What is the surface area and volume of pentagonal pyramid with a apothem of 3 square root of 2 and height of 3
I WILL GIVE BRAINLESS PLS GIVE STEPS
Answers
To find the surface area and volume of a pentagonal pyramid with an apothem of 3√2 and a height of 3, we need to use several formulas.
The apothem of a regular pentagon is the distance from the center of the pentagon to the midpoint of one of its sides. The area of a regular pentagon with side length s and apothem a is given by the formula:
A = (5/2) × s × a
The volume of a pyramid is given by the formula:
V = (1/3) × A × h
where A is the base area of the pyramid and h is the height of the pyramid.
To find the surface area of the pentagonal pyramid, we need to find the area of each face and add them together. Each face of the pentagonal pyramid is a triangle with one side as the base of the pyramid and the other two sides as the slant height of the pyramid. The slant height can be found using the Pythagorean theorem:
l = √(h^2 + a^2)
where h is the height of the pyramid and a is the apothem of the base.
Substituting the given values, we get:
l = √(3^2 + (3√2)^2)
l = √(9 + 18)
l = √27
l = 3√3
The base of the pyramid is a regular pentagon, so we can find its area using the formula:
A = (5/2) × s × a
where s is the length of one side of the pentagon.
The apothem of the pentagon is given as 3√2, so we can find the length of one side using the apothem and the formula for the apothem of a regular pentagon:
a = s / (2√(5-2√5))
3√2 = s / (2√(5-2√5))
s = 6√(5-2√5)
Therefore, the base area of the pyramid is:
A = (5/2) × s × a
A = (5/2) × 6√(5-2√5) × 3√2
A ≈ 31.18
To find the surface area of the pyramid, we need to find the area of each of the five triangular faces. Each face has the same base area A and the same slant height l, so we can use the formula for the area of a triangle:
A = (1/2) × b × h
where b is the length of the base and h is the height of the triangle (which is the slant height of the pyramid).
Substituting the given values, we get:
A = (1/2) × A × l
A = (1/2) × 31.18 × 3√3
A ≈ 26.83
Since there are five triangular faces, the total surface area of the pentagonal pyramid is:
S = 5 × A
S ≈ 134.13
To find the volume of the pyramid, we can use the formula:
V = (1/3) × A × h
Substituting the given values, we get:
V = (1/3) × 31.18 × 3
V ≈ 31.18
Therefore, the surface area of the pentagonal pyramid is approximately 134.13 square units, and the volume of the pyramid is approximately 31.18 cubic units.
Related Questions
5/12 = 8/n
What is N
Answers
Answer:
19.2
Step-by-step explanation:
Cross multiply to get 96=5n
n=19.2
Answer:
n= 96/5 or 19.2 or 19 1/5
Step-by-step explanation:
what is -2(-6+-y) in expanded form
p.s. I'm only a 7th grader so this is 7th grade math
Answers
Answer:
2 mutiplyed by (y + 6)
Step-by-step explanation:
Pull out like factors :
-6 - y = -1 • (y + 6)
at the end:
0 - -2 • (y + 6)
Final result :
2 • (y + 6) !
Fabrício corre diareamente em um parque perto de sua casa. Em certo dia ele deu 3,5 voltas na pista de corrida desse parque que mede 2,8 km qual foi a distância percorrida por Fabrício nesse dia?
Answers
Answer:
9.8 km
Step-by-step explanation:
3.5 * 2.8 = 9.8
lo siento si esto está mal, soy malo en esto.
What is the answer to this question?
What is the volume of this sphere?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Radius = 8 mm
Answers
Please help 8 through 10
Answers
(an outlier is a number that doesn’t really belong because it could be too small or too big. in this case, it’s too big)
9. The mean is 14
(you add all the numbers up and divide it by how many numbers you added with)
10. They are using mode because it is the most common number in the set. Their claim is misleading because some books are greater than 5 dollars
10. Which graph shows the solution to the inequality <-6?
Answers
-6x -6= help pls i don’t understand
Answers
The answer here is \(x=-1\)
\(Explanation\)
___________________________________________________________
\(-6x -6 = 0\)
\(-6x - 6 +6 = 0+6\)
\(-6x = 6\)
\(-6x/-6 = 6/-6\)
\(x = -1\)
3(0.5x-4)=3/2x-1.2
How do I solve this question
Answers
Answer:
Step-by-step explanation:
3(0.5x-4)=3/2x-1.2
We simplify the equation to the form, which is simple to understand
3(0.5x-4)=3/2x-1.2
Reorder the terms in parentheses
+(+1.5x-12)=/2x-1.2
Reorder the terms in parentheses
We move all terms containing x to the left and all other terms to the right.
