Rectangular garden has sides:
width, length, width, length
The perimeter is sum of all the 4 sides.
So, we can say:
84 = 2w + 2l
Where
w is width
l is length
Width is 19.5, so we find length:
84 = 2(19.5) + 2l
84 = 39 + 2l
2l = 45
l = 22.5 feet
Now, area is given by:
Area = length * width
Area = 22.5 * 19.5 = 438.75 sq. ft.
suppose that 15 inches of wire cost 60 cents. at the same rate, how much (in cents) will 11 inches of wire cost
The cost of 11 inches of wire will be 44 cents
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The 15 inches of wire costs 60 cents, so the cost of 1 inch of wire is;
Rate = 60/15 =4 cents
So the cost of 1 inch of wire which is the rate of 4 cents.
Now we have to find the cost (in cents) of 11 inches wire.
We know the cost of 1 inch of wire cost 4 cents so the cost of 11 inches of wire is;
= Total inches of wire x Price of 1 inch of wire
= 4 x 11
= 44
Tehrefore, The cost of 11 inches of wire is 44 cents
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The points H(3,-1), I(-6, -1), and J(3,-9) form a triangle. find the
perimeter of the triangle?
The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
The points which form a triangle are:
H(3,-1) ; I(-6,-1) and J(3,-9)
Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:
To find the length we have to find the distance between the points.
Using distance formula i.e.
[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]
Let the length of the sides be A1, A2 , A3
On applying the distance formula to H(3,-1) and I(-6,-1) ;
We get,
A1 = [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]
= [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]
= [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]
= [tex]\sqrt{81}[/tex]
= 9
On applying the distance formula to I(-6,-1) and J(3,-9);
We get,
A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{[ 81 + 64 ][/tex]
= [tex]\sqrt{145}[/tex]
= 12.04
On applying the distance formula to J(3,-9) and H(3,-1);
We get,
A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{ [ 0 + 64 ][/tex]
=[tex]\sqrt{64}[/tex]
= 8
Hence,
The perimeter is 9 + 12.04 + 8 = 29.04
The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
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What is the image of the point ( − 1 , 2 ) after a rotation of 270 counterclockwise about the origin?
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Solve the proportion. 7 42 = 1 w w=
When the given proportion is solved the value of w is calculated to be 6.
What is proportion?
A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.
When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.
for example 5/10 = 1/2, 5:10 = 1: 2
7:42 = 1 : w
[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]
[tex]\frac{1}6{} = \frac{1}{w}[/tex]w = 1 x 6
w = 6
When the given proportion is solved the value of w is calculated to be 6
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[tex]\rm\int_0^1 \frac{( {x}^ \varphi - 1 {)}^{2} }{ log {}^{2} (x) } dx\\[/tex]
I assume the natural logarithm, and not the base-10 log. Parameterize the integral as
[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]
Differentiate twice with respect to [tex]a[/tex].
[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]
[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]
Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].
[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]
[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]
[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]
Let [tex]a=\phi[/tex] to recover the original integral.
[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]
Using various properties of the golden ratio [tex]\phi[/tex], namely
[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]
[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]
[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]
we can simplify the result to
[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]
if p varies directly as q.for p =4.5 when q=12 .find(1) the relationship between p and q (2) p and q=16
( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12
( 2 ) If p and q is 16 then the direct variation is 1
What is direct variation?Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.
There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.
If p varies directly as q
for p = 4.5
when q = 12
Then p = kq
4.5 = 12k
k = 12/4.5
k = 8/3
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Fully factorise 8x+24y+16z
Answer:
8 ( x + 3y + 2z) we can take 8 common in the whole expression
b. The product (a - b)(a + b) is called the
when simplified, it is called
of two squares and, when simplified it is equivalent to
The product (a - b)(a + b) is called the special binomial product, when simplified it is called algebraic identity of two squares and, when simplified it is equivalent to a² - b²
What is simplification?An equivalent, simpler (typically shorter) mathematical expression is substituted for the original one through the process of simplification.
Computer algebra's simplification of algebraic expressionsLogic optimization involves simplification of boolean expressions.A more straightforward but typically non-equivalent formula results from simplification of conjunction elimination in inference in logic.simplification of fractionsIn propositional logic, simplification is a valid immediate inference, argument form, and inference rule that draws the conclusion that if the conjunction A + B is true, then A + B is true as well. By deriving one of the conjuncts of a conjunction on a line by itself, the rule enables the brevity of longer proofs.
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7 lorries can carry 987 cartons of books. How many cartons of books can each lorry carry
Answer:
141 each
Step-by-step explanation:
test score hours studying 2 3 4 test score 44 66 88 test score ratio hours studying 22 1 ? ?
The test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
What is a ratio?The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.
