Answer:
Increasing on it's domain [tex](-\infty,\infty)[/tex] because the slope is positive.
The domain and range are both all real numbers, also known as
[tex](-\infty,\infty)[/tex].
Step-by-step explanation:
All domain really means is what numbers can you plug in and you get number back from your function.
I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.
The domain is all real numbers.
In interval notation that is [tex](-\infty,\infty)[/tex].
Now the range is the set of numbers that get hit by y=3x+2.
Well y=3x+2 is a linear function that is increasing. I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.
If slope is positive, then the line is increasing.
If slope is negative, then the line is decreasing.
So y=3x+2 hits all values of y because it is increasing forever. The range is all real numbers. In interval notation that is [tex](-\infty,\infty)[/tex].
If f(x) = 5x + 4, which of the following is the inverse of (fx)?
Answer:
see explanation
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 5x + 4 ( subtract 4 from both sides )
y - 4 = 5x ( divide both sides by 5 )
[tex]\frac{y-4}{5}[/tex] = x
Change y back into terms of x
[tex]f^{-1}[/tex] (x) = [tex]\frac{x-4}{5}[/tex]
Tracey pays $18 to enter a theme park, plus $2 for each ride. Which of the following correctly describes the slope? A. she must pay a flat rate of $18. B. Her total cost increases by $2, for each ride purchased. C. Her total cost is at least $20. D. her total cost increased by $3, for each ride purchased
Answer:
B.
Step-by-step explanation:
You pay a one time fee of 18 dollars and then 2 dollars per ride.
The expression for that is 18+2r where r represents the number of rides and the output of (18+2r) is amount you spend.
f(r)=2r+18 when compared to f(x)=mx+b where m is slope and b is y-intercept
you should see that the slope is $2 per ride.
B. is the option that says this.
Answer: Option B
Her total cost increases by $2, for each ride purchased
Step-by-step explanation:
We know that $ 18 is the cost of the ticket. We do not know exactly how many trips you will make, but we know that the cost is $ 2 for each ride.
If we call "x" the number of rides then we know that the total cost "y" is:
[tex]y = 2x + 18[/tex]
Note that the cost increases by $2 for each ride
The equation of a line has the following form
[tex]y = mx + b[/tex]
Where m is the slope of the line.
In this case we have the following equation
[tex]y = 2x + 18[/tex]
Therefore [tex]m = 2[/tex]. Then the slope is the cost of $2 for each ride
Finally the answer is the option B. Her total cost increases by $2, for each ride purchased
If f = {(4, 2), (6, 1), (8, 4), (10, 2), (12,5)}, what is the range?
Range means all the y values included on the function/relation on the graph. In this case the y values/range is:
{1, 2, 4, 5}
^^^Remember to order them from smallest to largest and to a number only once if there are more then one of that number included in the range.
Hope this helped!
~Just a girl in love with Shawn Mendes
What is true of the function g(x)=-2x^2+5?
A) g(x) is the multiplication of g and x.
B) -2x^2+5 is the input of the function.
C) The variable x represents the independent variable.
D) The variable g represents the input of the function.
Answer:
C) The variable x represents the independent variable.
Step-by-step explanation:
The given function is [tex]g(x)=-2x^2+5[/tex].
g(x) is NOT the multiplication of g and x because g is a function of x.
[tex]x[/tex] is the input of the function.
[tex]-2x^2+5[/tex] is the output of the function.
The variable [tex]x[/tex] is called the independent variable because we plug in values of x to find g.
The variable g represents the output of the function NOT the input.
The correct choice is C
Need help in number 9. Thanks for helping
Answer:
B.
Step-by-step explanation:
The range is just the list of y-coordinates while the domain is just a list of the x-coordinates when it comes to a list of points.
So anyways all your y-coordinates are -2,-1,0,1,2. So that is your range.
Answer:
B.
Step-by-step explanation:
A veterinarian assistant has a 20 pound bag of cat food if he feeds each cat 2/5 pounds how many cats can he feed
Answer:
50
Step-by-step explanation:
20 / (2/5)
To divide by a fraction, multiply by the reciprocal.