0=0
We simplify left and right side of the equation.
0=0
0=0
This equation is an identity, so all real numbers are solutions.
Answer:
Use the distributive property for the ( ) then add your like terms to get
Step-by-step explanation:
So there are no soultions for your answer
utomobile trips there are major roads from city to city and major roads from city to city . how many different trips can be made from city to city passing through city ?
Answers
There are 8 different trips that can be made from City X to City Z, passing through City Y.
To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.
First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.
By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:
Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z
= 2 x 4
= 8
This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.
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Complete question is:
Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?
24. Anna went bowling. She spent less than or equal to $30, but spent more
than $25. Create a number line that shows all the possible amounts that
Anna may have spent at the bowling alley.
Answers
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
What is a number line?In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.
Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.
The inequality is given as,
$25 < x ≤ $30
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
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question 3 a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland?
Answers
Pan tool do the data analyst use to select the area on the map representing Finland.
What is data analyst?
A data analyst is working with the world happiness data in table. To use Pan tool to select the area on the map representing Finland.
A data professional examines data to uncover critical insights about a company's consumers and how the data may be utilized to address problems. They also share this information with corporate executives and other stakeholders.
Pan allows us to shift the map to focus on it or present the areas in the way we wish. Simply pick the Pan Option and move the map around to suit your needs. Alternatively, you may move the map by holding down the Shift key.
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solve for x pls helppppp
Answers
Answer:
I think it is 30 degrees.
Step-by-step explanation:
Alina had 3/5 much money as edna. edna had $32 more than alina. how muuch money would alina have if her mother gave her 1/6 more of what she had at first?
Answers
Alina has $22.4 if her mother gave her 1/6 more of what she had at first.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.To find how much money would Alina has if her mother gave her 1/6 more of what she had at first:
Alina has 3/5 much money as Edna.
Edna has $32.
Alina's mother gave her more 1/6 or 3/5.
So, first, we will find 1/6 of 3/5.
3/5 × 1/6 = 3/30Now, add 3/30 to 3/5.
3/5 + 3/30 = 21/30.Hence, Alina has 21/30 as much money as Edna.
Then,
$32 × 21/30 = $22.4Therefore, Alina has $22.4 if her mother gave her 1/6 more of what she had at first.
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1000+1000^3 I NEED HELP PLEASE
Answers
To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).
Following this order, we first need to evaluate the exponent, which gives:
1000^3 = 1,000,000,000
Then, we can substitute this value back into the expression:
1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000
Therefore, 1000 + 1000^3 equals 1,000,001,000.
Answer: 8000000000
Step-by-step explanation:
A store is having a 12-hour sale. The total number of shoppers who have entered the store t hours after it begins is modeled by the function S defined by S(t)=0.5t^4-16t^3+144t^2S(t)=0.5t 4
−16t 3
+144t 2
for 0\leq t\leq120≤t≤12. At time t=0, when the sale begins, there are no shoppers in the store. The rate at which shoppers leave the store, measured in shoppers per hour, is modeled by the function L defined by L(t)=-80+\frac{4400}{t^2-14t+55}L(t)=−80+ t 2
−14t+55
4400
for 0\leq t\leq120≤t≤12. According to the model, how many shoppers are in the store at the end of the sale (time t = 12)? Give your answer to the nearest whole number.
Answers
There are approximately 27,735 shoppers in the store at the end of the sale (t = 12).
What is a function?
A function is a mathematical concept that relates a set of inputs (called the domain) to a set of outputs (called the range). It is a rule or relationship that assigns a unique output value to each input value. In other words, for every input, there is exactly one corresponding output.
A function is typically denoted by a symbol, such as "f," followed by parentheses containing the input value. The output value is obtained by applying the rule or formula defined by the function to the input value.
To determine the number of shoppers in the store at the end of the sale (t = 12), we need to calculate the net change in the number of shoppers from the beginning of the sale to the end.
The net change in the number of shoppers is obtained by subtracting the number of shoppers leaving the store from the number of shoppers entering the store during the 12-hour sale.
Using the provided functions, we have:
\(S(t) = 0.5t^4 - 16t^3 + 144t^2\) (number of shoppers entering the store)
\(L(t) = -80 + \frac{4400}{t^2 - 14t + 55}\) (number of shoppers leaving the store)
To find the number of shoppers at the end of the sale (t = 12), we can calculate:
\(Number of shoppers =\int\limits^{12}_0(S(12) -L(t) )dt\)
Substituting the values into the equation:
\(Number of shoppers =\int\limits^{12}_0 (S(12) - (-80 + \frac{4400}{t^2 - 14t + 55}))dt\)
Evaluating the integral and substituting t = 12:
\(Number of shoppers =[(0.1t^5-4t^4+t^3 )- (-80t + {ln|t-11|-ln|t-5|})]\) evaluate from 0 to 12.