To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
If 2 hours of studying = 44 marks
If 3 hours of studying = 66 marks
If 4 hours of studying = 88 marks
Then total sum of hours of studying = 9 hours
9 hours of studying = Sum of all marks
= 44 + 66 + 88
= 198
1 hour of studying = 198/9
= 22 marks
So, the test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
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B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.
Answer
Tan (A) = 0.109 radians
Explanation:
The figure given is a right angles triangle
Given that AB = c is the hypotenus
AC = b = adjacent
BC = a = opposite
Tan A can be calculated using SOH CAH TOA
Tan A = opposite / adjacent
Tan A = BC / AC
BC = a = 4.020
We need to find b uisng pythagoras theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}[/tex]b = 11.307
Tan A = 4.020 / 11.307
Tan A = 0.3555
A = tan ^-1 (0.3555)
A = 19.570 degrees
Convert degrees to radian
since 1 pi = 180 degrees
x pi = 19.570
Cross multiply
19.570 * 1 = x * 180
x = 19.570 / 180
x = 0.109
Therefore, tan (A) is 0.109 radians
Finding Distance Using Absolute Value
3) Find the difference between each set of points on the number line. Confirm your answer by writing an absolute value statement for each example.
Points
Difference Between
Absolute Value Statement
23 and -45
23 – (-45) = 23 + 45 = 68
|23 – (-45) |= 68
-15 and 35
47 and -12
-43 and 27
-10 and 4
50 and -25
36 and -19
-30 and -40
-2 and 45
18 and 46
-10 and -44
-28 and 41
7 and -9
-52 and 28
22 and -50
-4 and -31
19 and 51
0 and -38
2 and -14
Distance using absolute value for each example are given below:
205916147555104328346916807227323816As given in the question,
Distance Using Absolute Value
Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.
1) –15 and 35
Distance Using Number Line –15 – (–35) = –15 + 35 = 20
Absolute Value Statement |–15 – (–35)| = 20
2) 47 and –12
Distance Using Number Line 47 – (–12) = 47 + 12 = 59
Absolute Value Statement |47 – (–12)| = 59
3) –43 and 27
Distance Using Number Line –43 – (–27) = –43+27 = – 16
Absolute Value Statement |–43 – (–27)| = 16
4) –10 and 4
Distance Using Number Line –10 – 4 = –14
Absolute Value Statement |–10 – 4| = 14
5) 50 and –25
Distance Using Number Line 50 – (–25) = 50 + 25 = 75
Absolute Value Statement |50 – (–25)| = 75
6) 36 and –19
Distance Using Number Line 36 – (–19) = 36+19 = 55
Absolute Value Statement |36 – (–19)| = 55
7) –30 and –40
Distance Using Number Line –30 – (–40) = –30 + 40 = 10
Absolute Value Statement |–30 – (–40)| = 10
8) –2 and –45
Distance Using Number Line –2 – (–45) = –2 + 45 = 43
Absolute Value Statement |–2 – (–45)| = 43
9) 18 and 46
Distance Using Number Line 18 – 46 = –28
Absolute Value Statement |18 – 46| = 28
10) –10 and –44
Distance Using Number Line –10 – (–44) = –10 + 44 = 34
Absolute Value Statement |–10 – (–44)| = 34
11) –28 and 41
Distance Using Number Line –28 – 41 = –69
Absolute Value Statement |–28 – 41| = 69
12) 7 and –9
Distance Using Number Line 7 – (–9) = 7+9 = 16
Absolute Value Statement |7 – (–9)| = 16
13) –52 and 28
Distance Using Number Line –52 – 28 = –80
Absolute Value Statement |–52 – 28| = 80
14) 22 and –50
Distance Using Number Line 22 – (–50) = 22 + 50 = 72
Absolute Value Statement |22 – (–50)| = 72
15) –4 and –31
Distance Using Number Line –4 – (–31) = –4 + 31 = 27
Absolute Value Statement |–4 – (–31)| = 27
16) 19 and 51
Distance Using Number Line 19 – 51 = –32
Absolute Value Statement |19 – 51| = 32
17) 0 and –38
Distance Using Number Line 0 – (–38) = 0+ 38 = 38
Absolute Value Statement |0 – (–38)| = 38
18) 2 and –14
Distance Using Number Line 2 – (–14) = 2+14 = 16
Absolute Value Statement |2 – (–14)| = 16
Therefore, distance using absolute value for each example are given below:
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The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.
Based on the number of shares outstanding and the market value, the price the stock is currently selling for is $31.40
How to find the selling price of the stock?To find the selling price of the stock the formula is:
= Equity value of stock / Number of stock outstanding
The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.
The selling price of the stock today then is:
= Equity value of stock / Number of stock outstanding
= 569,600 / 19,000
= $31.40
Full question is:
What is the stock selling for today?
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Which age group of this set of numbers has twice as many people as another age group?