20 × (5/2)
50
He can feed 50 cats.
50 cats
20 pounds is 100/5 pounds when written with a denominator of 5. Then you divide 100 by 2 and get 50.
5 ) Fred bought 5 new baseball trading cards to add to his collection. The next day his dog ate
half of his collection. There are now only 31 cards left. How many cards did Fred start with ?
Answer:
Just reverse the order. So double 31 is 62 then subtract 5. 57
Which formula gives the area of a parallelogram? (3)
Answer:
A = bh (the last one)
Step-by-step explanation:
To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply. The base and height of a parallelogram must be perpendicular.
Answer:
A=bh
Step-by-step explanation:
Pablo generates the function f(x) = 3/2(5/2)^x-1 to determine the x'th number in a sequence.
Which is an equivalent representation?
A: f(x+1) = 5/2 f(x)
B: f(x) = 5/2 f(x+1)
C: f(x+1) 3/2 f(x)
D: f(x+1) = 3/2 f(x+1)
Answer:
A.
f(x+1)=5/2f(x) with f(1)=3/2
Step-by-step explanation:
So we are looking for a recursive form of
[tex]f(x)=\frac{3}{2}(\frac{5}{2})^{x-1}[/tex].
This is the explicit form of a geometric sequence where [tex]r=5/2[/tex] and [tex]a_1=\frac{3}{2}[/tex].
The general form of an explicit equation for a geometric sequence is
[tex]a_1(r)^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex].
The recursive form of that sequence is:
[tex]a_{n+1}=ra_n \text{ where you give the first term value for } a_1[/tex].
So we have r=5/2 here so the answer is A.
f(x+1)=5/2f(x) with f(1)=3/2
By the way all this says is term is equal to 5/2 times previous term.
Answer:
A
Step-by-step explanation:
Edge 2021
Michael goes to a theme park and rides two different roller coasters that both begin on a raised platform. His height while on the first roller coaster, measured in feet from the platform height, can be modeled by the following graph, where t is the number of seconds since the ride began. His height while on the second roller coaster, measured in feet from the platform height, can be modeled by a trigonometric function, shown in the following table, where t is the number of seconds since the ride began. t 0 20 40 60 80 100 120 140 160 g(t) 0 50 100 50 0 -50 -100 -50 0 Which of the following best describes Michael's height while on the two roller coasters? A. While on the first roller coaster, the function modeling Michael's height switches from positive to negative every 60 seconds, meaning he changes from being at a height above the platform to below the platform every 60 seconds. While on the second roller coaster, this change occurs every 20 seconds. B. While on the first roller coaster, the function modeling Michael's height switches from positive to negative approximately every 40 seconds, meaning he changes from being at a height above the platform to below the platform approximately every 40 seconds. While on the second roller coaster, this change occurs every 80 seconds. C. While on the first roller coaster, the function modeling Michael's height switches from positive to negative every 40 seconds, meaning he changes from being at a height above the platform to below the platform every 40 seconds. While on the second roller coaster, this change occurs every 20 seconds. D. While on the first roller coaster, the function modeling Michael's height switches from positive to negative approximately every 80 seconds, meaning he changes from being at a height above the platform to below the platform approximately every 80 seconds. While on the second roller coaster, this change occurs every 40 seconds.
Answer:
on plato the answer is B, it reads the same as the answer c does on this example. Please make sure that you read the answers and match them up with the correct one on your side.
Step-by-step explanation:
Using the information provided, Michael's height changes from above to below the platform every 40 seconds for the second roller coaster. However, without more concrete information regarding the first roller coaster, a definitive answer for that cannot be provided.
Explanation:The topic in discussion here is the modeling of Michael's height changes on two different roller coasters using functions and graphs. Given the question, we can observe that the second roller coaster's height variations follow a pattern corresponding to a trigonometric function, changing from 0, to 50, to 100, and so forth, then repeating. From this pattern, we can infer that Michael's height on the second roller coaster oscillates from a positive value (above the platform) to a negative value (below the platform) and back every 40 seconds since the value of g(t) changes from positive to negative (or vice versa) at each 40-second interval.
