page
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
Given:
Total Area of Cover Page = X
Text Section is 3/8 the newspapers cover page
[tex]\texttt{Text Section Area} = \frac{3}{8} \times \texttt{Total Area of Cover Page}[/tex]
[tex]\texttt{Text Section Area} = \boxed {\frac{3}{8}X}[/tex]
The rest of cover page is Photographs Section
[tex]\texttt{Photographs Section Area} = (1 - \frac{3}{8}) \times \texttt{Total Area of Cover Page}[/tex]
[tex]\texttt{Photographs Section Area} = \boxed {\frac{5}{8}X}[/tex]
2/5 of the text is an article about endangered species.
[tex]\texttt{Endangered Species Article Section Area} = \frac{2}{5} \times \texttt{Text Section Area}[/tex]
[tex]\texttt{Endangered Species Article Section Area} = \frac{2}{5} \times \frac{3}{8}X[/tex]
[tex]\texttt{Endangered Species Article Section Area} = \frac{2 \times 3}{5 \times 8}X[/tex]
[tex]\texttt{Endangered Species Article Section Area} = \frac{6}{40}X[/tex]
[tex]\texttt{Endangered Species Article Section Area} = \frac{6 \div 2}{40 \div 2}X[/tex]
[tex]\texttt{Endangered Species Article Section Area} = \boxed {\frac{3}{20}X}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
NEED HELP ASAP PLEASE HELP
Use the figure below to find AC.
Select one:
a. 40
b. 20
c. 50
d. 60
if the measures of the angles of a triangle are represented by (x+30), (4x+30), and (10x-30), the triangle must be
Toys R us is having a 38% off sale on all of their backpacks. If a backpack normally cost $22 how much will it be on sale
Joaquim is baking giant cookies for the school bake sale. They will be sold for $20 for one large cookie or $20 for three small cookies. Which offer is the better buy? Explain your reasoning.
Three small cookies for $20 is a better buy than one large cookie for $20 because the cost per small cookie is cheaper ($6.67 per small cookie). You get more cookies for the same price.
To determine which offer is the better buy, let's compare the cost in terms of cookies:
One large cookie: $20 for 1 large cookie.Three small cookies: $20 for 3 small cookies.Next, let's find the cost per small cookie:
For the large cookie: $20 / 1 large cookie = $20 per large cookie.For the small cookies: $20 / 3 small cookies = $6.67 per small cookie (approximately).Therefore, since $6.67 per small cookie is less than $20 for 1 large cookie, the offer of three small cookies for $20 is the better buy. This way, you get three cookies for the same price as one large cookie.
Create three polynomials. Each must contain at least two terms. Choose three of the following properties:
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Write the equation of a circle with a center at (15, –35) and a diameter of 100.
(x – 15)2 + (y + 35)2 = 250
(x – 15)2 + (y + 35)2 = 50
(x – 15)2 + (y + 35)2 = 2500
(x – 15)2 + (y + 35)2 = 100
The main arena hall has dimensions 200 m by 85 m. On a large diagram on the office wall the scale is 1:40. What are the dimensions of the floor space on the diagram?
Answer:
500 cm by 212.5 cm
Step-by-step explanation:
Using the scale 1:40 on the 200 m dimension, we have 200/40 = 5 m. Each meter is 100 cm; this makes this 5(100) = 500 cm.
Using the scale on the 85 m dimension, we have 85/40 = 2.125 m. Each meter is 100 cm; this makes this 2.125(100) = 212.5 cm.
Answer:
500 cm by 212.5 cm
Step-by-step explanation:
Given :
The main arena hall has dimensions 200 m by 85 m.
On a large diagram on the office wall the scale is 1:40.
To Find: What are the dimensions of the floor space
Solution :
Length of arena hall = 200 m
Scale is 1:40
So, the length of the floor = [tex]\frac{200\times 1}{40}[/tex]
= [tex]5m[/tex]
Since 1 m = 100 cm
So, 5 m = 100*5 = 500 cm
Width of arena hall = 85 m
So, width of floor = [tex]\frac{85\times 1}{40}[/tex]
= [tex]2.125m[/tex]
Now 1 m = 100 cm
So, 2.125 m = 212.5 cm
Thus the dimensions of floor is 500 cm by 212.5 cm
If a piece of licorice is to be cut into 10 equal-side pieces. If the length of the piece of licorice is 2/3 yard, how long will each piece of licorice be?
Which are the solutions of x2 = –11x + 4?