A) 76-85
B) 15-25
C) 36-45
D) 46-55
Answer:I believe it is 15-25
Step-by-step explanation:
For the rhombus below, solve for y
Notice that this set of angles is congruent
herefore,
[tex]y-60=56[/tex]Solving for y ,
[tex]\begin{gathered} y=56+60 \\ \rightarrow y=116 \end{gathered}[/tex]nswer: 116
1. no association 2. negative association 3. positive association 4. nonlinear association
From the graph it can be observed that line fits curve and line has positive slope as increase in hours cause increase in miles.
The line with postive slope represent the positive relation between the variables. So there is postive association between miles and time spent for running.
Answer: positive association
The following are the temperatures in °C for the first 12 days of January: 4.5 , − 3 , − 2 , 2 , 2.5 , 3 , − 1 , 4 , − 2.5 , 7 , − 4 , 3.5 What is the median temperature for those 12 days? Give your answer as a decimal.
Answer:
First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0
Step-by-step explanation:
I have a problem what is 27 divided by 655
Answer:
0.04122137404 is the answer
Answer: 0.041221374
Step-by-step explanation: According to Bing, 0.041221374 is your answer.
a stack of 20 identical boxes. The stack is 180cm tall, Julia then removes 3 boxes from the top. How tall is the stack now
A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
As given in the question,
Number of identical boxes in a stack=20
Stack of 20 identical boxes are 180 cm tall
Height of 1 box=180/20
=9cm
Julia removes 3 boxes from the top
Height of 3 identical boxes=9 × 3
=27 cm
Height of stack after removing 3 boxes from the top
=Original height - height of 3 boxes
=180 -27
=153cm
Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
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Let g (x) be the reflection across the y-axis of the function f (x) = 5x + 8. Identify the rule for g (x). g(x) = 5x + 8g (x) = -5x+8g (x) = -5x -8g (x) = 5x - 8
Given a function f(x), we can write the function g(x), where g(x) is the reflection over teh y-axis of f(x) by:
[tex]g(x)=f(-x)[/tex]In this case, the function given is:
[tex]f(x)=5x+8[/tex]Thus the reflection over the y-axis is:
[tex]g(x)=f(-x)=5(-x)+8[/tex]Now simplify:
[tex]g(x)=-5x+8[/tex]hus the answer is:
g (x) = -5x+8 (second option)
Determine the momentum of a system that consists of two objects. One object, m1, has a mass of 6 kg and a velocity of 13 m/s in the direction of the positive x-axis and a second object, m2, has a mass of 14 kg and a velocity 7 m/s in the direction of the negative x-axis.
Answer:
The solution to the question will be explained better using the image below
Concept:
The formula to calculate momentum is given below as
[tex]\begin{gathered} momentum=mass\times velocity \\ m=mv \end{gathered}[/tex]The first momentum will be
[tex]\begin{gathered} m_1=m_1v_1 \\ m_1=6\times13 \\ m_1=78kg\text{ m/s} \end{gathered}[/tex]The second momentum will be
[tex]\begin{gathered} m_2=m_2v_2 \\ m_2=14kg\times7 \\ m_2=98kg\text{ m/s} \end{gathered}[/tex]Since they are moving in different directions,
We will substract both momentums
[tex]\begin{gathered} momentum=m_1v_1-m_2v_2 \\ momentum=78-98 \\ momentum=-20kg\text{ m/s} \end{gathered}[/tex]Hence,
The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis
We are flipping three coins. Outcomes in the sample space are represented by strings of Hs and Ts such as TTH and
HHT.
Todes!
a. How many elements are in this sample space?
b. Express the event "there are more heads than tails" as a set.
c. What is the probability that there are more heads than tails?
d. What is the probability that there are an equal number of heads and tails?
a. The elements are in this sample space = 8.
b. "there are more heads than tails" = 1.
c. Probability that there are more heads than tails = 1/8.
d. Probability for equal number of heads and tails = 0.
What is described the term probability?In a sample space, the probability of the an outcome is a number ranging from zero and 1, inclusive. The sum of all the probabilities inside the sample space should always equal 1. The probability of an event E, denoted by the symbol P(E), is defined as the total of the probabilities of a outcomes that comprise E.The formula for calculation the probability is;
P(E) = number of times E occurs/ number of times experiment is performed
The sample space of flipping three coins.
S = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
a. The elements are in this sample space.
The total element present on the sample space is 8.
b. "there are more heads than tails"
Sample space for more heads than tails is only HHH.
S = 1
c. The probability that there are more heads than tails.
Probability = number of heads than tails/total outcome
Probability = 1/8
d. The probability that there are an equal number of heads and tails
S = 0; Non outcome has equal number of head ans tail.
Probability = 0.
Thus, the probabilities of different situations are obtained.