However, without the details of the first roller coaster's function or graph, we cannot accurately determine how often Michael's height on the first coaster changes from positive to negative. Therefore, based on the given information, we cannot definitively choose between the provided answer options.
Learn more about Modeling Height Changes here:https://brainly.com/question/5449909
#SPJ3
what is (7x6)+(4x10)
Answer:
the answer is 82
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
just use a calculator
3x- 5=1 what does x represent
Answer:
x= 5/3
Step-by-step explanation:
3x- 5 = 1
first you have to move the constant or in this case the 5 to the other side to isolate x so to do that you have to ad 5 from both sides, that way itll cancel out from the left and add on the right
3x= 5
now, to isolate x, we have to divide by 3, that way you get
x= 5/3
F(x)=x^2 What is F(x)+f(x)+f(x)
Answer:
Step-by-step explanation:
F(x)=x^2 What is F(x)+F(x)+F(x) =3F(x) =3x²
Answer:
[tex]F(x)+F(x)+F(x)[/tex] = [tex]3x^{2}[/tex]
Step-by-step explanation:
Given is :
[tex]F(x)=x^{2}[/tex]
We have to find: [tex]F(x)+F(x)+F(x)[/tex]
This means we have to find [tex]x^{2} +x^{2} +x^{2}[/tex]
This becomes [tex]3x^{2}[/tex]
Hence, [tex]F(x)+F(x)+F(x)[/tex] = [tex]3x^{2}[/tex]
WILL GIVE BRAINSLIEST EASY. Find each product mentally. Show the steps used.
1. 9 x 44 = 2. 4 x 5 1/8 = 3. 7 x 3.8 =
Use the Distributive Property to rewrite each algebraic expression.
4. 8(x + 7) = 5. 6(11 + x) = 6. 8(x + 1) =
Answer:
1) 396
2) 20 1/2
3) 26.6
4) 8x + 56
5) 66 + 6x
6) 8x + 8
Step-by-step explanation:
* Lets explain how to solve the product mentally
# Remember the distributive property can help you to find the product
mentally the distributive property ⇒ a(b + c) = ab + ac
- Lets solve them
1)
- In 9 × 44 we can write 44 as (40 + 4)
∴ 9 × 44 = 9(40 + 4)
∵ 9(40 + 4) = 9 × 40 + 9 × 4
- Now lets multiply 9 by 40 and 9 by 4
∵ 9(40) = 360
∵ 9(4) = 36
∴ 9 × 40 + 9 × 4 = 360 + 36 = 396
∴ 9 × 44 = 396
2)
- In 4 × 5 1/8 we can write 5 1/8 as (5 + 1/8)
∴ 4 × 5 1/8 = 4(5 + 1/8)
∵ 4(5 + 1/8) = 4 × 5 + 4 × 1/8
- Now lets multiply 4 by 5 and 4 by 1/8
∵ 4(5) = 20
∵ 4(1/8) = 1/2
∴ 4 × 5 + 4 × 1/8 = 20 + 1/2 = 20 1/2
∴ 4 × 5 1/8 = 20 1/2
3)
- In 7 × 3.8 we can write 3.8 as (3 + 0.8)
∴ 7 × 3.8 = 7(3 + 0.8)
∵ 7(3 + 0.8) = 7 × 3 + 7 × 0.8
- Now lets multiply 7 by 3 and 7 by 0.8
∵ 7(3) = 21
∵ 7(0.8) = 5.6
∴ 7 × 3 + 7 × 0.8 = 21 + 5.6 = 26.6
∴ 7 × 3.8 = 26.6
- The distributive property ⇒ a(b + c) = ab + ac
4)
- In 8(x + 7) we will multiply 8 by x and 8 by 7 and add them
∵ 8 × x = 8x
∵ 8 × 7 = 56
∴ 8(x + 7) = 8x + 56
5)
- In 6(11 + x) we will multiply 6 by 11 and 6 by x and add them
∵ 6 × 11 = 66
∵ 6 × x = 6x
∴ 6(11 + x) = 66 + 6x
6)
- In 8(x + 1) we will multiply 8 by x and 8 by 1 and add them
∵ 8 × x = 8x
∵ 8 × 1 = 8
∴ 8(x + 1) = 8x + 8
In right triangle ABC, B is the right triangle and m C = 30. If AC = 10 what is AB?