Answer:
If your on edu the simple answer is A
Step-by-step explanation:
The area of the large cylinder’s piston in this hydraulic system is 3.14m2 . What is the output force
An airplane has a maximum capacity of 118 passengers. The flight attendant has loaded 40 passengers. Which inequality represents the solution set that shows the number of passengers, p, that can still load the plane? A) p ≥ 68 B) p ≤ 68 C) p ≤ 78 D) p ≥ 78
Answer:
Its C
Step-by-step explanation:
It is C because you can only load 78 more passengers
Answer:
c
Step-by-step explanation:
If p = the number of passengers that can still load the plane, then p + 40 ≤ 118.
Therefore,
p + 40 ≤ 118
p + 40 − 40 ≤ 118 − 40
p ≤ 78
Find the volume of the composite solid if the diameter is 8.7 yards. Round your answer to the nearest hundredth.
A.
220.76 yd3
B.
429.88 yd3
C.
535.02 yd3
D.
693.55 yd3
Answer: D. 693.55 yd3
Step-by-step explanation:
Given: The diameter of the composite solid = 8.7 yards
Then , the radius of the composite solid = [tex]\dfrac{8.7}{2}=4.35\ \text{yards}[/tex]
Height of cylinder = 9 yards
Height of cone = 8 yards
The volume of cylinder is given by :-
[tex]V_1=\pi r^2h\\\\\Rightarrow V_1=(3.14159265359)(4.35)^2(9)\\\\\Rightarrow V_1=535.021082888{ yards}^3[/tex]
The volume of cone is given by :-
[tex]V_2=\dfrac{1}{3}\pi r^2h\\\\\Rightarrow V=\dfrac{1}{3}(3.14159265359)(4.35)^2(8)\\\\\Rightarrow V=158.5247653\text{ yards}^3[/tex]
Now, Volume of the composite figure will be :
[tex]V=V_1+V_2\\\\\Rightarrow\ V=535.021082888+158.5247653\\\\\Rightarrow\ V=693.545848188\approx693.55\text{ yards}^3[/tex]
helpppppppppppppppppppppppppp
△ABC∼△LMN , AB is 8 inches, BC is 14 inches, and LM is 12 inches. What is MN ? Enter your answer in the box.
Answer:
The measure of MN is 21 inches.
Step-by-step explanation:
It is given that △ABC∼△LMN.
The corresponding sides of two similar triangles are proportional.
[tex]\frac{AB}{LM}=\frac{BC}{MN}[/tex]
[tex]\frac{8}{12}=\frac{14}{MN}[/tex]
[tex]8\times MN=14\times 12[/tex]
Divide both sides by 8.
[tex]MN=\frac{168}{8}[/tex]
[tex]MN=21[/tex]
Therefore we can say that if △ABC∼△LMN, then the measure of MN is 21 inches.
PLEASE HELP ASAP!!!!!
A 1.6km road rises vertically 400m. what is the angle of elevation of the road? angle of elevation = _ degree
Final answer:
To determine the angle of elevation of the road, we use the tangent ratio of rise (400m) to run (1600m), resulting in an angle of approximately 14 degrees.
Explanation:
To calculate the angle of elevation of the road, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this context, the opposite side is the rise, which is 400 meters (the vertical height the road climbs), and the adjacent side is the run, which is the horizontal distance of the road, 1.6 km or 1600 meters.
We can calculate the angle of elevation, ϴ (theta), using the formula:
tangent(ϴ) = opposite/adjacent
tangent(ϴ) = 400/1600
ϴ = arctangent(400/1600)
ϴ = arctangent(0.25)
After calculating arctangent(0.25), we find the angle of elevation is approximately 14 degrees.
jami can now mow 1/6 acre in 8 minutes. if her rate is constant, can jami mow 1 and 1/2 acres in one hour? explain ur reasoning.
A scale drawing of an automobile has a scale of 1 in.
The actual width of the car is 8 ft. What is the width on the scale drawing?
Which of the following ordered pairs is a solution of x + 1/2 y = 1?
(-2, 6)
(2, -6)
(-2, -6)
The correct ordered pairs are (-2, 6)
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables.
Given:
x + 1/2 y = 1
Now, we will take the ordered pairs (-2, 6)
So, substitute x= -2 and y= 6 in the given equation we get
x+ 1/2y
=-2 + 1/2(6)
=-2 + 3
=+1
Hence, the correct ordered pairs are (-2, 6)
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et f(x) = x2 + 6 and g(x) g(x) x+8/x . Find ( g o f)( -7)
a.63/55
b.259/49
c.-57/7
d.384/7
Answer:
A
Step-by-step explanation:
A function composition is where one function is substituted within another function and is written g(f(x)). Here we will substitute f(x) into g(x). For g(f(-7)), we substitute -7 for x.
[tex] \frac{x^2+6+8}{x^2+6}[/tex]
Now substitute -7 for x.
[tex]\frac{x^2+6+8}{x^2+6} = \frac{(-7)^2+6+8}{(-7)^2+6}=\frac{49+6+8}{49+6}=\frac{63}{55}[/tex]