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The product 7 and the square of a number
The algebraic expression for the statement the product 7 and the square of a number is 7x²
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.
These expressions are also composed of arithmetic operations which may include;
SubtractionMultiplicationAdditionBracketDivisionParentheses, etcFrom the information given, we have that;
The product 7 and the square of a number
Now, let the number be x
The square of x is x²
This statement is expressed as;
7x²
Thus, the expression is 7x²
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The complete question:
The product 7 and the square of a number. Write the algebraic expression
Represent the quadratic function
For the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
As given in the question,
From the table of ordered pairs, it is observed that the zeros of the quadratic function are at x = 6 and x = 8. The zeros are the points where the y value of the function becomes zero.
An equation of the function in the standard form is given by :
y = (x - 6)(x - 8)
⇒y = x (x - 8) - 6 (x - 8)
⇒ y = x² -8x -6x +48
⇒ y = x² -14x + 48
The quadratic function is represented as the product of the zeros of the graph when plotted on a Cartesian plane.
Therefore, for the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
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The mass of Earth is 5.97 × 10^24 kg.
The mass of Mercury is 3.29 × 10^23 kg.
The ratio of the mass of Earth to the mass
of Mercury can be written in the form
1: n.
Calculate the value of n.
Give your answer as an ordinary number
to 2 significant figures.
The value of n is 0.06.
What is the ratio between two quantities?A fraction that demonstrates how many times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. The ratio is represented by the sign ":". The expression a/b, which stands for the ratio of two quantities a and b (b ≠0), is used.Given:
The mass of Earth is 5.97 × 10²⁴ kg.
The mass of Mercury is 3.29 × 10²³ kg.
The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.
The ratio of the mass of Earth to the mass of Mercury can be calculated as,
= mass of Earth/mass of Mercury
⇒ [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]
⇒ n = 0.0551
⇒ n ≅ 0.06 ( 2 significant figures)
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A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground? Use radical equations and round to the nearest tenth.
The cell phone will takes about 4.7 seconds to reach the ground.
What are equations of motion?There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where u = initial velocity of the considered object
v = final velocity of the object
a = acceleration of the object
s = distance traveled by the object in 't' time.
Given that hang glider dropped his cell phone from a height of 450 feet:
Acceleration is rate of change of velocity.
[tex]s = ut + \dfrac{1}{2} at^2[/tex]
Height = h = 450 feet
Gravitational Acceleration = g = 9.8 feet/s²
Initial Velocity = u = 0 m/s
h = 1/2at²
h = √2h/g
h = √2 x 450/ 9.8
h = 9.58 s.
Therefore, the cell phone will take 9.58 seconds to reach the ground.
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Evaluate 1.5 X 3 - 0.5 ²
A. 2
B. 3.5
C. 4.25
D. 31.25
Answer:
c is the answer
Step-by-step explanation:
1.5 x 3 =4.5
4.5 - 0.25
= 4.25
Solve the formula for the small base b
Value of b is 2Ah - B.
What is area?The area that an object's shape designates as being within it. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area. Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.
On a piece of paper, draw a square with a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Numerous 2-D shapes, such as circles, triangles, squares, rectangles, parallelograms, and trapezoids, may be found all around us. On paper, you can trace each of these shapes. Since every shape is distinct and varied, its area is also determined in a different way.
Given Data
A= [tex]\frac{1}{2}[/tex]h ( B + b)
For the value of b
b + B = 2Ah
b = 2Ah - B
Value of b is 2Ah - B.
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Find the lateral surface area and volume of the solid object in picture
Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.
We will need to use the next formulas
[tex]\begin{gathered} A_{\text{hex}}=\frac{3\sqrt[]{3}}{2}a^2\to\text{Area of a regular hexagon (a is one of its sides)} \\ A_{\text{tri}}=\frac{bh}{2}\to\text{Area of a triangle} \end{gathered}[/tex]Therefore, the surface area is
[tex]\begin{gathered} A_{\text{figure}}=A_{\text{hex}}+6\cdot A_{\text{tri}}=\frac{3\sqrt[]{3}(3)^2}{2}+6\cdot\frac{(3\cdot10.3)}{2} \\ =\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}=\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}\approx23.4+92.7=116.1 \\ \Rightarrow A_{\text{figure}}=116.1 \end{gathered}[/tex]Lateral Area=116.1 m^2
As for the volume, the volume of a regular pyramid is
[tex]V=\frac{A_{\text{base}}\cdot h}{3}[/tex]In our case,
[tex]V=\frac{3\sqrt[]{3}a^2}{2}\cdot\frac{h}{3}=\frac{\sqrt[]{3}}{2}a^2h[/tex]Therefore,
[tex]\Rightarrow V=\frac{\sqrt[]{3}}{2}(3)^2\cdot10=45\sqrt[]{3}[/tex]Volume= 77.9 m^3