Using the law of sins:
Sin(angle) = Opposite Leg / Hypotenuse
Sin(30) = AB /10
Solve for AB:
AB = 10 * sin(30)
AB = 10 * 1/2
AB = 5
The answer is A.
A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form?
Answer:
B=n2 + 6n + 1
Step-by-step explanation:
A = n
B = 2n + 6
C = n^2 - 1
AB - C = n * (2n + 6) - (n^2 - 1) = 2n^2 + 6n - n^2 + 1 = n^2 + 6n + 1
Answer:
The simplest form of the expression AB-C is [tex]n^2+6n+1[/tex].
Step-by-step explanation:
In this exercise we only need to use the properties of arithmetic operations and a minimal knowledge of algebraic notation. We have the expressions
[tex]A = n[/tex],[tex]B=2n+6[/tex],[tex]C=n^2-1[/tex].Now we make the indicated operations, beginning by AB:
[tex]AB=n\cdot(2n+6) = 2n^2+6n[/tex] using the distributive property of multiplication.
Then, we make AB-C:
[tex]AB-C = 2n^2+6n - (n^2-1) = 2n^2+6n-n^2+1 = n^2+6n+1[/tex].
In the last step we must be vary careful with the change of signs in the expression inside parenthesis.
Find the length of CZ
Think for a minute.
CA = 17, right?
CZ is the remaining part of CA.
ZA = 16
CZ = CA - ZA
CZ = 17 - 16
CZ = 1
Did you follow?
Answer:
D 1
Step-by-step explanation:
CA = CZ + ZA
WE know CA = 17 and ZA = 16
17 = CZ + 16
Subtract 16 from each side
17-16 = CZ +16-16
1 = CZ
Select the correct answer from each drop-down menu.
consider the equation
-22 + 3x
___________ = 2
3x + 7
How do you begin isolating the variable x to one side of the equation?
A) Multiply both sides by 3x + 7.
Reset
B) Divide both sides by 3x + 7.
C) Multiply both sides by -22 + 3x.
D) Divide both sides by -22 + 3x.
The solution of the equation is
A) -12
B) -9
C) -6
D) -3
Answer:
A)Multiply both sides by 3x + 7.
Reset
A)the solution of the equation is x=-12
Step-by-step explanation:
Hello
let
to begin isolating we must multiply both sides by 3x + 7.
Reset
this way
[tex]\frac{-22+3x}{3x+7}=2\\\frac{-22+3x}{3x+7}*(3x+7)=2*(3x+7)\\-22+3x=2*(3x+7)[/tex]
let´s continue to find x
[tex]\\-22+3x=2*(3x+7)\\-22+3x=6x+14\\-22-14=6x-3x\\-36=3x\\x=\frac{-36}{3}\\ x=-12[/tex]
the solution of the equation is x=-12
have a great day
Solve 2cos theta+2=3 in the interval 0-2pi
Answer:
[tex]\theta=\frac{\pi}{3}, \frac{5\pi}{3}[/tex].
Step-by-step explanation:
[tex]2\cos(\theta)+2=3[/tex]
Subtract 2 on both sides:
[tex]2\cos(\theta)=3-2[/tex]
Simplify:
[tex]2\cos(\theta)=1[/tex]
Divide both sides by 2:
[tex]\cos(\theta)=\frac{1}{2}[/tex]
Now let's refer to the unit circle... When is the x-coordinate, 1/2?