Calculating further:
\(Number of shoppers = 24883.2 - [-80(12) +\frac{2200}{3}[ {ln|12-11|-ln|12-5|}]] + [-80(0) +\frac{2200}{3} [ {ln|0-11|-ln|0-5|}]]\)
Number of shoppers = 24883.2 - [-2273.95 ] + 578.2
Finally, we need to substitute t = 12 into the S(t) function to obtain the number of shoppers:
Number of shoppers = 24883.2+2852.15
Calculating:
Number of shoppers ≈ 27,735
Therefore, according to the model, there are approximately 27,735 shoppers in the store at the end of the sale (t = 12).
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Hank runs a successful hot dog stand right across from the arch at the University of Georgia in downtown Athens. Hank has to order his hot dogs, buns, mustard, relish, and all other condiments in bulk, as well as pay taxes, licensing fees, and other small business expenses. Therefore, Hank has a relatively large “sunk” cost associated with his business – it averages out to $950 per week just to keep the cart open. The cost of producing hot dogs is given by C(h) = 950 + .45(h). Where h is the number of hot dogs and C(h) is the cost. If he sold 100 hotdogs at $10.25 each, how much profit would he make for the week?
Answers
The profit he would make in one week is $30.
What is Hank's profit?Profit is the total revenue less total cost.
Total revenue = price of one hot dog x number of hotdogs sold
$10.25 x 100 = $1025
Total cost = 950 +( 0.45 x 100)
950 + 45 = 995
Profit = 1025 - 995 = $30
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Which of the following are true statements about David Hilbert?
He invented the point.
He was a German mathematician.
n He developed Hilbert's axioms.
He wrote a blography on Euclid.
Hilbert's Improvements to geometry are still used in textbooks today.
Answers
Answer:
he invented the point
he was a German mathematician
he Hilbert's improvements to geometry are still used in textbooks today
he developed Hilbert's axioms
Step-by-step explanation:
Answer:
He was a German mathematician.
If only one is true then you're good to go.
Whoops never mind.. :/
Which of the following is equal to g(x)?
A. 3ˣ - 1
B. 3ˣ + 2
C. 2(3)ˣ
D. 3ˣ + 1
Answers
I need help please help out right quick
Answers
Answer:
I'm answering the same
Step-by-step explanation:
I'm answering the same
Answer:
Y = 22
Step-by-step explanation:
use diamond to split 6 and 2
group 6 and 16
take out 2 and 8
and add y and 16
Y = 22
Increase 100kg by 30%
Answers
Answer:
130kg
Step-by-step explanation:
30% of 100 is 30
Answer:
133
Step-by-step explanation:
100/30 = 33.333
100+33=133
please help me solve this
\(\frac{7p^{2}-56p }{p^{2}+2p-80}\)÷\(\frac{7p}{p-7}\)
Answers
The simplified expression in the problem that we have in the question is;
(p - 7)/(p + 10)
How do you simplify an expression?
By merging like terms , using mathematical processes, and simplifying any complex or unnecessary components, one can simplify an expression and bring it to its simplest or most direct form. This is the task that we have in the problem before us here.
Looking at the expression in the question, we can simplify the quadratic involved to have that;
7p (p - 8) /(p - 8) (p + 10) * (p - 7)/7p
(p - 7)/(p + 10)
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during a cruise Mike wants to maintain his exercise schedule. He learns that on the ship’s track three laps is 5/8 of a mile. If mike wants to run 3 miles how many laps does he need to run
Answers
There were 15 bunnies at the pet store. Each of the 5 female bunnies had 5 babies! How many bunnies are there in the pet store now?
Answers
Answer:
45??!
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
If there were 15 bunnies 5 were females so there is 10 men and if each female had 5 babies each then that would be 25 babies plus the 10 men should be 35
(c) explain what would happen to the length of the interval if the confidence level were... (i) increased to 99% (ii) decreased to 80%
Answers
If the confidence level were increased to 99%, the width of the confidence interval increases, when decreased to 80%, the width of the confidence interval decreases.
What is confidence interval?A confidence interval provides a range of estimated values for a population parameter's real value. A confidence level is connected to confidence intervals. The width of the confidence interval grows as the confidence level increases. The width of the confidence interval reduces as the confidence level goes down.
Since the margin of error grows as the confidence level does as well, the confidence interval will be bigger. Hence it increases for 99% and decreases for 80%.