There are 2 places this happens on [0,2pi].
One is in the first quadrant and the other in the fourth quadrant.
It is at [tex]\theta=\frac{\pi}{3}, \frac{5\pi}{3}[/tex].
I need help ASAP please someone help me
Answer:
I know it has nothing to do with Christianity, so C and D are wrong. It's either A or B, but I'm more with the A. But I'm not sure so...
PLEASE HELPP!!
The graph of y = ax^2 + bx + c is shown below. Determine the solution set of 0 = ax^2 + bx + c.
Check the picture below.
something noteworthy to look at is that the graph doesn't cross the x-axis at -2, it simply comes down to it, touches it and it goes back up, it simply bounces off the x-axis, whenever that happens, that zero/solution/root has an even multiplicity.
when 0 = ax² + bx + c, we notice that y = 0, and for the graph that happens there, at x = -2, but that solution has an even multiplicity, and since the equation is a 2nd degree polynomial, thus x = -2 is there twice, namely
x = -2
x - 2 = 0
(x - 2)² = 0 <---- multiplicity of 2.
Answer:
-2
Step-by-step explanation:
:)
Classify the polynomial -3x5 by degree.
cubic
quadratic
quintic
constant
Answer:
quintic
Step-by-step explanation:
I will assume you mean
-3x^5
This is to the degree 5, since it is to the 5th power
cubic 3rd power
quadratic 2nd power
quintic 5th power
constant 0th power
Answer:
Quintic polynomial is a polynomial with degree 5
Step-by-step explanation:
[tex]-3x^5[/tex]
Given polynomial has degree 5 . Its a 5th degree polynomial
Cubic polynomial has degree 3
Quadratic polynomial has degree 2
Constant is a polynomial with a number without any variable like 2 or 4 or 15
Quintic polynomial is a polynomial with degree 5. Given polynomial has degree 5 . So it is Quintic
Les tried to evaluate 600 x 4 step by step.
600 X 4
Step 1
= 10 x 6 x 4
Step 2
= 10 x 24
Step 3
= 240
Find Les's mistake.
Choose 1 answer:
@ Step 1
B Step 2
C Step 3
DLes did not make a mistake.
Answer:
A Step 1
Step-by-step explanation:
600 X 4
6*100 *4
The mistake is in the first line
600 = 6*100 not 6*10
Could anyone answer and also provide explanation.
Answer:
b
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
2x + 3y = 1 ( subtract 2x from both sides )
3y = - 2x + 1 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form
with y- intercept c = [tex]\frac{1}{3}[/tex] ← does not pass through the origin
(b)
2x + 3y = 0 ( subtract 2x from both sides )
3y = - 2x + 0 ( dividing all sides by 3 ), gives
y = - [tex]\frac{2}{3}[/tex] x + 0 ← in slope- intercept form
with y- intercept c = 0 ← passes through the origin
(c)
2x + 3y = 6 ( subtract 2x from both sides )
3y = - 2x + 6 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 2
with y- intercept c = 2 ← does not pass through the origin
Graph y=lx-3l please answer fast
Answer:
(see attachment)
Step-by-step explanation:
With an absolute value graph, if the number is inside the brackets you move the graph in the opposite direction.
(Btw you should use Desmos. That's what I use all the time and it is a LIFESAVER)
(Also can I please have Brainliest, I need it to level up)
The graph of the function y = |x - 3| is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = |x - 3|
The above function is an absolute function that has been transformed as follows
Vertically stretched by a factor of 1Shifted right by 3 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
Read more about functions at
brainly.com/question/2456547
#SPJ2
Find an equation for the line perpendicular to y=−15x+3 with x-intercept at x = 3.
Write your answer in the form y=mx+b
bearing in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of the provided line then
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-15}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-15\implies -\cfrac{15}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{15}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{15}\implies \cfrac{1}{15}}}[/tex]
well, we know the x-intercept is at x = 3, recall when a graph intercepts the x-axis y = 0, so this point is (3 , 0). Then we're really looking for the equation of a line whose slope is 1/5 and runs through (3 , 0).
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{1}{5}(x-3)\implies y=\cfrac{1}{5}x-\cfrac{3}{5}[/tex]
Circle O is represented by the equation (x + 7)^2 + (y + 7)^2 = 16. What is the length of the radius of circle O?
Answer:
4
Step-by-step explanation:
The standard form of a circle is:
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and
r is the radius.
You compare your equation to mine you should see that:
-h=7 implies h=-7
-k=7 implies k=-7
r^2=16 implies r=4 since 4^2=16
The center is (-7,-7).
The radius is 4.
For this case we have that by definition, the equation of a circle in standard or canonical form is given by:
[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]
Where:
(h, k) is the center
r: It's the radio
We have the following equation:
[tex](x + 7) ^ 2 + (y + 7) ^ 2 = 16\\(x + 7) ^ 2 + (y + 7) ^ 2 = 4 ^ 2[/tex]
Thus, the radius is 4.
Answer:
4
Which of the following are solutions to the equation below?
Check all that apply.
5x2 - 2x + 16 = 4x2 + 6x
O A. -6
O B. 6
O C.-3
D. -4
E 4
O
F. 18
Answer:
E. x = 4Step-by-step explanation:
[tex]5x^2-2x+16=4x^2+6x\qquad\text{subtract}\ 4x^2\ \text{from both sides}\\\\x^2-2x+16=6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\x^2-8x+16=0\\\\\text{Put the values of}\ x\ \text{to the equation and check the equality:}\\\\A.\ x=-6\\\\(-6)^2-8(-6)+16=36+48+16=100\neq0\\\\B.\ x=6\\\\6^2-8(6)+16=36-48+16=4\neq0\\\\C.\ x=-3\\\\(-3)^2-8(-3)+16=9+24+16=49\neq0\\\\D.\ x=-4\\\\(-4)^2-8(-4)+16=16+32+16=64\neq0\\\\E.\ x=4\\\\4^2-8(4)+16=16-32+16=0\\\\F.\ x=18\\\\18^2-8(16)+16=324-128+16=212\neq0[/tex]
Answer:
E
Step-by-step explanation:
Which is the true solution to the radical equation y + 1 =
-2y-3?
Find the volume, lateral surface area and total surface area of a regular octagonal pyramid of base 6.2cm and perpendicular height of 14.8cm.
Answer:
V ≈ 915.7 cm³
LA ≈ 411.3 cm²
SA ≈ 596.9 cm²
Step-by-step explanation:
Volume of a pyramid is:
V = ⅓ Bh
where B is the area of the base and h is the height.
The base is a regular octagon. The area of a regular octagon is 2(1 + √2) s², where s is the side length.
Substituting:
V = ⅔ (1 + √2) s² h
Given that s = 6.2 and h = 14.8:
V = ⅔ (1 + √2) (6.2)² (14.8)
V ≈ 915.7 cm³
The lateral surface area is the area of the sides of the pyramid. Each side is a triangular face. We know the base length of the triangle is 6.2 cm. To find the area, we first need to use geometry to find the lateral height, or the height of the triangles.
The lateral height and the perpendicular height form a right triangle with the apothem of the octagon. If we find the apothem, we can use Pythagorean theorem to find the lateral height.
The apothem is two times the area of the octagon divided by its perimeter.
a = 2 [ 2(1 + √2) s² ] / (8s)
a = ½ (1 + √2) s
a ≈ 7.484
Therefore, the lateral height is:
l² = a² + h²
l ≈ 16.58
The lateral surface area is:
LA = 8 (½ s l)
LA = 4 (6.2) (16.58)
LA ≈ 411.3 cm²
The total surface area is the lateral area plus the base area.
SA = 2(1 + √2) s² + LA
SA = 2(1 + √2) (6.2)² + 411.3
SA ≈ 596.9 cm²
The volume is 915.7 cm³
The lateral surface area is 411.3 cm²
The total surface area is 596.9 cm²