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0 of 10 Save Find the equation of the line through the given point that is perpendicular to the given line. (The slope of the perpendicular line is the negative reciprocal of the slope of the given line if the given line is neither vertical nor horizontal) jedia 4 (a) y=-x+7, R(8,-1) (8.3.11) (b) 4y+8x-9=0, S(0,4) KILD (a) y- (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)
Answers
The equation of the line through point R(8,-1) that is perpendicular to the line y=-x+7 is y = x + 9.
To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line.
(a) Given line: y = -x + 7
The slope of the given line is -1.
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1.
Using the point-slope form of a line (y - y₁ = m(x - x₁)), we can substitute the coordinates of point R(8,-1) and the slope of the perpendicular line:
y - (-1) = 1(x - 8)
y + 1 = x - 8
Simplifying the equation, we get:
y = x - 9
So, the equation of the line through point R(8,-1) that is perpendicular to the line y = -x + 7 is y = x - 9.
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Solve the following differential equations by Separation of Variables:
a. dy/dx = 2yeˣ
b. dy/dx = eˣ/4y²
Answers
The general solution to the differential equation for:
a. dy/dx = 2yeˣ is:
y = Ce^(2e^x), where C is an arbitrary constant.
b. dy/dx = eˣ/4y² is:
y = [(3/4)(e^x + C)]^(1/3), where C is an arbitrary constant.
a. dy/dx = 2ye^x
Step 1: Rearrange the equation to have the variables separated.
dy/y = 2e^xdx
Step 2: Integrate both sides of the equation separately.
∫(dy/y) = ∫(2e^xdx)
The integral of (dy/y) is ln|y| + C1, where C1 is the constant of integration.
Step 3: Integrate the right side of the equation.
∫(2e^xdx) = 2∫(e^xdx) = 2e^x + C2, where C2 is another constant of integration.
Step 4: Set the integrals equal to each other.
ln|y| + C1 = 2e^x + C2
Step 5: Combine the constants into a single constant.
ln|y| = 2e^x + C
Here, C = C2 - C1 is the combined constant.
Step 6: Remove the natural logarithm by exponentiating both sides.
|y| = e^(2e^x + C)
Step 7: Remove the absolute value by considering both positive and negative cases.
y = ±e^(2e^x + C)
Therefore, the general solution to the differential equation is:
y = Ce^(2e^x), where C is an arbitrary constant.
b. dy/dx = e^x/(4y^2)
Step 1: Rearrange the equation to have the variables separated.
4y^2dy = e^xdx
Step 2: Integrate both sides of the equation separately.
∫(4y^2dy) = ∫(e^xdx)
The integral of (4y^2dy) can be evaluated as (4/3)y^3 + C1, where C1 is the constant of integration.
Step 3: Integrate the right side of the equation.
∫(e^xdx) = e^x + C2, where C2 is another constant of integration.
Step 4: Set the integrals equal to each other.
(4/3)y^3 + C1 = e^x + C2
Step 5: Combine the constants into a single constant.
(4/3)y^3 = e^x + (C2 - C1)
Here, C = C2 - C1 is the combined constant.
Step 6: Solve for y.
y^3 = (3/4)(e^x + C)
Step 7: Take the cube root of both sides.
y = [(3/4)(e^x + C)]^(1/3)
Therefore, the general solution to the differential equation is:
y = [(3/4)(e^x + C)]^(1/3), where C is an arbitrary constant.
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NO LINKS PLEASE thanks:)))
Answers
Answer:
c. it is not a solution to either equation
Step-by-step explanation:
let me know if this is incorrect
3. The system of equations for two liquid surge tanks in series is
A₁ dh'₁/dt = q'ᵢ - 1/R₁ h'₁, q'₁ = 1/R₁ h'₁
A₂ dh'₂/dt = 1/R₁ h'₁ - 1/R₂ h'₂ q'₂ = 1/R₂ h'₂
Using state-space notation, determine the matrices A,B,C, and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ , and the output variable is the flow rate deviation, q'₂.
Answers
The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.
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Find the area.
A hexagon with side length 6m.
Answers
Answer:
93.53m.
Step-by-step explanation:
.
Solve for x and y-intercepts and show the work! Im on a timed test!
2x - 3y = 12
Answers
Answer:
Equation: y=2/3x-4
y intercept is (0,-4)
x intercept is (6, 0)
Step-by-step explanation:
Answer:
x=3/2y+6
y=2/3x-4
Step-by-step explanation:
To find Y
divide both sides with -3
-3y=-2x+12/:-3
y=2/3x-4
to find x
2x=3y+12
divide both sides with 2
2x=3y+12/:2
x=3/2y+6
Hope this helped :)